diff --git a/.gitattributes b/.gitattributes index 41aef290fd..e9406c8db1 100644 --- a/.gitattributes +++ b/.gitattributes @@ -8,3 +8,28 @@ upstream/** -whitespace references/copied-centers/pr29/** -whitespace references/copied-centers/pr33/** -whitespace references/semantic-bulk/** -whitespace + +# Immutable contributor archives retain original CRLF and whitespace bytes. +references/frame-compiler/pr69/** -text -whitespace +references/frame-compiler/pr70/** -text -whitespace +references/frame-compiler/pr71/** -text -whitespace + +# Preserve original contributor and frozen discovery bytes. +references/frame-compiler/pr74/** -text -whitespace +references/frame-compiler/pr78/** -text -whitespace +references/frame-compiler/pr79/** -text -whitespace +references/frame-compiler/indexed-r5/** -text -whitespace +# Byte-identical credited PR74 extracts retain original trailing blank lines. +scripts/experiments/indexed_cycle_nodeops.py -whitespace + +# Final construction archives retain exact Git bytes, CRLF and notices. +references/frame-compiler/pr82/** -text -whitespace +references/frame-compiler/pr84/** -text -whitespace +references/frame-compiler/final-r10/** -text -whitespace + +# Aligned construction archives preserve exact original bytes and notices. +references/frame-compiler/pr88/** -text -whitespace +references/frame-compiler/pr74-aligned/** -text -whitespace +references/frame-compiler/aligned-r11/** -text -whitespace +# Preserve the compiled Lean command receipt verbatim. +research/aligned-composition/lean/receipts/** -text -whitespace diff --git a/.github/workflows/verify.yml b/.github/workflows/verify.yml index 6bd374e1ca..58876ecb0c 100644 --- a/.github/workflows/verify.yml +++ b/.github/workflows/verify.yml @@ -16,7 +16,7 @@ jobs: fail-fast: false matrix: python-version: ['3.11', '3.13', '3.14'] - group: [community, producers, certificates, ternary, research, tests, strips, clones, positive, joint, pair] + group: [community, producers, certificates, ternary, research, tests, strips, clones, positive, joint, pair, balanced, indexed, final, aligned] steps: - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 with: diff --git a/Makefile b/Makefile index 84fe8290f3..c672277330 100644 --- a/Makefile +++ b/Makefile @@ -23,6 +23,10 @@ verify: $(MAKE) verify-positive $(MAKE) verify-joint $(MAKE) verify-pair + $(MAKE) verify-balanced + $(MAKE) verify-indexed + $(MAKE) verify-final + $(MAKE) verify-aligned $(MAKE) verify-tests verify-community: community-audit-check community-followup-check copied-reversed-producer copied-reversed-check copied-fixed-reversed-producer copied-fixed-reversed-check @@ -428,3 +432,61 @@ pair-assembly-verify: pair-assembly-producer pair-assembly-check .PHONY: verify-pair verify-pair: pair-assembly-verify python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify + +.PHONY: balanced-split-verify verify-balanced +balanced-split-verify: + python3 scripts/experiments/verify_balanced_split.py + python3 scripts/experiments/audit_balanced_split_completion.py + python3 scripts/experiments/audit_balanced_split_exchange.py + python3 -m unittest discover -s tests -p 'test_balanced_split*.py' -v + +verify-balanced: balanced-split-verify + +.PHONY: indexed-cycle-verify verify-indexed +indexed-cycle-verify: + python3 scripts/experiments/verify_indexed_cycle.py + python3 scripts/experiments/audit_indexed_cycle_completion.py + python3 scripts/experiments/audit_indexed_cycle_exchange.py + python3 scripts/experiments/audit_indexed_cycle_cycles.py + python3 scripts/experiments/audit_indexed_cycle_retired.py + python3 scripts/experiments/audit_indexed_cycle_pending.py + python3 -m unittest discover -s tests -p 'test_indexed_cycle*.py' -v + +verify-indexed: indexed-cycle-verify + +.PHONY: final-frame-verify verify-final +final-frame-verify: + python3 scripts/experiments/verify_final_frame.py + python3 scripts/experiments/audit_final_frame_completion.py + python3 scripts/experiments/audit_final_frame_exchange.py + python3 scripts/experiments/audit_final_frame_cycles.py + python3 scripts/experiments/audit_final_frame_retired.py + python3 scripts/experiments/audit_final_frame_pending.py + python3 scripts/experiments/audit_final_frame_three_cycles.py + python3 scripts/experiments/audit_final_frame_pricing.py + python3 -m unittest discover -s tests -p 'test_final_frame*.py' -v + +verify-final: final-frame-verify + +.PHONY: aligned-composition-verify verify-aligned +aligned-composition-verify: + python3 scripts/experiments/verify_aligned_composition.py + python3 scripts/experiments/audit_aligned_composition_completion.py + python3 scripts/experiments/audit_aligned_composition_exchange.py + python3 scripts/experiments/audit_aligned_composition_cycles.py + python3 scripts/experiments/audit_aligned_composition_retired.py + python3 scripts/experiments/audit_aligned_composition_pending.py + python3 scripts/experiments/audit_aligned_composition_three_cycles.py + python3 scripts/experiments/audit_aligned_composition_pricing.py + python3 scripts/experiments/audit_aligned_composition_lean.py + python3 -m unittest discover -s tests -p 'test_aligned_composition*.py' -v + python3 -m unittest discover -s tests -p 'test_lean_axiom_output.py' -v + +verify-aligned: aligned-composition-verify diff --git a/NOTICE b/NOTICE index b565637758..d5170811d5 100644 --- a/NOTICE +++ b/NOTICE @@ -302,3 +302,42 @@ inherited PR #48 sources. The stacked witness in research/pair-assembly/frame uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Balanced coarse split composition (2026-10-08) +--------------------------------------------- +Eumemic / @eumemic supplied PR69's balanced coarse sums, with OpenAI Codex +assistance. Alejandro Zarzuelo Urdiales / @alejandrozu supplied PR70's bounded +carry-exchange strategy with the AI disclosures retained in the source archive. +Chafik Boukhalfa / @chafreaky, with OpenAI Codex assistance, selected the row/ +half-plane coarse rules, future-compatible unit completion, exact integer-price +carry adaptation, composition and this certificate package. The PR71 anchored +split vector, schedules, arithmetic, pending controls and their contributor +chain are retained as credited above. Original PR69/70 sources, licenses and +notices and the complete published PR71 baseline are preserved under +references/frame-compiler. All earlier notices remain applicable. + +Indexed two-cycle composition (2026-10-08): Chafik Boukhalfa with OpenAI Codex assistance. Thomas DiFiore (@tomdif, PR74) supplied exact node ordering and coordinate relabeling, including the selected h25 permutation. Rohan Arun (@rohanarun, PR78) supplied the coordinate-flag search idea. Balanced multi-splits, exact retired/pending indices, bounded two-cycles, late-output routing and selected-coordinate certification compose inherited PR57/59/60/62/63/65/67/68/69/70/71/79 work. All original authorship, Apache-2.0 and AI disclosures remain in unchanged contributor archives. + +Final frame composition: Chafik Boukhalfa with OpenAI Codex assistance. Rank-preserving tie orders extend Thomas DiFiore PR74; coordinate-aware oracle pricing is adapted from Rohan Arun PR82. Three-donor cycles extend the credited bounded carrier exchange strategy. All earlier authors, OpenAI/manuscript, Apache-2.0 and AI-assistance notices remain attached in preserved archives. + +Aligned frame composition: Chafik Boukhalfa with OpenAI Codex assistance. Thomas DiFiore PR74 supplies aligned firstK partitions, multi-pair anchoring, depth-dependent coarse sums and the selected coordinate maps. The previously credited R10 compiler composes these with the selected pricing and three-cycle settings. The additive Lean arithmetic companion was prepared with OpenAI assistance; all previous author, Apache-2.0, OpenAI/manuscript and AI-assistance notices remain attached. diff --git a/README.md b/README.md index 035c259b68..c46a5a24d9 100644 --- a/README.md +++ b/README.md @@ -21,6 +21,39 @@ speedup. The model and general reduction are inherited from OpenAI's [Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · [Independent arithmetic check](docs/research/community-pair-arithmetic.json) +## Additional conditional construction: balanced coarse split frames + +The [balanced-split proof and reproduction guide](research/balanced-split/README.md) +gives **κ=25872812736433/500000000000000000=5.1745625472866e-5**, approximately +**0.6437453019850683%** above the complete published PR71 witness. It composes +PR69 balanced coarse sums and a bounded PR70 carry exchange with PR71's +anchored split graph, future unit completion and profile-cost pending controls. +All actual words, dirty inputs, paid profiles and 47 strict assembly constraints +are checked by `make balanced-split-verify`. This finite conditional construction +retains the inherited all-size hypotheses and contributor notices. Chafik +Boukhalfa prepared the selected composition with OpenAI Codex assistance. + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + ## What changed **Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange @@ -149,3 +182,15 @@ The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate CC0 license and notices. The pinned original OpenAI manuscript remains unchanged under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). This project is not an official OpenAI release or endorsement. + +### Indexed two-cycle finite witness + +[Indexed-cycle proof and evidence](research/indexed-cycle/README.md) gives κ = 261356445457/5000000000000000 with W=132466108. It combines attributed balanced multi-splits, exact frame indexes, bounded carry two-cycles, PR74 node ordering and coordinate flags; all-size transfer remains inherited. Verify with `make indexed-cycle-verify`. The comparison is to pinned historical PR74/PR79 witnesses observed 2026-10-08. + +### Final frame composition + +The [final finite composition](research/final-frame/README.md) gives conditional κ=5.2514124198891e-5 using rank-preserving envelope ties, coordinate-aware prices and bounded three-donor exchanges. Run `make final-frame-verify`; all inherited gates remain included in `make verify`. This is a finite conditional certificate, not a practical benchmark or complete formal multiplication theorem. + +### Aligned frame composition + +The [aligned finite composition](research/aligned-composition/README.md) certifies conditional κ=5.2789616935221e-5 and adds a 197-theorem Lean rational arithmetic companion. Run `make aligned-composition-verify` and `make formal-historical-verify`; all existing gates remain. 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ten exact rational recoveries", + "geometry": "Unchanged fixed-I+J original-envelope projector and CRT formulas", + "producer": "PR62/63 interval pair assembly, selected aligned-composition partition and point permutation, rank-preserving selected node order, natural execution, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring, PR69 balanced coarse sums, future unit completion and bounded PR70-derived single exchanges, two-cycles and selected three-donor cycles, PR82 coordinate-aware heuristic pricing, exact frame indices, late-output routing and PR74/78-inspired coordinate relabeling; complete literal words", + "proof_scope": "Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. 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No external claimed bound is imported as a proof." + } + } +} diff --git a/certificates/balanced-split-completion-validation.json b/certificates/balanced-split-completion-validation.json new file mode 100644 index 0000000000..33d3576de1 --- /dev/null +++ b/certificates/balanced-split-completion-validation.json @@ -0,0 +1,16 @@ +{ + "baseline_source_sha256": "58f13f82ce1bb7f2b5549e17628bc6034e5e05cb24db2acb9a91c24820872f70", + "priority_fixture": "Compatible future use count first, fixed symbolic support popcount second, input index last. Backward and nonnested uses excluded.", + "proof": [ + "The desired output rows followed by selected carry rows are independent by the unchanged checks. Scanning every standard unit vector in any order and retaining it only when independent must extend that fixed prefix to a basis of the whole input-role space: otherwise all standard units would belong to a proper final span, a contradiction.", + "The new priority produces a permutation of precisely those same input indices; it never alters the already selected output/carrier rows and changes only the independent completion rows labelled retired. Rank and full-basis checks remain mandatory.", + "Gaussian elimination and its reversed literal XOR synthesis are unchanged. A square full-rank binary basis is invertible on arbitrary inputs, including dirty roles. Physical frame and clearing charges are still determined by the regenerated actual word.", + "Future-use counts are computed from fixed graph incidence and order. Popcounts use fixed symbolic linear signals already checked against graph values, not runtime input values. The word remains input-independent.", + "Matching, pending lifecycles, the two pending-frame containment checks, and next-use profile costs are byte-identical to the frozen compiler. Their prior legality argument applies unchanged." + ], + "scope": "Checks only our new completion strategy and composed finite witnesses. No mathematical optimality or all-size transfer claim.", + "source_sha256": "a6a423c49737a1f59495a6ba012ed2edcf971e56fa7f0a422b8c9e21212668e6", + "status": "PASS future-completion source delta, actual-use priority and invertible unit-basis extension", + "tested_independent_completions": 2250, + "tested_literal_xors": 34141 +} diff --git a/certificates/balanced-split-exchange-validation.json b/certificates/balanced-split-exchange-validation.json new file mode 100644 index 0000000000..b13cb60d69 --- /dev/null +++ b/certificates/balanced-split-exchange-validation.json @@ -0,0 +1,23 @@ +{ + "exercised_exchange_types": { + "different_region": 103, + "new_future_use": 582, + "same_future_use": 205, + "same_region": 684 + }, + "only_executable_change": "The inserted fixed-price carry-exchange segment; all graph synthesis, future completion, pending controls and physical charging unchanged.", + "proof": [ + "Every candidate edge retains the pre-existing temporal and envelope eligibility. The source changes no candidate construction. Prices are fixed deterministic integers and only rank legal candidates; they are not acceptance bounds for the final moment.", + "If a candidate has an already occupied future use, removing that use owner preserves partition uniqueness. Its destination region either drops the same carrier before the independence test or must support the additional independent row. A different old region only loses a row, which preserves independence.", + "For an unoccupied future use, the code drops one selected edge from the same region and explicitly checks independence with that edge removed. The old future use becomes free and the new use is assigned once. Both cases preserve cardinality.", + "Each accepted exchange strictly reduces the fixed integer price. Only three passes over a finite deterministic priority order are allowed. Final assertions check matching cardinality and every output/carrier row independence; no maximality or final-moment optimality is claimed.", + "After the legal selection changes, the unchanged invertible physical synthesis constructs a fresh word. Selected candidate acceptance must still use full arbitrary-dirty replay, actual frame profiles and exact arithmetic." + ], + "random_matroid_cases": 800, + "scope": "Audits our composition/adaptation only. 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+ "research/reordered-rank-pair/paired-candidate.json": "34a500d739537235dfc5d24325c22856ca4567b9eac998a3bce9b13db5501940", + "research/reordered-rank-pair/test_negative.py": "88832242e6f74e3fe08d109d4f21ff188a9ca0ae50c3e8f31da0243fe9501510", + "research/reordered-rank-pair/verify.py": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352", + "scripts/exclusion_circuit.py": "b253f9d7318becda1c1f3b24e2287ed44a9c27fcea00cf9d531afb950d0457a0", + "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3", + "scripts/experiments/binary_frame_profiles.cpp": "8e2e391d3ee57cbb1372c68e4aa031e1b861321536eabd642ada54e12e678669", + "scripts/experiments/binary_frame_replay.py": "392e78e62d7685c99a5888a7da743ea6c3dcad631af4a743c91e0c09348442bc", + "scripts/experiments/rank_pair_compiler.py": "9984aaccf880e4840402322d76678bfddb33ce7e494af78430a43429f51b85fd", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34" + }, + "repo": "rohanarun/integer-mult-bounds", + "scope": "Authenticated PR65 finite source closure and complete published baseline physical words, profiles and arithmetic. Original upstream sources and notices are preserved byte-for-byte. Actual inherited dependencies are additionally checked through the shared PR48 manifest.", + "shared_dependency_manifest": "../pr48/SOURCE.json", + "shared_dependency_manifest_sha256": "6ccc673f88d3650d75ed600b082fe2fc2866dd88a172d182a38c1d0cd27d24b3" + }, + "pr67": { + "author": "Rohan Arun with OpenAI assistance", + "commit": "b3745601e947a94316bf25c2c6263d93c06e3364", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "5931cb7d43e09380594b113018cac70258fb66e0673b91f706b01ea482c1be1a", + "research/slot-cost-rank-pair/README.md": "e0fcd8e732c8b8becb3d860eb83dc979ed5e6b33ba16caf9dca1e44f7929c340", + "research/slot-cost-rank-pair/arithmetic/certificate.json": "e66f955f1b76ce3db7ecb84294993a072f42f972b8f3040015c12e6dc953d698", + "research/slot-cost-rank-pair/compiler.py": "29296211e0532aaf19101a6b2f2ceaebe374af95ae3acd63e63656db0afef7ae", + "research/slot-cost-rank-pair/frame-compiler.json": "eb5c0b401e677d3958ecfcd6d8de3bc825c4fb66d1cf79c3fcbcf23938ca6e69", + "research/slot-cost-rank-pair/paired-candidate.json": "be0322ad60f73923953f242eaffaf114ff12438e8617dae38888b77fa03184cc", + "research/slot-cost-rank-pair/profile_oracle.cpp": "d1f6b650de9fb5842b412595369271d9eeb6f54045c76c0fb5cad29854955c35", + "research/slot-cost-rank-pair/verify.py": "3c1d2eac9d3d2f13b60503deaa84e11ab2975aa84af71c8ad74584c5902b2d77" + }, + "repo": "rohanarun/integer-mult-bounds", + "scope": "Preserved immutable source and reported complete baseline profile/arithmetic for all-rank profile-cost reclamation. This package verifies its own composed words, actual paid profile and exact improvement.", + "shared_dependency_manifest": "../pr48/SOURCE.json", + "shared_dependency_manifest_sha256": "6ccc673f88d3650d75ed600b082fe2fc2866dd88a172d182a38c1d0cd27d24b3" + }, + "pr68": { + "author": "Dominik Scholz with OpenAI assistance", + "commit": "734c58e225e9d2254570c3b50296ed96943f62ea", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "d9db68e85db965bf7037d535ddc354b096b7c3b8f4cb0eb4887dc61eba5eae23", + "research/global-anchor-screen/PROOF.md": "3023c8c039acb3afc2a1e0c2ee55dcffaa4a1a2961076222ae20b03d0f3c6a38", + "research/global-anchor-screen/SOURCE.json": "f6249b8f91c7721a59ecc6d43a3f2ec65162578203bd430ef76732a3937399f3", + "research/global-anchor-screen/compiler-frozen.py": "12d646fa9ad69e4f3c532fe69080d8fe1509cde0968a6ab52a9d60273803adc0", + "research/global-anchor-screen/selected-manifest.json": "97bd86fc20fb3aee2d1adacd6a485b12e918b7340d2d3ca70e1318889e13e3a0", + "research/global-anchor-screen/selected_compile.py": "86bdfcf599c6b131e376773fe177bca57a9f63c9b60bad5de8aa00982d779b22" + }, + "repo": "DominikScholz/integer-mult-bounds", + "scope": "Preserved original pending live-carrier compiler, selected driver, proof and source provenance. This package composes the pending lifecycle and both containment checks with PR67 profile-cost selection and its own next-use scoring.", + "shared_dependency_manifest": "../pr48/SOURCE.json", + "shared_dependency_manifest_sha256": "6ccc673f88d3650d75ed600b082fe2fc2866dd88a172d182a38c1d0cd27d24b3" + }, + "split_operation": { + "author": "Rohan Garg / rohangar1 with OpenAI Codex assistance", + "commit": "641f22e52913db784f3b6ff1176b0c2945aae45b", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "f85437ee441f2a028660dd5e8dbdc0ec7b52bb55c04ea34fa4829c154bfd0ac1", + "research/split-skip/SOURCE.json": "7c2b4646a3ecfef6f881da5c43e4bd0fa9a4d1b00548b8ab458d897e16735134", + "research/split-skip/split_graph.py": "9b16ba907cbd58611fb64bfb9211be7809d54822d44c78fc6167cf4ba79eb905" + }, + "repo": "CrocSwap/integer-mult-bounds", + "scope": "Preserved original split-pair operation and attribution. These files document the adapted grouping operation; they are not imported by this producer. Actual imported source closure is PR65 plus shared PR48." + } + }, + "status": "Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed" +} diff --git a/certificates/split-pair-profiles-23.json b/certificates/split-pair-profiles-23.json new file mode 100644 index 0000000000..bf40dc76b4 --- /dev/null +++ b/certificates/split-pair-profiles-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27455,"loss":506,"rank_sum":631971,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38745,"crt_matrices":5750,"crt_disagreements":0,"blocks":[0,357148,21253,8022,5466,4156,3835,3250,2612,2109,1750,1529,1008,863,555,461,234,149,40,9,0,23,0,0]} diff --git a/certificates/split-pair-profiles-25.json b/certificates/split-pair-profiles-25.json new file mode 100644 index 0000000000..2f4bb6b9e9 --- /dev/null +++ b/certificates/split-pair-profiles-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":36015,"loss":600,"rank_sum":900975,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52075,"crt_matrices":7444,"crt_disagreements":0,"blocks":[0,492698,27869,10467,7897,5674,5027,4110,3809,3047,2490,2047,1814,1443,1151,898,567,470,271,163,47,13,0,25,0,0]} diff --git a/certificates/split-pair-repository-validation.json b/certificates/split-pair-repository-validation.json new file mode 100644 index 0000000000..5d54439696 --- /dev/null +++ b/certificates/split-pair-repository-validation.json @@ -0,0 +1,20 @@ +{ + "base_commit": "fc74109a6978cb1849547e0dcb9d9df995ddaac5", + "construction": "Anchored split frames with profile-cost pending live reclamation", + "focused_verification": { + "certificate_sha256": "0fcb53fa374273efab6370953c966e8fa065dbfdba43691843a4788cb2cda42e", + "command": "make -j1 split-pair-verify", + "completed_at": "2026-10-08T19:06:05.451986+00:00", + "exit_code": 0, + "full_repository": "PENDING", + "independent_source_receipt_sha256": "89a3b9123f908acf2c877c1c676abfaf44a986db9366c6d675b5e129bc4fcab9", + "independent_tests_receipt_sha256": "db7c44f82fba9f585617438c059088a7991accbe9d48be5c78ef969d73cd504f", + "log_sha256": "076411072dd88e92b155c39a5223bffc846a205f76379ad509790f8cbfeb89c3", + "source_sha256": "9d5a4a7c4cf459f4c5731809de93cfb4b873cb8c9ea95a1be9239733a9a93c72", + "status": "PASS deterministic selected-word regeneration, both physical replays/profiles, exact moment/assembly and 23 focused tests" + }, + "full_repository_command": "make -j1 verify", + "independent_audit": "PASS frozen source/proof/physical/arithmetic integration; receipts bound in focused result", + "scope": "Only finite conditional construction; inherited all-size hypotheses remain.", + "status": "PENDING expanded full repository verification" +} diff --git a/certificates/split-pair-transitions-23.json b/certificates/split-pair-transitions-23.json new file mode 100644 index 0000000000..1a389c32fd --- /dev/null +++ b/certificates/split-pair-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27455, + "frames": 59803, + "distinct_transitions": 152272, + "singles": 15939, + "rank_mass": 631971, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69190, + "2": 73632, + "3": 10224, + "4": 15382, + "5": 6461, + "6": 1593, + "7": 694, + "8": 1229, + "9": 411, + "10": 539, + "11": 98, + "12": 671, + "13": 254, + "14": 1927, + "15": 439, + "16": 440, + "17": 487, + "18": 3417, + "19": 6882, + "21": 171, + "22": 23 + }, + "word_sha256": "b0379d99fd6c10307da0d0fc526ed6171f19105a47bae61730fc3745ef60bd9e", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/certificates/split-pair-transitions-25.json b/certificates/split-pair-transitions-25.json new file mode 100644 index 0000000000..e5864300a1 --- /dev/null +++ b/certificates/split-pair-transitions-25.json @@ -0,0 +1,37 @@ +{ + "h": 25, + "v": 2300, + "R": 36015, + "frames": 84845, + "distinct_transitions": 212584, + "singles": 20700, + "rank_mass": 900975, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 91026, + "2": 108047, + "3": 13560, + "4": 19874, + "5": 8387, + "6": 2967, + "7": 1127, + "8": 1443, + "9": 664, + "10": 791, + "11": 38, + "12": 758, + "13": 149, + "14": 681, + "15": 167, + "16": 2265, + "17": 680, + "18": 566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "word_sha256": "4c956749f0ec72c61875c51099afdf23e69ccea268a9b43b8d46da2ffdb24903", + "copied_centers": 25, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/certificates/split-pair-validation.json b/certificates/split-pair-validation.json new file mode 100644 index 0000000000..4afc1578e3 --- /dev/null +++ b/certificates/split-pair-validation.json @@ -0,0 +1,237 @@ +{ + "axes": { + "23": { + "profile": { + "R": 27455, + "blocks": [ + 0, + 357148, + 21253, + 8022, + 5466, + 4156, + 3835, + 3250, + 2612, + 2109, + 1750, + 1529, + 1008, + 863, + 555, + 461, + 234, + 149, + 40, + 9, + 0, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 5750, + "distinct_matrices": 38745, + "field_prime": 2305843009213693951, + "frames": 59803, + "h": 23, + "loss": 506, + "rank_sum": 631971, + "v": 1771 + }, + "replay": { + "elementary_xors": 162103, + "full_basis_vectors": 30997, + "h": 23, + "histogram": { + "0": 175253, + "1": 58564, + "2": 78945, + "3": 10224, + "4": 15382, + "5": 6461, + "6": 1593, + "7": 694, + "8": 1229, + "9": 411, + "10": 539, + "11": 98, + "12": 671, + "13": 254, + "14": 1927, + "15": 439, + "16": 440, + "17": 487, + "18": 3417, + "19": 6882, + "21": 171, + "22": 23 + }, + "output_roles": 5336, + "rank_mass": 631971, + "roles": 27455, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 673206 + }, + "transitions": { + "R": 27455, + "copied_centers": 23, + "distinct_transitions": 152272, + "frames": 59803, + "h": 23, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69190, + "2": 73632, + "3": 10224, + "4": 15382, + "5": 6461, + "6": 1593, + "7": 694, + "8": 1229, + "9": 411, + "10": 539, + "11": 98, + "12": 671, + "13": 254, + "14": 1927, + "15": 439, + "16": 440, + "17": 487, + "18": 3417, + "19": 6882, + "21": 171, + "22": 23 + }, + "rank_mass": 631971, + "singles": 15939, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 1771, + "word_sha256": "b0379d99fd6c10307da0d0fc526ed6171f19105a47bae61730fc3745ef60bd9e" + } + }, + "25": { + "profile": { + "R": 36015, + "blocks": [ + 0, + 492698, + 27869, + 10467, + 7897, + 5674, + 5027, + 4110, + 3809, + 3047, + 2490, + 2047, + 1814, + 1443, + 1151, + 898, + 567, + 470, + 271, + 163, + 47, + 13, + 0, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 7444, + "distinct_matrices": 52075, + "field_prime": 2305843009213693951, + "frames": 84845, + "h": 25, + "loss": 600, + "rank_sum": 900975, + "v": 2300 + }, + "replay": { + "elementary_xors": 225757, + "full_basis_vectors": 40615, + "h": 25, + "histogram": { + "0": 242882, + "1": 77226, + "2": 114947, + "3": 13560, + "4": 19874, + "5": 8387, + "6": 2967, + "7": 1127, + "8": 1443, + "9": 664, + "10": 791, + "11": 38, + "12": 758, + "13": 149, + "14": 681, + "15": 167, + "16": 2265, + "17": 680, + "18": 566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "output_roles": 6925, + "rank_mass": 900975, + "roles": 36015, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 935228 + }, + "transitions": { + "R": 36015, + "copied_centers": 25, + "distinct_transitions": 212584, + "frames": 84845, + "h": 25, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 91026, + "2": 108047, + "3": 13560, + "4": 19874, + "5": 8387, + "6": 2967, + "7": 1127, + "8": 1443, + "9": 664, + "10": 791, + "11": 38, + "12": 758, + "13": 149, + "14": 681, + "15": 167, + "16": 2265, + "17": 680, + "18": 566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "rank_mass": 900975, + "singles": 20700, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 2300, + "word_sha256": "4c956749f0ec72c61875c51099afdf23e69ccea268a9b43b8d46da2ffdb24903" + } + } + }, + "bit_saving": "12854322426487/250000000000000000", + "certificate_sha256": "41dff686032f16e98840761c8b11cfbfaa713843ecac1557edba6a4dddcb485e", + "kappa": "51414646104039/1000000000000000000", + "margins": 7, + "producer_words_regenerated_and_matched": true, + "scope": "Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.", + "source_binding": "Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.", + "status": "PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly", + "strict_constraints": 47 +} diff --git a/certificates/split-pair-word-23.json.gz b/certificates/split-pair-word-23.json.gz new file mode 100644 index 0000000000..38b82cbb3d Binary files /dev/null and b/certificates/split-pair-word-23.json.gz differ diff --git a/certificates/split-pair-word-25.json.gz b/certificates/split-pair-word-25.json.gz new file mode 100644 index 0000000000..da9935d15a Binary files /dev/null and b/certificates/split-pair-word-25.json.gz differ diff --git a/formal/lean/AuditAll.lean b/formal/lean/AuditAll.lean index a8b5830180..35db025283 100644 --- a/formal/lean/AuditAll.lean +++ b/formal/lean/AuditAll.lean @@ -1,3 +1,4 @@ +import KappaCheck.AlignedFrameComposition import KappaCheck import PRChecksA import PRChecksB @@ -388,3 +389,201 @@ import PRChecksC #print axioms PRChecksC.PR9.constraints_strict #print axioms PRChecksC.PR9.margin_values #print axioms PRChecksC.PR9.kappa_witness + +#print axioms KappaCheck.AlignedFrameComposition.network_counts +#print axioms KappaCheck.AlignedFrameComposition.rank_mass +#print axioms KappaCheck.AlignedFrameComposition.count_1 +#print axioms KappaCheck.AlignedFrameComposition.count_2 +#print axioms KappaCheck.AlignedFrameComposition.count_3 +#print axioms KappaCheck.AlignedFrameComposition.count_4 +#print axioms KappaCheck.AlignedFrameComposition.count_5 +#print axioms KappaCheck.AlignedFrameComposition.count_6 +#print axioms KappaCheck.AlignedFrameComposition.count_7 +#print axioms KappaCheck.AlignedFrameComposition.count_8 +#print axioms KappaCheck.AlignedFrameComposition.count_9 +#print axioms KappaCheck.AlignedFrameComposition.count_10 +#print axioms KappaCheck.AlignedFrameComposition.count_11 +#print axioms KappaCheck.AlignedFrameComposition.count_12 +#print axioms KappaCheck.AlignedFrameComposition.count_13 +#print axioms KappaCheck.AlignedFrameComposition.count_14 +#print axioms KappaCheck.AlignedFrameComposition.count_15 +#print axioms KappaCheck.AlignedFrameComposition.count_16 +#print axioms KappaCheck.AlignedFrameComposition.count_17 +#print axioms KappaCheck.AlignedFrameComposition.count_18 +#print axioms KappaCheck.AlignedFrameComposition.count_19 +#print axioms KappaCheck.AlignedFrameComposition.count_20 +#print axioms KappaCheck.AlignedFrameComposition.count_21 +#print axioms KappaCheck.AlignedFrameComposition.count_22 +#print axioms KappaCheck.AlignedFrameComposition.count_23 +#print axioms KappaCheck.AlignedFrameComposition.count_25 +#print axioms KappaCheck.AlignedFrameComposition.count_481 +#print axioms KappaCheck.AlignedFrameComposition.count_525 +#print axioms KappaCheck.AlignedFrameComposition.count_529 +#print axioms KappaCheck.AlignedFrameComposition.complete_child_support +#print axioms KappaCheck.AlignedFrameComposition.strict_child_contraction +#print axioms KappaCheck.AlignedFrameComposition.slack_a_positive +#print axioms KappaCheck.AlignedFrameComposition.slack_a_below_b +#print axioms KappaCheck.AlignedFrameComposition.slack_b_below_one_over32 +#print axioms KappaCheck.AlignedFrameComposition.slack_beta_positive +#print axioms KappaCheck.AlignedFrameComposition.slack_beta_below_one +#print axioms KappaCheck.AlignedFrameComposition.slack_phase_leaf_above_bit +#print axioms KappaCheck.AlignedFrameComposition.slack_q_positive +#print axioms KappaCheck.AlignedFrameComposition.slack_q_below_internal +#print axioms KappaCheck.AlignedFrameComposition.slack_q_below_leaf +#print axioms KappaCheck.AlignedFrameComposition.slack_c_positive +#print axioms KappaCheck.AlignedFrameComposition.slack_c_below_one +#print axioms KappaCheck.AlignedFrameComposition.slack_q_below_reservations +#print axioms KappaCheck.AlignedFrameComposition.slack_lambda_above_tau +#print axioms KappaCheck.AlignedFrameComposition.slack_lambda_above_sigma +#print axioms KappaCheck.AlignedFrameComposition.slack_lambda_above_internal +#print axioms KappaCheck.AlignedFrameComposition.slack_lambda_prime_above_lambda +#print axioms KappaCheck.AlignedFrameComposition.slack_compact_leaf +#print axioms KappaCheck.AlignedFrameComposition.slack_compact_reservations +#print axioms KappaCheck.AlignedFrameComposition.slack_lambda_prime_below_one +#print axioms KappaCheck.AlignedFrameComposition.slack_epsilon_positive +#print axioms KappaCheck.AlignedFrameComposition.slack_epsilon_below_one +#print axioms KappaCheck.AlignedFrameComposition.slack_guard_width +#print axioms KappaCheck.AlignedFrameComposition.slack_K_geometry +#print axioms KappaCheck.AlignedFrameComposition.slack_K_dominates_log +#print axioms KappaCheck.AlignedFrameComposition.slack_record_suffix +#print axioms KappaCheck.AlignedFrameComposition.slack_phase_local +#print axioms KappaCheck.AlignedFrameComposition.slack_phase_boundary +#print axioms KappaCheck.AlignedFrameComposition.slack_gamma_sublinear +#print axioms KappaCheck.AlignedFrameComposition.slack_cell_above_band +#print axioms KappaCheck.AlignedFrameComposition.slack_prime_interval_packing +#print axioms KappaCheck.AlignedFrameComposition.slack_alpha_positive +#print axioms KappaCheck.AlignedFrameComposition.slack_alpha_below_one +#print axioms KappaCheck.AlignedFrameComposition.slack_alpha_below_one_fourth +#print axioms KappaCheck.AlignedFrameComposition.slack_delta_positive +#print axioms KappaCheck.AlignedFrameComposition.slack_delta_below_one_eighth +#print axioms KappaCheck.AlignedFrameComposition.slack_short_record_fallback +#print axioms KappaCheck.AlignedFrameComposition.slack_small_field_exposure +#print axioms KappaCheck.AlignedFrameComposition.slack_artificial_boundary +#print axioms KappaCheck.AlignedFrameComposition.slack_literal_scalar_guard +#print axioms KappaCheck.AlignedFrameComposition.slack_row_product_gap +#print axioms KappaCheck.AlignedFrameComposition.slack_g1_above_kappa +#print axioms KappaCheck.AlignedFrameComposition.slack_g2_above_kappa +#print axioms KappaCheck.AlignedFrameComposition.slack_g3_above_kappa +#print axioms KappaCheck.AlignedFrameComposition.slack_g4_above_kappa +#print axioms KappaCheck.AlignedFrameComposition.slack_g5_above_kappa +#print axioms KappaCheck.AlignedFrameComposition.slack_g6_above_kappa +#print axioms KappaCheck.AlignedFrameComposition.slack_g7_above_kappa +#print axioms KappaCheck.AlignedFrameComposition.margins_strict +#print axioms KappaCheck.AlignedFrameComposition.balanced_identities +#print axioms KappaCheck.AlignedFrameComposition.controlling_margin +#print axioms KappaCheck.AlignedFrameComposition.gain_over_original +#print axioms KappaCheck.AlignedFrameComposition.finite_bridge +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_1 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_1 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_2 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_2 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_3 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_3 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_4 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_4 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_5 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_5 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_6 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_6 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_7 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_7 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_8 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_8 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_9 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_9 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_10 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_10 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_11 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_11 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_12 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_12 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_13 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_13 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_14 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_14 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_15 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_15 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_16 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_16 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_17 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_17 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_18 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_18 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_19 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_19 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_20 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_20 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_21 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_21 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_22 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_22 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_23 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_23 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_25 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_25 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_481 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_481 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_525 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_525 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_529 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_529 +#print axioms KappaCheck.AlignedFrameComposition.accepted_profile_link +#print axioms KappaCheck.AlignedFrameComposition.accepted_moment +#print axioms KappaCheck.AlignedFrameComposition.accepted_paid_moment +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_1 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_1 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_2 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_2 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_3 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_3 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_4 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_4 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_5 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_5 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_6 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_6 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_7 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_7 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_8 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_8 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_9 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_9 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_10 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_10 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_11 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_11 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_12 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_12 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_13 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_13 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_14 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_14 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_15 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_15 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_16 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_16 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_17 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_17 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_18 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_18 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_19 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_19 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_20 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_20 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_21 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_21 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_22 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_22 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_23 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_23 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_25 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_25 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_481 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_481 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_525 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_525 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_529 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_529 +#print axioms KappaCheck.AlignedFrameComposition.rejected_profile_link +#print axioms KappaCheck.AlignedFrameComposition.rejected_moment +#print axioms KappaCheck.AlignedFrameComposition.rejected_paid_moment diff --git a/formal/lean/KappaCheck.lean b/formal/lean/KappaCheck.lean index fae11c72de..b4c671f007 100644 --- a/formal/lean/KappaCheck.lean +++ b/formal/lean/KappaCheck.lean @@ -5,3 +5,5 @@ import KappaCheck.Guard import KappaCheck.Frames import KappaCheck.Movement import KappaCheck.Layout + +import KappaCheck.AlignedFrameComposition diff --git a/formal/lean/KappaCheck/AlignedFrameComposition.lean b/formal/lean/KappaCheck/AlignedFrameComposition.lean new file mode 100644 index 0000000000..7564087ec3 --- /dev/null +++ b/formal/lean/KappaCheck/AlignedFrameComposition.lean @@ -0,0 +1,1029 @@ +import Mathlib.Tactic.NormNum +import Mathlib.Data.Nat.Choose.Basic + +/-! +Exact arithmetic supplement for the frozen final frame composition. +Prepared with OpenAI assistance; inherited formulas retain their upstream credits. + +This file proves rational arithmetic only. The supplied physical profile arrays, +the analytic validity of the logarithm and Taylor enclosures, and the all-size +tape/prime/recovery hypotheses are outside this module. It does not assert an +unconditional multiplication theorem. No sorry, native_decide, or new axioms. +The theorem statements recompute counts and parameter formulas rather than +merely asserting positivity of externally supplied fractions. +-/ +namespace KappaCheck.AlignedFrameComposition +set_option maxRecDepth 10000 +set_option maxHeartbeats 4000000 + +-- Frozen selection SHA256: 43a762adf17b2338b2d7ec486fd6eb17d00d1d221e7f1e4041711cbce9964ea7 +-- Complete portfolio SHA256: 5ecde1320034b152779c702d7ccefdf953a00f678a62adcfd8c3ef7a8fb1cf31 +def m : ℕ := 23 * 25 +def n : ℕ := Nat.choose 23 3 * Nat.choose 25 3 +def roles23 : ℕ := 26387 +def blocks23 : List ℕ := [0, 371505, 11855, 16183, 4817, 3983, 3154, 2137, 1923, 1415, 1172, 853, 822, 499, 393, 293, 268, 68, 320, 0, 171, 23, 0, 0] +def roles25 : ℕ := 34772 +def blocks25 : List ℕ := [0, 504683, 18260, 19030, 7746, 4400, 4491, 3537, 3136, 2209, 2257, 1550, 1493, 910, 909, 469, 581, 263, 210, 59, 387, 101, 169, 25, 0, 0] +def width : ℕ := 2*n + Nat.choose 25 3 * roles23 + Nat.choose 23 3 * roles25 +def counts : List (ℕ × ℕ) := + [(1, 23*n), (21, 4*n), (17, 2*n), (481, 2*n), (23, 2*n), + (23, Nat.choose 25 3 * roles23), (529, Nat.choose 25 3 * roles23), + (25, Nat.choose 23 3 * roles25), (525, Nat.choose 23 3 * roles25)] ++ + (blocks23.zipIdx.map fun (c,t) => (t, Nat.choose 25 3 * c)) ++ + (blocks25.zipIdx.map fun (c,t) => (t, Nat.choose 23 3 * c)) +def count (t : ℕ) : ℕ := + (counts.map fun p => if p.1 = t then p.2 else 0).sum +def mass : ℕ := (counts.map fun p => p.1*p.2).sum + +theorem network_counts : m = 575 ∧ n = 4073300 ∧ width = 130417912 := by + norm_num [m, n, width, roles23, roles25, Nat.choose] + +theorem rank_mass : mass = 74988452500 ∧ m*width-mass = 1846900 := by + norm_num [mass, counts, blocks23, blocks25, n, m, width, roles23, roles25, Nat.choose] + +theorem count_1 : count 1 = 1841940993 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_2 : count 2 = 59604960 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_3 : count 3 = 70923030 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_4 : count 4 = 24797266 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_5 : count 5 = 16953300 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_6 : count 6 = 15207761 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_7 : count 7 = 11179127 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_8 : count 8 = 9976756 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_9 : count 9 = 7166639 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_10 : count 10 = 6692747 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_11 : count 11 = 4706950 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_12 : count 12 = 4534703 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_13 : count 13 = 2759310 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_14 : count 14 = 2513739 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_15 : count 15 = 1504499 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_16 : count 16 = 1645351 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_17 : count 17 = 8768773 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_18 : count 18 = 1107910 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_19 : count 19 = 104489 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_20 : count 20 = 1078677 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_21 : count 21 = 16524971 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_22 : count 22 = 299299 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_23 : count 23 = 68880975 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_25 : count 25 = 61581212 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_481 : count 481 = 8146600 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_525 : count 525 = 61581212 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +theorem count_529 : count 529 = 60690100 := by + norm_num [count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose] + +def childSizes : List ℕ := [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 481, 525, 529] +theorem complete_child_support : ∀ p ∈ counts, p.2 ≠ 0 → p.1 ∈ childSizes := by + norm_num [counts, blocks23, blocks25, n, roles23, roles25, Nat.choose, childSizes] + +theorem strict_child_contraction : ∀ t ∈ childSizes, 0 < t ∧ t < m := by + norm_num [childSizes, m] + +def a : ℚ := 52792403826155 / 1000000000000000000 +def b : ℚ := 717 / 10000000 +def kappa : ℚ := 52789616935221 / 1000000000000000000 +def eta : ℚ := 1 / 1000000000000 +def beta : ℚ := 1 / 20 +def tau : ℚ := 1-a +def sigma : ℚ := 1-b +def qParam : ℚ := a*(1-2*eta) +def lp : ℚ := 1-qParam +def c : ℚ := qParam+eta/4 +def epsilon : ℚ := (1-eta)/(1+qParam) +def lam : ℚ := (tau+lp)/2 +def g : ℚ := epsilon*qParam +def r : ℚ := (g+1-epsilon)/2 +def delta : ℚ := eta/8 +def internal : ℚ := tau+(1-beta)*max (sigma-tau) 0 +def leaf : ℚ := sigma+beta*(1-sigma) +def complexWidth : ℕ := 537696432 +def complexRank : ℕ := 421548223824 +def scalar : ℕ := 4793351472 +def guardE : ℕ := 64*(complexWidth+784+scalar+1)^3 +def guardB : ℕ := complexRank+guardE +def literal : ℕ := 2*scalar*complexWidth^2+8*complexRank+4*complexWidth+4+32*784 +def guardC : ℕ := 32*784*guardB^2 +def literalGap : ℚ := (guardE : ℚ)-literal +def rowGap : ℚ := 2000-(51/25)*(9*27+20*30) +def margins : List ℚ := [1-epsilon,a,g,a,min (1-epsilon-delta) (r-delta),1-epsilon-delta,epsilon] + +theorem slack_a_positive : (a) = ((10558480765231 / 200000000000000000) : ℚ) ∧ (0 : ℚ) < (a) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_a_below_b : (b-a) = ((3781519234769 / 200000000000000000) : ℚ) ∧ (0 : ℚ) < (b-a) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_b_below_one_over32 : (1/32-b) = ((311783 / 10000000) : ℚ) ∧ (0 : ℚ) < (1/32-b) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_beta_positive : (beta) = ((1 / 20) : ℚ) ∧ (0 : ℚ) < (beta) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_beta_below_one : (1-beta) = ((19 / 20) : ℚ) ∧ (0 : ℚ) < (1-beta) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_phase_leaf_above_bit : ((1-beta)*b-a) = ((3064519234769 / 200000000000000000) : ℚ) ∧ (0 : ℚ) < ((1-beta)*b-a) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_q_positive : (qParam) = ((5279240382604941519234769 / 100000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (qParam) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_q_below_internal : (1-internal-qParam) = ((10558480765231 / 100000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-internal-qParam) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_q_below_leaf : (1-leaf-qParam) = ((1532259617395058480765231 / 100000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-leaf-qParam) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_c_positive : (c) = ((5279240407604941519234769 / 100000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (c) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_c_below_one : (1-c) = ((99994720759592395058480765231 / 100000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-c) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_q_below_reservations : (c-qParam) = ((1 / 4000000000000) : ℚ) ∧ (0 : ℚ) < (c-qParam) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_lambda_above_tau : (lam-tau) = ((10558480765231 / 200000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lam-tau) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_lambda_above_sigma : (lam-sigma) = ((3781519234779558480765231 / 200000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lam-sigma) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_lambda_above_internal : (lam-internal) = ((10558480765231 / 200000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lam-internal) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_lambda_prime_above_lambda : (lp-lam) = ((10558480765231 / 200000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lp-lam) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_compact_leaf : (lp-leaf) = ((1532259617395058480765231 / 100000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lp-leaf) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_compact_reservations : (lp-(1-c)) = ((1 / 4000000000000) : ℚ) ∧ (0 : ℚ) < (lp-(1-c)) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_lambda_prime_below_one : (qParam) = ((5279240382604941519234769 / 100000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (qParam) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_epsilon_positive : (epsilon) = ((99999999999900000000000000000 / 100005279240382604941519234769) : ℚ) ∧ (0 : ℚ) < (epsilon) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_epsilon_below_one : (1-epsilon) = ((5279240482604941519234769 / 100005279240382604941519234769) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_guard_width : (1-epsilon) = ((5279240482604941519234769 / 100005279240382604941519234769) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_K_geometry : (1-epsilon*(1+c)) = ((75005279240407604941519234769 / 100005279240382604941519234769000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon*(1+c)) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_K_dominates_log : (epsilon*c) = ((5279240407599662278827164058480765231 / 100005279240382604941519234769000000000000) : ℚ) ∧ (0 : ℚ) < (epsilon*c) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_record_suffix : (1-epsilon) = ((5279240482604941519234769 / 100005279240382604941519234769) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_phase_local : (1-epsilon-delta) = ((42233923760834252913495547058480765231 / 800042233923060839532153878152000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon-delta) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_phase_boundary : (r-delta) = ((8446784672162627190393025458480765231 / 160008446784612167906430775630400000000000) : ℚ) ∧ (0 : ℚ) < (r-delta) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_gamma_sublinear : (1-epsilon-r) = ((1 / 2000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon-r) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_cell_above_band : (epsilon-(1-r)/2) = ((199999999999699994720759617395058480765231 / 400021116961530419766076939076000000000000) : ℚ) ∧ (0 : ℚ) < (epsilon-(1-r)/2) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_prime_interval_packing : (1-epsilon) = ((5279240482604941519234769 / 100005279240382604941519234769) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_alpha_positive : (r) = ((10558480865204603798086933058480765231 / 200010558480765209883038469538000000000000) : ℚ) ∧ (0 : ℚ) < (r) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_alpha_below_one : (1-r) = ((199999999999900005279240382604941519234769 / 200010558480765209883038469538000000000000) : ℚ) ∧ (0 : ℚ) < (1-r) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_alpha_below_one_fourth : (1/4-r) = ((49992081139326097866961530451441519234769 / 200010558480765209883038469538000000000000) : ℚ) ∧ (0 : ℚ) < (1/4-r) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_delta_positive : (delta) = ((1 / 8000000000000) : ℚ) ∧ (0 : ℚ) < (delta) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_delta_below_one_eighth : (1/8-delta) = ((999999999999 / 8000000000000) : ℚ) ∧ (0 : ℚ) < (1/8-delta) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_short_record_fallback : (epsilon-a) = ((19998944096162718865234979846828072503338483361 / 20001055848076520988303846953800000000000000000) : ℚ) ∧ (0 : ℚ) < (epsilon-a) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_small_field_exposure : (1-epsilon-g) = ((1 / 1000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon-g) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_artificial_boundary : (8-epsilon+r-delta-g) = ((5600337871385586732094952173030824557704307 / 800042233923060839532153878152000000000000) : ℚ) ∧ (0 : ℚ) < (8-epsilon+r-delta-g) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_literal_scalar_guard : (literalGap) = (9693793493753822316795466474748 : ℚ) ∧ (0 : ℚ) < (literalGap) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_row_product_gap : (rowGap) = ((7007 / 25) : ℚ) ∧ (0 : ℚ) < (rowGap) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_g1_above_kappa : ((1-epsilon)-kappa) = ((100005334854822405963918081036101051 / 100005279240382604941519234769000000000000000000) : ℚ) ∧ (0 : ℚ) < ((1-epsilon)-kappa) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_g2_above_kappa : ((a)-kappa) = ((1393445467 / 500000000000000000) : ℚ) ∧ (0 : ℚ) < ((a)-kappa) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_g3_above_kappa : ((g)-kappa) = ((55614439801022398846267101051 / 100005279240382604941519234769000000000000000000) : ℚ) ∧ (0 : ℚ) < ((g)-kappa) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_g4_above_kappa : ((a)-kappa) = ((1393445467 / 500000000000000000) : ℚ) ∧ (0 : ℚ) < ((a)-kappa) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_g5_above_kappa : ((min (1-epsilon-delta) (r-delta))-kappa) = ((37502035329583277875468559305476051 / 100005279240382604941519234769000000000000000000) : ℚ) ∧ (0 : ℚ) < ((min (1-epsilon-delta) (r-delta))-kappa) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_g6_above_kappa : ((1-epsilon-delta)-kappa) = ((87504674949774580346228176689976051 / 100005279240382604941519234769000000000000000000) : ℚ) ∧ (0 : ℚ) < ((1-epsilon-delta)-kappa) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem slack_g7_above_kappa : ((epsilon)-kappa) = ((99994720759517400393335587636963918081036101051 / 100005279240382604941519234769000000000000000000) : ℚ) ∧ (0 : ℚ) < ((epsilon)-kappa) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem margins_strict : ∀ x ∈ margins, kappa < x := by + norm_num [margins, a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem balanced_identities : 1-epsilon-g = eta ∧ 1-epsilon-r = eta/2 ∧ 1-epsilon*(1+c) = eta-epsilon*eta/4 := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem controlling_margin : g < kappa+1/1000000000000000000 ∧ kappa < g := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem gain_over_original : kappa > (384569/10000000000 : ℚ) ∧ kappa > (409953/10000000000 : ℚ) ∧ (1/2^15 : ℚ) < kappa ∧ kappa < (1/2^14 : ℚ) := by + norm_num [a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +theorem finite_bridge : 575^9 > (2:ℕ)*529^9 ∧ 575^8 ≤ (2:ℕ)*529^8 ∧ 784^20 > (2:ℕ)*756^20 ∧ 784^19 ≤ (2:ℕ)*756^19 ∧ (2:ℕ)^26 ≤ width ∧ width < (2:ℕ)^27 ∧ (2:ℕ)^29 ≤ complexWidth ∧ complexWidth < (2:ℕ)^30 ∧ guardE > literal ∧ 2*guardB*(784-756) ≥ complexRank+guardE ∧ guardC > 2*guardB+18 := by + norm_num [width, n, roles23, roles25, Nat.choose, a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar] + +-- Rounded exponential bounds are supplied here. Their weighted sums and +-- their domination of the degree-eight Taylor arithmetic are checked below. +-- Analytic connections to real log/exp remain external to this supplement. +def taylor8 (x : ℚ) : ℚ := 1+x+x^2/2+x^3/6+x^4/24+x^5/120+x^6/720+x^7/5040+x^8/40320 +def expUpper (x : ℚ) : ℚ := taylor8 x+x^9/362880/(1-x/10) + +def accepted_1 : ℚ := (10003355187430811436301506884590968371643 / 10000000000000000000000000000000000000000) +theorem accepted_interval_1 : (0 : ℚ) ≤ a*(3177185020398675220004135749131 / 500000000000000000000000000000) ∧ a*(3177185020398675220004135749131 / 500000000000000000000000000000) ≤ a*(6354370040797350440008271498263 / 1000000000000000000000000000000) ∧ a*(6354370040797350440008271498263 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_1 : expUpper (a*(6354370040797350440008271498263 / 1000000000000000000000000000000)) ≤ accepted_1 := by + norm_num [expUpper, taylor8, a, accepted_1] + +def accepted_2 : ℚ := (10002989142293451273171593526174883283451 / 10000000000000000000000000000000000000000) +theorem accepted_interval_2 : (0 : ℚ) ≤ a*(1415305715059351282647759844201 / 250000000000000000000000000000) ∧ a*(1415305715059351282647759844201 / 250000000000000000000000000000) ≤ a*(1132244572047481026118207875361 / 200000000000000000000000000000) ∧ a*(1132244572047481026118207875361 / 200000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_2 : expUpper (a*(1132244572047481026118207875361 / 200000000000000000000000000000)) ≤ accepted_2 := by + norm_num [expUpper, taylor8, a, accepted_2] + +def accepted_3 : ℚ := (10002775025823826712873382847907587702911 / 10000000000000000000000000000000000000000) +theorem accepted_interval_3 : (0 : ℚ) ≤ a*(262787887606462037430651313067 / 50000000000000000000000000000) ∧ a*(262787887606462037430651313067 / 50000000000000000000000000000) ≤ a*(5255757752129240748613026261341 / 1000000000000000000000000000000) ∧ a*(5255757752129240748613026261341 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_3 : expUpper (a*(5255757752129240748613026261341 / 1000000000000000000000000000000)) ≤ accepted_3 := by + norm_num [expUpper, taylor8, a, accepted_3] + +def accepted_4 : ℚ := (10002623110550501292874892056529826574567 / 10000000000000000000000000000000000000000) +theorem accepted_interval_4 : (0 : ℚ) ≤ a*(2484037839838729910586903627673 / 500000000000000000000000000000) ∧ a*(2484037839838729910586903627673 / 500000000000000000000000000000) ≤ a*(4968075679677459821173807255347 / 1000000000000000000000000000000) ∧ a*(4968075679677459821173807255347 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_4 : expUpper (a*(4968075679677459821173807255347 / 1000000000000000000000000000000)) ≤ accepted_4 := by + norm_num [expUpper, taylor8, a, accepted_4] + +def accepted_5 : ℚ := (2500626319374711445506337453244448044473 / 2500000000000000000000000000000000000000) +theorem accepted_interval_5 : (0 : ℚ) ≤ a*(1186233032090812516351878041259 / 250000000000000000000000000000) ∧ a*(1186233032090812516351878041259 / 250000000000000000000000000000) ≤ a*(4744932128363250065407512165037 / 1000000000000000000000000000000) ∧ a*(4744932128363250065407512165037 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_5 : expUpper (a*(4744932128363250065407512165037 / 1000000000000000000000000000000)) ≤ accepted_5 := by + norm_num [expUpper, taylor8, a, accepted_5] + +def accepted_6 : ℚ := (10002409001915877196548506453272943391457 / 10000000000000000000000000000000000000000) +theorem accepted_interval_6 : (0 : ℚ) ≤ a*(4562610571569295439195794139881 / 1000000000000000000000000000000) ∧ a*(4562610571569295439195794139881 / 1000000000000000000000000000000) ≤ a*(2281305285784647719597897069941 / 500000000000000000000000000000) ∧ a*(2281305285784647719597897069941 / 500000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_6 : expUpper (a*(2281305285784647719597897069941 / 500000000000000000000000000000)) ≤ accepted_6 := by + norm_num [expUpper, taylor8, a, accepted_6] + +def accepted_7 : ℚ := (2500581900698318395642073696120815915489 / 2500000000000000000000000000000000000000) +theorem accepted_interval_7 : (0 : ℚ) ≤ a*(4408459891742037134902918754819 / 1000000000000000000000000000000) ∧ a*(4408459891742037134902918754819 / 1000000000000000000000000000000) ≤ a*(220422994587101856745145937741 / 50000000000000000000000000000) ∧ a*(220422994587101856745145937741 / 50000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_7 : expUpper (a*(220422994587101856745145937741 / 50000000000000000000000000000)) ≤ accepted_7 := by + norm_num [expUpper, taylor8, a, accepted_7] + +def accepted_8 : ℚ := (10002257092201471363988158192070974714601 / 10000000000000000000000000000000000000000) +theorem accepted_interval_8 : (0 : ℚ) ≤ a*(66795757798711164246196486467 / 15625000000000000000000000000) ∧ a*(66795757798711164246196486467 / 15625000000000000000000000000) ≤ a*(4274928499117514511756575133889 / 1000000000000000000000000000000) ∧ a*(4274928499117514511756575133889 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_8 : expUpper (a*(4274928499117514511756575133889 / 1000000000000000000000000000000)) ≤ accepted_8 := by + norm_num [expUpper, taylor8, a, accepted_8] + +def accepted_9 : ℚ := (10002194897864301657979067676219328248557 / 10000000000000000000000000000000000000000) +theorem accepted_interval_9 : (0 : ℚ) ≤ a*(4157145463461131057217781024417 / 1000000000000000000000000000000) ∧ a*(4157145463461131057217781024417 / 1000000000000000000000000000000) ≤ a*(2078572731730565528608890512209 / 500000000000000000000000000000) ∧ a*(2078572731730565528608890512209 / 500000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_9 : expUpper (a*(2078572731730565528608890512209 / 500000000000000000000000000000)) ≤ accepted_9 := by + norm_num [expUpper, taylor8, a, accepted_9] + +def accepted_10 : ℚ := (5001069631730795364866219488772806507267 / 5000000000000000000000000000000000000000) +theorem accepted_interval_10 : (0 : ℚ) ≤ a*(2025892473901652377995140021789 / 500000000000000000000000000000) ∧ a*(2025892473901652377995140021789 / 500000000000000000000000000000) ≤ a*(4051784947803304755990280043579 / 1000000000000000000000000000000) ∧ a*(4051784947803304755990280043579 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_10 : expUpper (a*(4051784947803304755990280043579 / 1000000000000000000000000000000)) ≤ accepted_10 := by + norm_num [expUpper, taylor8, a, accepted_10] + +def accepted_11 : ℚ := (10002088936289163062957430790317836045217 / 10000000000000000000000000000000000000000) +theorem accepted_interval_11 : (0 : ℚ) ≤ a*(3956474767998979895946327920297 / 1000000000000000000000000000000) ∧ a*(3956474767998979895946327920297 / 1000000000000000000000000000000) ≤ a*(1978237383999489947973163960149 / 500000000000000000000000000000) ∧ a*(1978237383999489947973163960149 / 500000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_11 : expUpper (a*(1978237383999489947973163960149 / 500000000000000000000000000000)) ≤ accepted_11 := by + norm_num [expUpper, taylor8, a, accepted_11] + +def accepted_12 : ℚ := (500102149570078051572238975318143787567 / 500000000000000000000000000000000000000) +theorem accepted_interval_12 : (0 : ℚ) ≤ a*(3869463391009350129778562018423 / 1000000000000000000000000000000) ∧ a*(3869463391009350129778562018423 / 1000000000000000000000000000000) ≤ a*(483682923876168766222320252303 / 125000000000000000000000000000) ∧ a*(483682923876168766222320252303 / 125000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_12 : expUpper (a*(483682923876168766222320252303 / 125000000000000000000000000000)) ≤ accepted_12 := by + norm_num [expUpper, taylor8, a, accepted_12] + +def accepted_13 : ℚ := (5001000363194215412824161557833931245023 / 5000000000000000000000000000000000000000) +theorem accepted_interval_13 : (0 : ℚ) ≤ a*(3789420683335813703954784056697 / 1000000000000000000000000000000) ∧ a*(3789420683335813703954784056697 / 1000000000000000000000000000000) ≤ a*(1894710341667906851977392028349 / 500000000000000000000000000000) ∧ a*(1894710341667906851977392028349 / 500000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_13 : expUpper (a*(1894710341667906851977392028349 / 500000000000000000000000000000)) ≤ accepted_13 := by + norm_num [expUpper, taylor8, a, accepted_13] + +def accepted_14 : ℚ := (10001961595257533350854888857953597009453 / 10000000000000000000000000000000000000000) +theorem accepted_interval_14 : (0 : ℚ) ≤ a*(3715312711182091825485686633361 / 1000000000000000000000000000000) ∧ a*(3715312711182091825485686633361 / 1000000000000000000000000000000) ≤ a*(1857656355591045912742843316681 / 500000000000000000000000000000) ∧ a*(1857656355591045912742843316681 / 500000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_14 : expUpper (a*(1857656355591045912742843316681 / 500000000000000000000000000000)) ≤ accepted_14 := by + norm_num [expUpper, taylor8, a, accepted_14] + +def accepted_15 : ℚ := (250048129129595846749566354536254898103 / 250000000000000000000000000000000000000) +theorem accepted_interval_15 : (0 : ℚ) ≤ a*(3646319839695140374012266928113 / 1000000000000000000000000000000) ∧ a*(3646319839695140374012266928113 / 1000000000000000000000000000000) ≤ a*(1823159919847570187006133464057 / 500000000000000000000000000000) ∧ a*(1823159919847570187006133464057 / 500000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_15 : expUpper (a*(1823159919847570187006133464057 / 500000000000000000000000000000)) ≤ accepted_15 := by + norm_num [expUpper, taylor8, a, accepted_15] + +def accepted_16 : ℚ := (500094554362293568651157626675808595793 / 500000000000000000000000000000000000000) +theorem accepted_interval_16 : (0 : ℚ) ≤ a*(3581781318557569202339343012429 / 1000000000000000000000000000000) ∧ a*(3581781318557569202339343012429 / 1000000000000000000000000000000) ≤ a*(358178131855756920233934301243 / 100000000000000000000000000000) ∧ a*(358178131855756920233934301243 / 100000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_16 : expUpper (a*(358178131855756920233934301243 / 100000000000000000000000000000)) ≤ accepted_16 := by + norm_num [expUpper, taylor8, a, accepted_16] + +def accepted_17 : ℚ := (2000371815209893715990125475253531588243 / 2000000000000000000000000000000000000000) +theorem accepted_interval_17 : (0 : ℚ) ≤ a*(3521156696741134359758736880389 / 1000000000000000000000000000000) ∧ a*(3521156696741134359758736880389 / 1000000000000000000000000000000) ≤ a*(352115669674113435975873688039 / 100000000000000000000000000000) ∧ a*(352115669674113435975873688039 / 100000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_17 : expUpper (a*(352115669674113435975873688039 / 100000000000000000000000000000)) ≤ accepted_17 := by + norm_num [expUpper, taylor8, a, accepted_17] + +def accepted_18 : ℚ := (10001828895184531552662296367755603258471 / 10000000000000000000000000000000000000000) +theorem accepted_interval_18 : (0 : ℚ) ≤ a*(3463998282901185747800548902959 / 1000000000000000000000000000000) ∧ a*(3463998282901185747800548902959 / 1000000000000000000000000000000) ≤ a*(43299978536264821847506861287 / 12500000000000000000000000000) ∧ a*(43299978536264821847506861287 / 12500000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_18 : expUpper (a*(43299978536264821847506861287 / 12500000000000000000000000000)) ≤ accepted_18 := by + norm_num [expUpper, taylor8, a, accepted_18] + +def accepted_19 : ℚ := (10001800346619198540731263851600207293969 / 10000000000000000000000000000000000000000) +theorem accepted_interval_19 : (0 : ℚ) ≤ a*(1704965530815454989999622033187 / 500000000000000000000000000000) ∧ a*(1704965530815454989999622033187 / 500000000000000000000000000000) ≤ a*(27279448493047279839993952531 / 8000000000000000000000000000) ∧ a*(27279448493047279839993952531 / 8000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_19 : expUpper (a*(27279448493047279839993952531 / 8000000000000000000000000000)) ≤ accepted_19 := by + norm_num [expUpper, taylor8, a, accepted_19] + +def accepted_20 : ℚ := (5000886631408803918937931522522045324127 / 5000000000000000000000000000000000000000) +theorem accepted_interval_20 : (0 : ℚ) ≤ a*(83965944181083986164326198053 / 25000000000000000000000000000) ∧ a*(83965944181083986164326198053 / 25000000000000000000000000000) ≤ a*(3358637767243359446573047922121 / 1000000000000000000000000000000) ∧ a*(3358637767243359446573047922121 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_20 : expUpper (a*(3358637767243359446573047922121 / 1000000000000000000000000000000)) ≤ accepted_20 := by + norm_num [expUpper, taylor8, a, accepted_20] + +def accepted_21 : ℚ := (10001747500782808572431534092953530248277 / 10000000000000000000000000000000000000000) +theorem accepted_interval_21 : (0 : ℚ) ≤ a*(413730950384240930438459189737 / 125000000000000000000000000000) ∧ a*(413730950384240930438459189737 / 125000000000000000000000000000) ≤ a*(3309847603073927443507673517897 / 1000000000000000000000000000000) ∧ a*(3309847603073927443507673517897 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_21 : expUpper (a*(3309847603073927443507673517897 / 1000000000000000000000000000000)) ≤ accepted_21 := by + norm_num [expUpper, taylor8, a, accepted_21] + +def accepted_22 : ℚ := (10001722937486763959646233420754369152731 / 10000000000000000000000000000000000000000) +theorem accepted_interval_22 : (0 : ℚ) ≤ a*(3263327587439034586529095798839 / 1000000000000000000000000000000) ∧ a*(3263327587439034586529095798839 / 1000000000000000000000000000000) ≤ a*(81583189685975864663227394971 / 25000000000000000000000000000) ∧ a*(81583189685975864663227394971 / 25000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_22 : expUpper (a*(81583189685975864663227394971 / 25000000000000000000000000000)) ≤ accepted_22 := by + norm_num [expUpper, taylor8, a, accepted_22] + +def accepted_23 : ℚ := (2000339893263411175150443996908118155021 / 2000000000000000000000000000000000000000) +theorem accepted_interval_23 : (0 : ℚ) ≤ a*(804718956217050187300379666613 / 250000000000000000000000000000) ∧ a*(804718956217050187300379666613 / 250000000000000000000000000000) ≤ a*(3218875824868200749201518666453 / 1000000000000000000000000000000) ∧ a*(3218875824868200749201518666453 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_23 : expUpper (a*(3218875824868200749201518666453 / 1000000000000000000000000000000)) ≤ accepted_23 := by + norm_num [expUpper, taylor8, a, accepted_23] + +def accepted_25 : ℚ := (10001655439777341409928794291140256708281 / 10000000000000000000000000000000000000000) +theorem accepted_interval_25 : (0 : ℚ) ≤ a*(313549421592914969080675283181 / 100000000000000000000000000000) ∧ a*(313549421592914969080675283181 / 100000000000000000000000000000) ≤ a*(3135494215929149690806752831811 / 1000000000000000000000000000000) ∧ a*(3135494215929149690806752831811 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_25 : expUpper (a*(3135494215929149690806752831811 / 1000000000000000000000000000000)) ≤ accepted_25 := by + norm_num [expUpper, taylor8, a, accepted_25] + +def accepted_481 : ℚ := (10000094236347566049853859114967129582319 / 10000000000000000000000000000000000000000) +theorem accepted_interval_481 : (0 : ℚ) ≤ a*(35700554138317851917337677133 / 200000000000000000000000000000) ∧ a*(35700554138317851917337677133 / 200000000000000000000000000000) ≤ a*(89251385345794629793344192833 / 500000000000000000000000000000) ∧ a*(89251385345794629793344192833 / 500000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_481 : expUpper (a*(89251385345794629793344192833 / 500000000000000000000000000000)) ≤ accepted_481 := by + norm_num [expUpper, taylor8, a, accepted_481] + +def accepted_525 : ℚ := (10000048026303844125101140750756918734051 / 10000000000000000000000000000000000000000) +theorem accepted_interval_525 : (0 : ℚ) ≤ a*(22742944551431673576538712861 / 250000000000000000000000000000) ∧ a*(22742944551431673576538712861 / 250000000000000000000000000000) ≤ a*(18194355641145338861230970289 / 200000000000000000000000000000) ∧ a*(18194355641145338861230970289 / 200000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_525 : expUpper (a*(18194355641145338861230970289 / 200000000000000000000000000000)) ≤ accepted_525 := by + norm_num [expUpper, taylor8, a, accepted_525] + +def accepted_529 : ℚ := (1000004401925259229481104531257806676897 / 1000000000000000000000000000000000000000) +theorem accepted_interval_529 : (0 : ℚ) ≤ a*(41690804469525529197382917321 / 500000000000000000000000000000) ∧ a*(41690804469525529197382917321 / 500000000000000000000000000000) ≤ a*(83381608939051058394765834643 / 1000000000000000000000000000000) ∧ a*(83381608939051058394765834643 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem accepted_taylor_529 : expUpper (a*(83381608939051058394765834643 / 1000000000000000000000000000000)) ≤ accepted_529 := by + norm_num [expUpper, taylor8, a, accepted_529] + +def acceptedMoment : ℚ := + ((1*1841940993 : ℚ)/(575*130417912))*accepted_1 + + ((2*59604960 : ℚ)/(575*130417912))*accepted_2 + + ((3*70923030 : ℚ)/(575*130417912))*accepted_3 + + ((4*24797266 : ℚ)/(575*130417912))*accepted_4 + + ((5*16953300 : ℚ)/(575*130417912))*accepted_5 + + ((6*15207761 : ℚ)/(575*130417912))*accepted_6 + + ((7*11179127 : ℚ)/(575*130417912))*accepted_7 + + ((8*9976756 : ℚ)/(575*130417912))*accepted_8 + + ((9*7166639 : ℚ)/(575*130417912))*accepted_9 + + ((10*6692747 : ℚ)/(575*130417912))*accepted_10 + + ((11*4706950 : ℚ)/(575*130417912))*accepted_11 + + ((12*4534703 : ℚ)/(575*130417912))*accepted_12 + + ((13*2759310 : ℚ)/(575*130417912))*accepted_13 + + ((14*2513739 : ℚ)/(575*130417912))*accepted_14 + + ((15*1504499 : ℚ)/(575*130417912))*accepted_15 + + ((16*1645351 : ℚ)/(575*130417912))*accepted_16 + + ((17*8768773 : ℚ)/(575*130417912))*accepted_17 + + ((18*1107910 : ℚ)/(575*130417912))*accepted_18 + + ((19*104489 : ℚ)/(575*130417912))*accepted_19 + + ((20*1078677 : ℚ)/(575*130417912))*accepted_20 + + ((21*16524971 : ℚ)/(575*130417912))*accepted_21 + + ((22*299299 : ℚ)/(575*130417912))*accepted_22 + + ((23*68880975 : ℚ)/(575*130417912))*accepted_23 + + ((25*61581212 : ℚ)/(575*130417912))*accepted_25 + + ((481*8146600 : ℚ)/(575*130417912))*accepted_481 + + ((525*61581212 : ℚ)/(575*130417912))*accepted_525 + + ((529*60690100 : ℚ)/(575*130417912))*accepted_529 +def acceptedFromCounts : ℚ := + ((1*(count 1 : ℚ))/(m*width))*accepted_1 + + ((2*(count 2 : ℚ))/(m*width))*accepted_2 + + ((3*(count 3 : ℚ))/(m*width))*accepted_3 + + ((4*(count 4 : ℚ))/(m*width))*accepted_4 + + ((5*(count 5 : ℚ))/(m*width))*accepted_5 + + ((6*(count 6 : ℚ))/(m*width))*accepted_6 + + ((7*(count 7 : ℚ))/(m*width))*accepted_7 + + ((8*(count 8 : ℚ))/(m*width))*accepted_8 + + ((9*(count 9 : ℚ))/(m*width))*accepted_9 + + ((10*(count 10 : ℚ))/(m*width))*accepted_10 + + ((11*(count 11 : ℚ))/(m*width))*accepted_11 + + ((12*(count 12 : ℚ))/(m*width))*accepted_12 + + ((13*(count 13 : ℚ))/(m*width))*accepted_13 + + ((14*(count 14 : ℚ))/(m*width))*accepted_14 + + ((15*(count 15 : ℚ))/(m*width))*accepted_15 + + ((16*(count 16 : ℚ))/(m*width))*accepted_16 + + ((17*(count 17 : ℚ))/(m*width))*accepted_17 + + ((18*(count 18 : ℚ))/(m*width))*accepted_18 + + ((19*(count 19 : ℚ))/(m*width))*accepted_19 + + ((20*(count 20 : ℚ))/(m*width))*accepted_20 + + ((21*(count 21 : ℚ))/(m*width))*accepted_21 + + ((22*(count 22 : ℚ))/(m*width))*accepted_22 + + ((23*(count 23 : ℚ))/(m*width))*accepted_23 + + ((25*(count 25 : ℚ))/(m*width))*accepted_25 + + ((481*(count 481 : ℚ))/(m*width))*accepted_481 + + ((525*(count 525 : ℚ))/(m*width))*accepted_525 + + ((529*(count 529 : ℚ))/(m*width))*accepted_529 +theorem accepted_profile_link : acceptedFromCounts = acceptedMoment := by + norm_num [acceptedFromCounts, acceptedMoment, m, width, n, roles23, roles25, Nat.choose, count_1, count_10, count_11, count_12, count_13, count_14, count_15, count_16, count_17, count_18, count_19, count_2, count_20, count_21, count_22, count_23, count_25, count_3, count_4, count_481, count_5, count_525, count_529, count_6, count_7, count_8, count_9] + +theorem accepted_moment : acceptedMoment < 1 ∧ acceptedMoment = (45921799999999999986718939153021994591711554531 / 45921800000000000000000000000000000000000000000) := by + norm_num [acceptedMoment, accepted_1, accepted_10, accepted_11, accepted_12, accepted_13, accepted_14, accepted_15, accepted_16, accepted_17, accepted_18, accepted_19, accepted_2, accepted_20, accepted_21, accepted_22, accepted_23, accepted_25, accepted_3, accepted_4, accepted_481, accepted_5, accepted_525, accepted_529, accepted_6, accepted_7, accepted_8, accepted_9] + +theorem accepted_paid_moment : acceptedFromCounts < 1 := by + rw [accepted_profile_link] + exact accepted_moment.1 + +def rejected_1 : ℚ := (10003355187430811499866527395056080467997 / 10000000000000000000000000000000000000000) +theorem rejected_interval_1 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(3177185020398675220004135749131 / 500000000000000000000000000000) ∧ (a+1/1000000000000000000)*(3177185020398675220004135749131 / 500000000000000000000000000000) ≤ (a+1/1000000000000000000)*(6354370040797350440008271498263 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(6354370040797350440008271498263 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_1 : rejected_1 ≤ taylor8 ((a+1/1000000000000000000)*(3177185020398675220004135749131 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_1] + +def rejected_2 : ℚ := (10002989142293451329800744329233123034741 / 10000000000000000000000000000000000000000) +theorem rejected_interval_2 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(1415305715059351282647759844201 / 250000000000000000000000000000) ∧ (a+1/1000000000000000000)*(1415305715059351282647759844201 / 250000000000000000000000000000) ≤ (a+1/1000000000000000000)*(1132244572047481026118207875361 / 200000000000000000000000000000) ∧ (a+1/1000000000000000000)*(1132244572047481026118207875361 / 200000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_2 : rejected_2 ≤ taylor8 ((a+1/1000000000000000000)*(1415305715059351282647759844201 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_2] + +def rejected_3 : ℚ := (10002775025823826765445545232685930877759 / 10000000000000000000000000000000000000000) +theorem rejected_interval_3 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(262787887606462037430651313067 / 50000000000000000000000000000) ∧ (a+1/1000000000000000000)*(262787887606462037430651313067 / 50000000000000000000000000000) ≤ (a+1/1000000000000000000)*(5255757752129240748613026261341 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(5255757752129240748613026261341 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_3 : rejected_3 ≤ taylor8 ((a+1/1000000000000000000)*(262787887606462037430651313067 / 50000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_3] + +def rejected_4 : ℚ := (2500655777637625335642170166258868801979 / 2500000000000000000000000000000000000000) +theorem rejected_interval_4 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(2484037839838729910586903627673 / 500000000000000000000000000000) ∧ (a+1/1000000000000000000)*(2484037839838729910586903627673 / 500000000000000000000000000000) ≤ (a+1/1000000000000000000)*(4968075679677459821173807255347 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(4968075679677459821173807255347 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_4 : rejected_4 ≤ taylor8 ((a+1/1000000000000000000)*(2484037839838729910586903627673 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_4] + +def rejected_5 : ℚ := (10002505277498845829486558468305031292667 / 10000000000000000000000000000000000000000) +theorem rejected_interval_5 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(1186233032090812516351878041259 / 250000000000000000000000000000) ∧ (a+1/1000000000000000000)*(1186233032090812516351878041259 / 250000000000000000000000000000) ≤ (a+1/1000000000000000000)*(4744932128363250065407512165037 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(4744932128363250065407512165037 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_5 : rejected_5 ≤ taylor8 ((a+1/1000000000000000000)*(1186233032090812516351878041259 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_5] + +def rejected_6 : ℚ := (10002409001915877242185603506574209342913 / 10000000000000000000000000000000000000000) +theorem rejected_interval_6 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(4562610571569295439195794139881 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(4562610571569295439195794139881 / 1000000000000000000000000000000) ≤ (a+1/1000000000000000000)*(2281305285784647719597897069941 / 500000000000000000000000000000) ∧ (a+1/1000000000000000000)*(2281305285784647719597897069941 / 500000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_6 : rejected_6 ≤ taylor8 ((a+1/1000000000000000000)*(4562610571569295439195794139881 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_6] + +def rejected_7 : ℚ := (10002327602793273626663154845461687901127 / 10000000000000000000000000000000000000000) +theorem rejected_interval_7 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(4408459891742037134902918754819 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(4408459891742037134902918754819 / 1000000000000000000000000000000) ≤ (a+1/1000000000000000000)*(220422994587101856745145937741 / 50000000000000000000000000000) ∧ (a+1/1000000000000000000)*(220422994587101856745145937741 / 50000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_7 : rejected_7 ≤ taylor8 ((a+1/1000000000000000000)*(4408459891742037134902918754819 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_7] + +def rejected_8 : ℚ := (1000225709220147140674709209102332522021 / 1000000000000000000000000000000000000000) +theorem rejected_interval_8 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(66795757798711164246196486467 / 15625000000000000000000000000) ∧ (a+1/1000000000000000000)*(66795757798711164246196486467 / 15625000000000000000000000000) ≤ (a+1/1000000000000000000)*(4274928499117514511756575133889 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(4274928499117514511756575133889 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_8 : rejected_8 ≤ taylor8 ((a+1/1000000000000000000)*(66795757798711164246196486467 / 15625000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_8] + +def rejected_9 : ℚ := (10002194897864301699559646820529980541793 / 10000000000000000000000000000000000000000) +theorem rejected_interval_9 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(4157145463461131057217781024417 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(4157145463461131057217781024417 / 1000000000000000000000000000000) ≤ (a+1/1000000000000000000)*(2078572731730565528608890512209 / 500000000000000000000000000000) ∧ (a+1/1000000000000000000)*(2078572731730565528608890512209 / 500000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_9 : rejected_9 ≤ taylor8 ((a+1/1000000000000000000)*(4157145463461131057217781024417 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_9] + +def rejected_10 : ℚ := (10002139263461590770258956291071719040393 / 10000000000000000000000000000000000000000) +theorem rejected_interval_10 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(2025892473901652377995140021789 / 500000000000000000000000000000) ∧ (a+1/1000000000000000000)*(2025892473901652377995140021789 / 500000000000000000000000000000) ≤ (a+1/1000000000000000000)*(4051784947803304755990280043579 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(4051784947803304755990280043579 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_10 : rejected_10 ≤ taylor8 ((a+1/1000000000000000000)*(2025892473901652377995140021789 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_10] + +def rejected_11 : ℚ := (2000417787257832620506088658805533126881 / 2000000000000000000000000000000000000000) +theorem rejected_interval_11 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(3956474767998979895946327920297 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(3956474767998979895946327920297 / 1000000000000000000000000000000) ≤ (a+1/1000000000000000000)*(1978237383999489947973163960149 / 500000000000000000000000000000) ∧ (a+1/1000000000000000000)*(1978237383999489947973163960149 / 500000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_11 : rejected_11 ≤ taylor8 ((a+1/1000000000000000000)*(3956474767998979895946327920297 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_11] + +def rejected_12 : ℚ := (10002042991401561070147318696892863889617 / 10000000000000000000000000000000000000000) +theorem rejected_interval_12 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(3869463391009350129778562018423 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(3869463391009350129778562018423 / 1000000000000000000000000000000) ≤ (a+1/1000000000000000000)*(483682923876168766222320252303 / 125000000000000000000000000000) ∧ (a+1/1000000000000000000)*(483682923876168766222320252303 / 125000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_12 : rejected_12 ≤ taylor8 ((a+1/1000000000000000000)*(3869463391009350129778562018423 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_12] + +def rejected_13 : ℚ := (312562522699638464485940985718250456479 / 312500000000000000000000000000000000000) +theorem rejected_interval_13 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(3789420683335813703954784056697 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(3789420683335813703954784056697 / 1000000000000000000000000000000) ≤ (a+1/1000000000000000000)*(1894710341667906851977392028349 / 500000000000000000000000000000) ∧ (a+1/1000000000000000000)*(1894710341667906851977392028349 / 500000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_13 : rejected_13 ≤ taylor8 ((a+1/1000000000000000000)*(3789420683335813703954784056697 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_13] + +def rejected_14 : ℚ := (10001961595257533388015303909569022972699 / 10000000000000000000000000000000000000000) +theorem rejected_interval_14 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(3715312711182091825485686633361 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(3715312711182091825485686633361 / 1000000000000000000000000000000) ≤ (a+1/1000000000000000000)*(1857656355591045912742843316681 / 500000000000000000000000000000) ∧ (a+1/1000000000000000000)*(1857656355591045912742843316681 / 500000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_14 : rejected_14 ≤ taylor8 ((a+1/1000000000000000000)*(3715312711182091825485686633361 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_14] + +def rejected_15 : ℚ := (10001925165183833906452872346406102984941 / 10000000000000000000000000000000000000000) +theorem rejected_interval_15 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(3646319839695140374012266928113 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(3646319839695140374012266928113 / 1000000000000000000000000000000) ≤ (a+1/1000000000000000000)*(1823159919847570187006133464057 / 500000000000000000000000000000) ∧ (a+1/1000000000000000000)*(1823159919847570187006133464057 / 500000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_15 : rejected_15 ≤ taylor8 ((a+1/1000000000000000000)*(3646319839695140374012266928113 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_15] + +def rejected_16 : ℚ := (1000189108724587140884773918006088804391 / 1000000000000000000000000000000000000000) +theorem rejected_interval_16 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(3581781318557569202339343012429 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(3581781318557569202339343012429 / 1000000000000000000000000000000) ≤ (a+1/1000000000000000000)*(358178131855756920233934301243 / 100000000000000000000000000000) ∧ (a+1/1000000000000000000)*(358178131855756920233934301243 / 100000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_16 : rejected_16 ≤ taylor8 ((a+1/1000000000000000000)*(3581781318557569202339343012429 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_16] + +def rejected_17 : ℚ := (10001859076049468615168740441760338415449 / 10000000000000000000000000000000000000000) +theorem rejected_interval_17 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(3521156696741134359758736880389 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(3521156696741134359758736880389 / 1000000000000000000000000000000) ≤ (a+1/1000000000000000000)*(352115669674113435975873688039 / 100000000000000000000000000000) ∧ (a+1/1000000000000000000)*(352115669674113435975873688039 / 100000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_17 : rejected_17 ≤ taylor8 ((a+1/1000000000000000000)*(3521156696741134359758736880389 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_17] + +def rejected_18 : ℚ := (10001828895184531587308614486546283814127 / 10000000000000000000000000000000000000000) +theorem rejected_interval_18 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(3463998282901185747800548902959 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(3463998282901185747800548902959 / 1000000000000000000000000000000) ≤ (a+1/1000000000000000000)*(43299978536264821847506861287 / 12500000000000000000000000000) ∧ (a+1/1000000000000000000)*(43299978536264821847506861287 / 12500000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_18 : rejected_18 ≤ taylor8 ((a+1/1000000000000000000)*(3463998282901185747800548902959 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_18] + +def rejected_19 : ℚ := (10001800346619198574836713525767813923699 / 10000000000000000000000000000000000000000) +theorem rejected_interval_19 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(1704965530815454989999622033187 / 500000000000000000000000000000) ∧ (a+1/1000000000000000000)*(1704965530815454989999622033187 / 500000000000000000000000000000) ≤ (a+1/1000000000000000000)*(27279448493047279839993952531 / 8000000000000000000000000000) ∧ (a+1/1000000000000000000)*(27279448493047279839993952531 / 8000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_19 : rejected_19 ≤ taylor8 ((a+1/1000000000000000000)*(1704965530815454989999622033187 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_19] + +def rejected_20 : ℚ := (2500443315704401967867049116237037674879 / 2500000000000000000000000000000000000000) +theorem rejected_interval_20 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(83965944181083986164326198053 / 25000000000000000000000000000) ∧ (a+1/1000000000000000000)*(83965944181083986164326198053 / 25000000000000000000000000000) ≤ (a+1/1000000000000000000)*(3358637767243359446573047922121 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(3358637767243359446573047922121 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_20 : rejected_20 ≤ taylor8 ((a+1/1000000000000000000)*(83965944181083986164326198053 / 25000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_20] + +def rejected_21 : ℚ := (10001747500782808605535794084970152975453 / 10000000000000000000000000000000000000000) +theorem rejected_interval_21 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(413730950384240930438459189737 / 125000000000000000000000000000) ∧ (a+1/1000000000000000000)*(413730950384240930438459189737 / 125000000000000000000000000000) ≤ (a+1/1000000000000000000)*(3309847603073927443507673517897 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(3309847603073927443507673517897 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_21 : rejected_21 ≤ taylor8 ((a+1/1000000000000000000)*(413730950384240930438459189737 / 125000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_21] + +def rejected_22 : ℚ := (2500430734371690998071282951144176062319 / 2500000000000000000000000000000000000000) +theorem rejected_interval_22 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(3263327587439034586529095798839 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(3263327587439034586529095798839 / 1000000000000000000000000000000) ≤ (a+1/1000000000000000000)*(81583189685975864663227394971 / 25000000000000000000000000000) ∧ (a+1/1000000000000000000)*(81583189685975864663227394971 / 25000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_22 : rejected_22 ≤ taylor8 ((a+1/1000000000000000000)*(3263327587439034586529095798839 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_22] + +def rejected_23 : ℚ := (5000849733158527953973224302132873373081 / 5000000000000000000000000000000000000000) +theorem rejected_interval_23 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(804718956217050187300379666613 / 250000000000000000000000000000) ∧ (a+1/1000000000000000000)*(804718956217050187300379666613 / 250000000000000000000000000000) ≤ (a+1/1000000000000000000)*(3218875824868200749201518666453 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(3218875824868200749201518666453 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_23 : rejected_23 ≤ taylor8 ((a+1/1000000000000000000)*(804718956217050187300379666613 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_23] + +def rejected_25 : ℚ := (10001655439777341441288927072278426167767 / 10000000000000000000000000000000000000000) +theorem rejected_interval_25 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(313549421592914969080675283181 / 100000000000000000000000000000) ∧ (a+1/1000000000000000000)*(313549421592914969080675283181 / 100000000000000000000000000000) ≤ (a+1/1000000000000000000)*(3135494215929149690806752831811 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(3135494215929149690806752831811 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_25 : rejected_25 ≤ taylor8 ((a+1/1000000000000000000)*(313549421592914969080675283181 / 100000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_25] + +def rejected_481 : ℚ := (5000047118173783025819451821666081022959 / 5000000000000000000000000000000000000000) +theorem rejected_interval_481 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(35700554138317851917337677133 / 200000000000000000000000000000) ∧ (a+1/1000000000000000000)*(35700554138317851917337677133 / 200000000000000000000000000000) ≤ (a+1/1000000000000000000)*(89251385345794629793344192833 / 500000000000000000000000000000) ∧ (a+1/1000000000000000000)*(89251385345794629793344192833 / 500000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_481 : rejected_481 ≤ taylor8 ((a+1/1000000000000000000)*(35700554138317851917337677133 / 200000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_481] + +def rejected_525 : ℚ := (2000009605260768825202172580370489299563 / 2000000000000000000000000000000000000000) +theorem rejected_interval_525 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(22742944551431673576538712861 / 250000000000000000000000000000) ∧ (a+1/1000000000000000000)*(22742944551431673576538712861 / 250000000000000000000000000000) ≤ (a+1/1000000000000000000)*(18194355641145338861230970289 / 200000000000000000000000000000) ∧ (a+1/1000000000000000000)*(18194355641145338861230970289 / 200000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_525 : rejected_525 ≤ taylor8 ((a+1/1000000000000000000)*(22742944551431673576538712861 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_525] + +def rejected_529 : ℚ := (500002200962629614782243253618234113253 / 500000000000000000000000000000000000000) +theorem rejected_interval_529 : (0 : ℚ) ≤ (a+1/1000000000000000000)*(41690804469525529197382917321 / 500000000000000000000000000000) ∧ (a+1/1000000000000000000)*(41690804469525529197382917321 / 500000000000000000000000000000) ≤ (a+1/1000000000000000000)*(83381608939051058394765834643 / 1000000000000000000000000000000) ∧ (a+1/1000000000000000000)*(83381608939051058394765834643 / 1000000000000000000000000000000) < 1 := by + norm_num [a] + +theorem rejected_taylor_529 : rejected_529 ≤ taylor8 ((a+1/1000000000000000000)*(41690804469525529197382917321 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, a, rejected_529] + +def rejectedMoment : ℚ := + ((1*1841940993 : ℚ)/(575*130417912))*rejected_1 + + ((2*59604960 : ℚ)/(575*130417912))*rejected_2 + + ((3*70923030 : ℚ)/(575*130417912))*rejected_3 + + ((4*24797266 : ℚ)/(575*130417912))*rejected_4 + + ((5*16953300 : ℚ)/(575*130417912))*rejected_5 + + ((6*15207761 : ℚ)/(575*130417912))*rejected_6 + + ((7*11179127 : ℚ)/(575*130417912))*rejected_7 + + ((8*9976756 : ℚ)/(575*130417912))*rejected_8 + + ((9*7166639 : ℚ)/(575*130417912))*rejected_9 + + ((10*6692747 : ℚ)/(575*130417912))*rejected_10 + + ((11*4706950 : ℚ)/(575*130417912))*rejected_11 + + ((12*4534703 : ℚ)/(575*130417912))*rejected_12 + + ((13*2759310 : ℚ)/(575*130417912))*rejected_13 + + ((14*2513739 : ℚ)/(575*130417912))*rejected_14 + + ((15*1504499 : ℚ)/(575*130417912))*rejected_15 + + ((16*1645351 : ℚ)/(575*130417912))*rejected_16 + + ((17*8768773 : ℚ)/(575*130417912))*rejected_17 + + ((18*1107910 : ℚ)/(575*130417912))*rejected_18 + + ((19*104489 : ℚ)/(575*130417912))*rejected_19 + + ((20*1078677 : ℚ)/(575*130417912))*rejected_20 + + ((21*16524971 : ℚ)/(575*130417912))*rejected_21 + + ((22*299299 : ℚ)/(575*130417912))*rejected_22 + + ((23*68880975 : ℚ)/(575*130417912))*rejected_23 + + ((25*61581212 : ℚ)/(575*130417912))*rejected_25 + + ((481*8146600 : ℚ)/(575*130417912))*rejected_481 + + ((525*61581212 : ℚ)/(575*130417912))*rejected_525 + + ((529*60690100 : ℚ)/(575*130417912))*rejected_529 +def rejectedFromCounts : ℚ := + ((1*(count 1 : ℚ))/(m*width))*rejected_1 + + ((2*(count 2 : ℚ))/(m*width))*rejected_2 + + ((3*(count 3 : ℚ))/(m*width))*rejected_3 + + ((4*(count 4 : ℚ))/(m*width))*rejected_4 + + ((5*(count 5 : ℚ))/(m*width))*rejected_5 + + ((6*(count 6 : ℚ))/(m*width))*rejected_6 + + ((7*(count 7 : ℚ))/(m*width))*rejected_7 + + ((8*(count 8 : ℚ))/(m*width))*rejected_8 + + ((9*(count 9 : ℚ))/(m*width))*rejected_9 + + ((10*(count 10 : ℚ))/(m*width))*rejected_10 + + ((11*(count 11 : ℚ))/(m*width))*rejected_11 + + ((12*(count 12 : ℚ))/(m*width))*rejected_12 + + ((13*(count 13 : ℚ))/(m*width))*rejected_13 + + ((14*(count 14 : ℚ))/(m*width))*rejected_14 + + ((15*(count 15 : ℚ))/(m*width))*rejected_15 + + ((16*(count 16 : ℚ))/(m*width))*rejected_16 + + ((17*(count 17 : ℚ))/(m*width))*rejected_17 + + ((18*(count 18 : ℚ))/(m*width))*rejected_18 + + ((19*(count 19 : ℚ))/(m*width))*rejected_19 + + ((20*(count 20 : ℚ))/(m*width))*rejected_20 + + ((21*(count 21 : ℚ))/(m*width))*rejected_21 + + ((22*(count 22 : ℚ))/(m*width))*rejected_22 + + ((23*(count 23 : ℚ))/(m*width))*rejected_23 + + ((25*(count 25 : ℚ))/(m*width))*rejected_25 + + ((481*(count 481 : ℚ))/(m*width))*rejected_481 + + ((525*(count 525 : ℚ))/(m*width))*rejected_525 + + ((529*(count 529 : ℚ))/(m*width))*rejected_529 +theorem rejected_profile_link : rejectedFromCounts = rejectedMoment := by + norm_num [rejectedFromCounts, rejectedMoment, m, width, n, roles23, roles25, Nat.choose, count_1, count_10, count_11, count_12, count_13, count_14, count_15, count_16, count_17, count_18, count_19, count_2, count_20, count_21, count_22, count_23, count_25, count_3, count_4, count_481, count_5, count_525, count_529, count_6, count_7, count_8, count_9] + +theorem rejected_moment : 1 < rejectedMoment ∧ rejectedMoment = (32604478000000000005782543032459327907899102761243 / 32604478000000000000000000000000000000000000000000) := by + norm_num [rejectedMoment, rejected_1, rejected_10, rejected_11, rejected_12, rejected_13, rejected_14, rejected_15, rejected_16, rejected_17, rejected_18, rejected_19, rejected_2, rejected_20, rejected_21, rejected_22, rejected_23, rejected_25, rejected_3, rejected_4, rejected_481, rejected_5, rejected_525, rejected_529, rejected_6, rejected_7, rejected_8, rejected_9] + +theorem rejected_paid_moment : 1 < rejectedFromCounts := by + rw [rejected_profile_link] + exact rejected_moment.1 + +end KappaCheck.AlignedFrameComposition +#print axioms KappaCheck.AlignedFrameComposition.network_counts +#print axioms KappaCheck.AlignedFrameComposition.rank_mass +#print axioms KappaCheck.AlignedFrameComposition.count_1 +#print axioms KappaCheck.AlignedFrameComposition.count_2 +#print axioms KappaCheck.AlignedFrameComposition.count_3 +#print axioms KappaCheck.AlignedFrameComposition.count_4 +#print axioms KappaCheck.AlignedFrameComposition.count_5 +#print axioms KappaCheck.AlignedFrameComposition.count_6 +#print axioms KappaCheck.AlignedFrameComposition.count_7 +#print axioms KappaCheck.AlignedFrameComposition.count_8 +#print axioms KappaCheck.AlignedFrameComposition.count_9 +#print axioms KappaCheck.AlignedFrameComposition.count_10 +#print axioms KappaCheck.AlignedFrameComposition.count_11 +#print axioms KappaCheck.AlignedFrameComposition.count_12 +#print axioms KappaCheck.AlignedFrameComposition.count_13 +#print axioms KappaCheck.AlignedFrameComposition.count_14 +#print axioms KappaCheck.AlignedFrameComposition.count_15 +#print axioms KappaCheck.AlignedFrameComposition.count_16 +#print axioms KappaCheck.AlignedFrameComposition.count_17 +#print axioms KappaCheck.AlignedFrameComposition.count_18 +#print axioms KappaCheck.AlignedFrameComposition.count_19 +#print axioms KappaCheck.AlignedFrameComposition.count_20 +#print axioms KappaCheck.AlignedFrameComposition.count_21 +#print axioms KappaCheck.AlignedFrameComposition.count_22 +#print axioms KappaCheck.AlignedFrameComposition.count_23 +#print axioms KappaCheck.AlignedFrameComposition.count_25 +#print axioms KappaCheck.AlignedFrameComposition.count_481 +#print axioms KappaCheck.AlignedFrameComposition.count_525 +#print axioms KappaCheck.AlignedFrameComposition.count_529 +#print axioms KappaCheck.AlignedFrameComposition.complete_child_support +#print axioms KappaCheck.AlignedFrameComposition.strict_child_contraction +#print axioms KappaCheck.AlignedFrameComposition.slack_a_positive +#print axioms KappaCheck.AlignedFrameComposition.slack_a_below_b +#print axioms KappaCheck.AlignedFrameComposition.slack_b_below_one_over32 +#print axioms KappaCheck.AlignedFrameComposition.slack_beta_positive +#print axioms KappaCheck.AlignedFrameComposition.slack_beta_below_one +#print axioms KappaCheck.AlignedFrameComposition.slack_phase_leaf_above_bit +#print axioms KappaCheck.AlignedFrameComposition.slack_q_positive +#print axioms KappaCheck.AlignedFrameComposition.slack_q_below_internal +#print axioms KappaCheck.AlignedFrameComposition.slack_q_below_leaf +#print axioms KappaCheck.AlignedFrameComposition.slack_c_positive +#print axioms KappaCheck.AlignedFrameComposition.slack_c_below_one +#print axioms KappaCheck.AlignedFrameComposition.slack_q_below_reservations +#print axioms KappaCheck.AlignedFrameComposition.slack_lambda_above_tau +#print axioms KappaCheck.AlignedFrameComposition.slack_lambda_above_sigma +#print axioms KappaCheck.AlignedFrameComposition.slack_lambda_above_internal +#print axioms KappaCheck.AlignedFrameComposition.slack_lambda_prime_above_lambda +#print axioms KappaCheck.AlignedFrameComposition.slack_compact_leaf +#print axioms KappaCheck.AlignedFrameComposition.slack_compact_reservations +#print axioms KappaCheck.AlignedFrameComposition.slack_lambda_prime_below_one +#print axioms KappaCheck.AlignedFrameComposition.slack_epsilon_positive +#print axioms KappaCheck.AlignedFrameComposition.slack_epsilon_below_one +#print axioms KappaCheck.AlignedFrameComposition.slack_guard_width +#print axioms KappaCheck.AlignedFrameComposition.slack_K_geometry +#print axioms KappaCheck.AlignedFrameComposition.slack_K_dominates_log +#print axioms KappaCheck.AlignedFrameComposition.slack_record_suffix +#print axioms KappaCheck.AlignedFrameComposition.slack_phase_local +#print axioms KappaCheck.AlignedFrameComposition.slack_phase_boundary +#print axioms KappaCheck.AlignedFrameComposition.slack_gamma_sublinear +#print axioms KappaCheck.AlignedFrameComposition.slack_cell_above_band +#print axioms KappaCheck.AlignedFrameComposition.slack_prime_interval_packing +#print axioms KappaCheck.AlignedFrameComposition.slack_alpha_positive +#print axioms KappaCheck.AlignedFrameComposition.slack_alpha_below_one +#print axioms KappaCheck.AlignedFrameComposition.slack_alpha_below_one_fourth +#print axioms KappaCheck.AlignedFrameComposition.slack_delta_positive +#print axioms KappaCheck.AlignedFrameComposition.slack_delta_below_one_eighth +#print axioms KappaCheck.AlignedFrameComposition.slack_short_record_fallback +#print axioms KappaCheck.AlignedFrameComposition.slack_small_field_exposure +#print axioms KappaCheck.AlignedFrameComposition.slack_artificial_boundary +#print axioms KappaCheck.AlignedFrameComposition.slack_literal_scalar_guard +#print axioms KappaCheck.AlignedFrameComposition.slack_row_product_gap +#print axioms KappaCheck.AlignedFrameComposition.slack_g1_above_kappa +#print axioms KappaCheck.AlignedFrameComposition.slack_g2_above_kappa +#print axioms KappaCheck.AlignedFrameComposition.slack_g3_above_kappa +#print axioms KappaCheck.AlignedFrameComposition.slack_g4_above_kappa +#print axioms KappaCheck.AlignedFrameComposition.slack_g5_above_kappa +#print axioms KappaCheck.AlignedFrameComposition.slack_g6_above_kappa +#print axioms KappaCheck.AlignedFrameComposition.slack_g7_above_kappa +#print axioms KappaCheck.AlignedFrameComposition.margins_strict +#print axioms KappaCheck.AlignedFrameComposition.balanced_identities +#print axioms KappaCheck.AlignedFrameComposition.controlling_margin +#print axioms KappaCheck.AlignedFrameComposition.gain_over_original +#print axioms KappaCheck.AlignedFrameComposition.finite_bridge +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_1 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_1 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_2 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_2 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_3 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_3 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_4 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_4 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_5 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_5 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_6 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_6 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_7 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_7 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_8 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_8 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_9 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_9 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_10 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_10 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_11 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_11 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_12 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_12 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_13 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_13 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_14 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_14 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_15 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_15 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_16 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_16 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_17 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_17 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_18 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_18 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_19 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_19 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_20 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_20 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_21 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_21 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_22 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_22 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_23 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_23 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_25 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_25 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_481 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_481 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_525 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_525 +#print axioms KappaCheck.AlignedFrameComposition.accepted_interval_529 +#print axioms KappaCheck.AlignedFrameComposition.accepted_taylor_529 +#print axioms KappaCheck.AlignedFrameComposition.accepted_profile_link +#print axioms KappaCheck.AlignedFrameComposition.accepted_moment +#print axioms KappaCheck.AlignedFrameComposition.accepted_paid_moment +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_1 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_1 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_2 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_2 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_3 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_3 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_4 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_4 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_5 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_5 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_6 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_6 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_7 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_7 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_8 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_8 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_9 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_9 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_10 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_10 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_11 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_11 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_12 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_12 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_13 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_13 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_14 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_14 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_15 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_15 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_16 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_16 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_17 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_17 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_18 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_18 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_19 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_19 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_20 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_20 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_21 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_21 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_22 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_22 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_23 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_23 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_25 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_25 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_481 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_481 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_525 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_525 +#print axioms KappaCheck.AlignedFrameComposition.rejected_interval_529 +#print axioms KappaCheck.AlignedFrameComposition.rejected_taylor_529 +#print axioms KappaCheck.AlignedFrameComposition.rejected_profile_link +#print axioms KappaCheck.AlignedFrameComposition.rejected_moment +#print axioms KappaCheck.AlignedFrameComposition.rejected_paid_moment diff --git a/formal/lean/SOURCES.md b/formal/lean/SOURCES.md index f2203fb62d..223af9d0a2 100644 --- a/formal/lean/SOURCES.md +++ b/formal/lean/SOURCES.md @@ -79,3 +79,298 @@ Line numbers refer to this branch, based on `6e56487`. | [`scoped_ceiling_exact`](KappaCheck/CrocSwap.lean#L559) | κ < U for every admissible choice with this motif | [compact-control-note.tex:143–146](../../notes/compact-control-note.tex#L143-L146)
[compact-control-note.tex:146](../../notes/compact-control-note.tex#L146) | — | — | | | [`ceiling_facts`](KappaCheck/CrocSwap.lean#L585) | U < 8.369598075·10⁻¹¹ < 2⁻³³; κ > 0.99 U | [compact-control-note.tex:146](../../notes/compact-control-note.tex#L146)
[compact-control-note.tex:148](../../notes/compact-control-note.tex#L148) | — | — | | | [`witness_meets_ceiling`](KappaCheck/CrocSwap.lean#L590) | their witness satisfies every hypothesis | — | — | — | Non-vacuity check for `scoped_ceiling_exact`; no source line. | +| [`m`](KappaCheck/AlignedFrameComposition.lean#L21) | m | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`n`](KappaCheck/AlignedFrameComposition.lean#L22) | n | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`roles23`](KappaCheck/AlignedFrameComposition.lean#L23) | roles23 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`blocks23`](KappaCheck/AlignedFrameComposition.lean#L24) | blocks23 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`roles25`](KappaCheck/AlignedFrameComposition.lean#L25) | roles25 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`blocks25`](KappaCheck/AlignedFrameComposition.lean#L26) | blocks25 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`width`](KappaCheck/AlignedFrameComposition.lean#L27) | width | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`counts`](KappaCheck/AlignedFrameComposition.lean#L28) | counts | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count`](KappaCheck/AlignedFrameComposition.lean#L34) | count | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`mass`](KappaCheck/AlignedFrameComposition.lean#L36) | mass | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`network_counts`](KappaCheck/AlignedFrameComposition.lean#L38) | network counts | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rank_mass`](KappaCheck/AlignedFrameComposition.lean#L41) | rank mass | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_1`](KappaCheck/AlignedFrameComposition.lean#L44) | count 1 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_2`](KappaCheck/AlignedFrameComposition.lean#L47) | count 2 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_3`](KappaCheck/AlignedFrameComposition.lean#L50) | count 3 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_4`](KappaCheck/AlignedFrameComposition.lean#L53) | count 4 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_5`](KappaCheck/AlignedFrameComposition.lean#L56) | count 5 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_6`](KappaCheck/AlignedFrameComposition.lean#L59) | count 6 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_7`](KappaCheck/AlignedFrameComposition.lean#L62) | count 7 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_8`](KappaCheck/AlignedFrameComposition.lean#L65) | count 8 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_9`](KappaCheck/AlignedFrameComposition.lean#L68) | count 9 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_10`](KappaCheck/AlignedFrameComposition.lean#L71) | count 10 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_11`](KappaCheck/AlignedFrameComposition.lean#L74) | count 11 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_12`](KappaCheck/AlignedFrameComposition.lean#L77) | count 12 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_13`](KappaCheck/AlignedFrameComposition.lean#L80) | count 13 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_14`](KappaCheck/AlignedFrameComposition.lean#L83) | count 14 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_15`](KappaCheck/AlignedFrameComposition.lean#L86) | count 15 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_16`](KappaCheck/AlignedFrameComposition.lean#L89) | count 16 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_17`](KappaCheck/AlignedFrameComposition.lean#L92) | count 17 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_18`](KappaCheck/AlignedFrameComposition.lean#L95) | count 18 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_19`](KappaCheck/AlignedFrameComposition.lean#L98) | count 19 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_20`](KappaCheck/AlignedFrameComposition.lean#L101) | count 20 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_21`](KappaCheck/AlignedFrameComposition.lean#L104) | count 21 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_22`](KappaCheck/AlignedFrameComposition.lean#L107) | count 22 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_23`](KappaCheck/AlignedFrameComposition.lean#L110) | count 23 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_25`](KappaCheck/AlignedFrameComposition.lean#L113) | count 25 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_481`](KappaCheck/AlignedFrameComposition.lean#L116) | count 481 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_525`](KappaCheck/AlignedFrameComposition.lean#L119) | count 525 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`count_529`](KappaCheck/AlignedFrameComposition.lean#L122) | count 529 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`childSizes`](KappaCheck/AlignedFrameComposition.lean#L125) | childSizes | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`complete_child_support`](KappaCheck/AlignedFrameComposition.lean#L126) | complete child support | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`strict_child_contraction`](KappaCheck/AlignedFrameComposition.lean#L129) | strict child contraction | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`a`](KappaCheck/AlignedFrameComposition.lean#L132) | a | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`b`](KappaCheck/AlignedFrameComposition.lean#L133) | b | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`kappa`](KappaCheck/AlignedFrameComposition.lean#L134) | kappa | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`eta`](KappaCheck/AlignedFrameComposition.lean#L135) | eta | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`beta`](KappaCheck/AlignedFrameComposition.lean#L136) | beta | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`tau`](KappaCheck/AlignedFrameComposition.lean#L137) | tau | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`sigma`](KappaCheck/AlignedFrameComposition.lean#L138) | sigma | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`qParam`](KappaCheck/AlignedFrameComposition.lean#L139) | qParam | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`lp`](KappaCheck/AlignedFrameComposition.lean#L140) | lp | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`c`](KappaCheck/AlignedFrameComposition.lean#L141) | c | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`epsilon`](KappaCheck/AlignedFrameComposition.lean#L142) | epsilon | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`lam`](KappaCheck/AlignedFrameComposition.lean#L143) | lam | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`g`](KappaCheck/AlignedFrameComposition.lean#L144) | g | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`r`](KappaCheck/AlignedFrameComposition.lean#L145) | r | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`delta`](KappaCheck/AlignedFrameComposition.lean#L146) | delta | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`internal`](KappaCheck/AlignedFrameComposition.lean#L147) | internal | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`leaf`](KappaCheck/AlignedFrameComposition.lean#L148) | leaf | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`complexWidth`](KappaCheck/AlignedFrameComposition.lean#L149) | complexWidth | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`complexRank`](KappaCheck/AlignedFrameComposition.lean#L150) | complexRank | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`scalar`](KappaCheck/AlignedFrameComposition.lean#L151) | scalar | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`guardE`](KappaCheck/AlignedFrameComposition.lean#L152) | guardE | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`guardB`](KappaCheck/AlignedFrameComposition.lean#L153) | guardB | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`literal`](KappaCheck/AlignedFrameComposition.lean#L154) | literal | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`guardC`](KappaCheck/AlignedFrameComposition.lean#L155) | guardC | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`literalGap`](KappaCheck/AlignedFrameComposition.lean#L156) | literalGap | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rowGap`](KappaCheck/AlignedFrameComposition.lean#L157) | rowGap | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`margins`](KappaCheck/AlignedFrameComposition.lean#L158) | margins | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_a_positive`](KappaCheck/AlignedFrameComposition.lean#L160) | slack a positive | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_a_below_b`](KappaCheck/AlignedFrameComposition.lean#L163) | slack a below b | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_b_below_one_over32`](KappaCheck/AlignedFrameComposition.lean#L166) | slack b below one over32 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_beta_positive`](KappaCheck/AlignedFrameComposition.lean#L169) | slack beta positive | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_beta_below_one`](KappaCheck/AlignedFrameComposition.lean#L172) | slack beta below one | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_phase_leaf_above_bit`](KappaCheck/AlignedFrameComposition.lean#L175) | slack phase leaf above bit | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_q_positive`](KappaCheck/AlignedFrameComposition.lean#L178) | slack q positive | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_q_below_internal`](KappaCheck/AlignedFrameComposition.lean#L181) | slack q below internal | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_q_below_leaf`](KappaCheck/AlignedFrameComposition.lean#L184) | slack q below leaf | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_c_positive`](KappaCheck/AlignedFrameComposition.lean#L187) | slack c positive | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_c_below_one`](KappaCheck/AlignedFrameComposition.lean#L190) | slack c below one | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_q_below_reservations`](KappaCheck/AlignedFrameComposition.lean#L193) | slack q below reservations | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_lambda_above_tau`](KappaCheck/AlignedFrameComposition.lean#L196) | slack lambda above tau | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_lambda_above_sigma`](KappaCheck/AlignedFrameComposition.lean#L199) | slack lambda above sigma | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_lambda_above_internal`](KappaCheck/AlignedFrameComposition.lean#L202) | slack lambda above internal | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_lambda_prime_above_lambda`](KappaCheck/AlignedFrameComposition.lean#L205) | slack lambda prime above lambda | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_compact_leaf`](KappaCheck/AlignedFrameComposition.lean#L208) | slack compact leaf | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_compact_reservations`](KappaCheck/AlignedFrameComposition.lean#L211) | slack compact reservations | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_lambda_prime_below_one`](KappaCheck/AlignedFrameComposition.lean#L214) | slack lambda prime below one | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_epsilon_positive`](KappaCheck/AlignedFrameComposition.lean#L217) | slack epsilon positive | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_epsilon_below_one`](KappaCheck/AlignedFrameComposition.lean#L220) | slack epsilon below one | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_guard_width`](KappaCheck/AlignedFrameComposition.lean#L223) | slack guard width | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_K_geometry`](KappaCheck/AlignedFrameComposition.lean#L226) | slack K geometry | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_K_dominates_log`](KappaCheck/AlignedFrameComposition.lean#L229) | slack K dominates log | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_record_suffix`](KappaCheck/AlignedFrameComposition.lean#L232) | slack record suffix | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_phase_local`](KappaCheck/AlignedFrameComposition.lean#L235) | slack phase local | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_phase_boundary`](KappaCheck/AlignedFrameComposition.lean#L238) | slack phase boundary | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_gamma_sublinear`](KappaCheck/AlignedFrameComposition.lean#L241) | slack gamma sublinear | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_cell_above_band`](KappaCheck/AlignedFrameComposition.lean#L244) | slack cell above band | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_prime_interval_packing`](KappaCheck/AlignedFrameComposition.lean#L247) | slack prime interval packing | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_alpha_positive`](KappaCheck/AlignedFrameComposition.lean#L250) | slack alpha positive | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_alpha_below_one`](KappaCheck/AlignedFrameComposition.lean#L253) | slack alpha below one | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_alpha_below_one_fourth`](KappaCheck/AlignedFrameComposition.lean#L256) | slack alpha below one fourth | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_delta_positive`](KappaCheck/AlignedFrameComposition.lean#L259) | slack delta positive | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_delta_below_one_eighth`](KappaCheck/AlignedFrameComposition.lean#L262) | slack delta below one eighth | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_short_record_fallback`](KappaCheck/AlignedFrameComposition.lean#L265) | slack short record fallback | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_small_field_exposure`](KappaCheck/AlignedFrameComposition.lean#L268) | slack small field exposure | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_artificial_boundary`](KappaCheck/AlignedFrameComposition.lean#L271) | slack artificial boundary | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_literal_scalar_guard`](KappaCheck/AlignedFrameComposition.lean#L274) | slack literal scalar guard | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_row_product_gap`](KappaCheck/AlignedFrameComposition.lean#L277) | slack row product gap | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_g1_above_kappa`](KappaCheck/AlignedFrameComposition.lean#L280) | slack g1 above kappa | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_g2_above_kappa`](KappaCheck/AlignedFrameComposition.lean#L283) | slack g2 above kappa | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_g3_above_kappa`](KappaCheck/AlignedFrameComposition.lean#L286) | slack g3 above kappa | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_g4_above_kappa`](KappaCheck/AlignedFrameComposition.lean#L289) | slack g4 above kappa | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_g5_above_kappa`](KappaCheck/AlignedFrameComposition.lean#L292) | slack g5 above kappa | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_g6_above_kappa`](KappaCheck/AlignedFrameComposition.lean#L295) | slack g6 above kappa | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`slack_g7_above_kappa`](KappaCheck/AlignedFrameComposition.lean#L298) | slack g7 above kappa | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`margins_strict`](KappaCheck/AlignedFrameComposition.lean#L301) | margins strict | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`balanced_identities`](KappaCheck/AlignedFrameComposition.lean#L304) | balanced identities | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`controlling_margin`](KappaCheck/AlignedFrameComposition.lean#L307) | controlling margin | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`gain_over_original`](KappaCheck/AlignedFrameComposition.lean#L310) | gain over original | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`finite_bridge`](KappaCheck/AlignedFrameComposition.lean#L313) | finite bridge | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`taylor8`](KappaCheck/AlignedFrameComposition.lean#L319) | taylor8 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`expUpper`](KappaCheck/AlignedFrameComposition.lean#L320) | expUpper | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_1`](KappaCheck/AlignedFrameComposition.lean#L322) | accepted 1 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_1`](KappaCheck/AlignedFrameComposition.lean#L323) | accepted interval 1 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_1`](KappaCheck/AlignedFrameComposition.lean#L326) | accepted taylor 1 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_2`](KappaCheck/AlignedFrameComposition.lean#L329) | accepted 2 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_2`](KappaCheck/AlignedFrameComposition.lean#L330) | accepted interval 2 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_2`](KappaCheck/AlignedFrameComposition.lean#L333) | accepted taylor 2 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_3`](KappaCheck/AlignedFrameComposition.lean#L336) | accepted 3 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_3`](KappaCheck/AlignedFrameComposition.lean#L337) | accepted interval 3 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_3`](KappaCheck/AlignedFrameComposition.lean#L340) | accepted taylor 3 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_4`](KappaCheck/AlignedFrameComposition.lean#L343) | accepted 4 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_4`](KappaCheck/AlignedFrameComposition.lean#L344) | accepted interval 4 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_4`](KappaCheck/AlignedFrameComposition.lean#L347) | accepted taylor 4 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_5`](KappaCheck/AlignedFrameComposition.lean#L350) | accepted 5 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_5`](KappaCheck/AlignedFrameComposition.lean#L351) | accepted interval 5 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_5`](KappaCheck/AlignedFrameComposition.lean#L354) | accepted taylor 5 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_6`](KappaCheck/AlignedFrameComposition.lean#L357) | accepted 6 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_6`](KappaCheck/AlignedFrameComposition.lean#L358) | accepted interval 6 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_6`](KappaCheck/AlignedFrameComposition.lean#L361) | accepted taylor 6 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_7`](KappaCheck/AlignedFrameComposition.lean#L364) | accepted 7 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_7`](KappaCheck/AlignedFrameComposition.lean#L365) | accepted interval 7 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_7`](KappaCheck/AlignedFrameComposition.lean#L368) | accepted taylor 7 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_8`](KappaCheck/AlignedFrameComposition.lean#L371) | accepted 8 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_8`](KappaCheck/AlignedFrameComposition.lean#L372) | accepted interval 8 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_8`](KappaCheck/AlignedFrameComposition.lean#L375) | accepted taylor 8 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_9`](KappaCheck/AlignedFrameComposition.lean#L378) | accepted 9 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_9`](KappaCheck/AlignedFrameComposition.lean#L379) | accepted interval 9 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_9`](KappaCheck/AlignedFrameComposition.lean#L382) | accepted taylor 9 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_10`](KappaCheck/AlignedFrameComposition.lean#L385) | accepted 10 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_10`](KappaCheck/AlignedFrameComposition.lean#L386) | accepted interval 10 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_10`](KappaCheck/AlignedFrameComposition.lean#L389) | accepted taylor 10 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_11`](KappaCheck/AlignedFrameComposition.lean#L392) | accepted 11 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_11`](KappaCheck/AlignedFrameComposition.lean#L393) | accepted interval 11 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_11`](KappaCheck/AlignedFrameComposition.lean#L396) | accepted taylor 11 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_12`](KappaCheck/AlignedFrameComposition.lean#L399) | accepted 12 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_12`](KappaCheck/AlignedFrameComposition.lean#L400) | accepted interval 12 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_12`](KappaCheck/AlignedFrameComposition.lean#L403) | accepted taylor 12 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_13`](KappaCheck/AlignedFrameComposition.lean#L406) | accepted 13 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_13`](KappaCheck/AlignedFrameComposition.lean#L407) | accepted interval 13 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_13`](KappaCheck/AlignedFrameComposition.lean#L410) | accepted taylor 13 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_14`](KappaCheck/AlignedFrameComposition.lean#L413) | accepted 14 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_14`](KappaCheck/AlignedFrameComposition.lean#L414) | accepted interval 14 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_14`](KappaCheck/AlignedFrameComposition.lean#L417) | accepted taylor 14 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_15`](KappaCheck/AlignedFrameComposition.lean#L420) | accepted 15 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_15`](KappaCheck/AlignedFrameComposition.lean#L421) | accepted interval 15 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_15`](KappaCheck/AlignedFrameComposition.lean#L424) | accepted taylor 15 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_16`](KappaCheck/AlignedFrameComposition.lean#L427) | accepted 16 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_16`](KappaCheck/AlignedFrameComposition.lean#L428) | accepted interval 16 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_16`](KappaCheck/AlignedFrameComposition.lean#L431) | accepted taylor 16 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_17`](KappaCheck/AlignedFrameComposition.lean#L434) | accepted 17 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_17`](KappaCheck/AlignedFrameComposition.lean#L435) | accepted interval 17 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_17`](KappaCheck/AlignedFrameComposition.lean#L438) | accepted taylor 17 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_18`](KappaCheck/AlignedFrameComposition.lean#L441) | accepted 18 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_18`](KappaCheck/AlignedFrameComposition.lean#L442) | accepted interval 18 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_18`](KappaCheck/AlignedFrameComposition.lean#L445) | accepted taylor 18 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_19`](KappaCheck/AlignedFrameComposition.lean#L448) | accepted 19 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_19`](KappaCheck/AlignedFrameComposition.lean#L449) | accepted interval 19 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_19`](KappaCheck/AlignedFrameComposition.lean#L452) | accepted taylor 19 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_20`](KappaCheck/AlignedFrameComposition.lean#L455) | accepted 20 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_20`](KappaCheck/AlignedFrameComposition.lean#L456) | accepted interval 20 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_20`](KappaCheck/AlignedFrameComposition.lean#L459) | accepted taylor 20 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_21`](KappaCheck/AlignedFrameComposition.lean#L462) | accepted 21 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_21`](KappaCheck/AlignedFrameComposition.lean#L463) | accepted interval 21 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_21`](KappaCheck/AlignedFrameComposition.lean#L466) | accepted taylor 21 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_22`](KappaCheck/AlignedFrameComposition.lean#L469) | accepted 22 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_22`](KappaCheck/AlignedFrameComposition.lean#L470) | accepted interval 22 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_22`](KappaCheck/AlignedFrameComposition.lean#L473) | accepted taylor 22 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_23`](KappaCheck/AlignedFrameComposition.lean#L476) | accepted 23 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_23`](KappaCheck/AlignedFrameComposition.lean#L477) | accepted interval 23 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_23`](KappaCheck/AlignedFrameComposition.lean#L480) | accepted taylor 23 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_25`](KappaCheck/AlignedFrameComposition.lean#L483) | accepted 25 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_25`](KappaCheck/AlignedFrameComposition.lean#L484) | accepted interval 25 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_25`](KappaCheck/AlignedFrameComposition.lean#L487) | accepted taylor 25 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_481`](KappaCheck/AlignedFrameComposition.lean#L490) | accepted 481 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_481`](KappaCheck/AlignedFrameComposition.lean#L491) | accepted interval 481 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_481`](KappaCheck/AlignedFrameComposition.lean#L494) | accepted taylor 481 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_525`](KappaCheck/AlignedFrameComposition.lean#L497) | accepted 525 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_525`](KappaCheck/AlignedFrameComposition.lean#L498) | accepted interval 525 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_525`](KappaCheck/AlignedFrameComposition.lean#L501) | accepted taylor 525 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_529`](KappaCheck/AlignedFrameComposition.lean#L504) | accepted 529 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_interval_529`](KappaCheck/AlignedFrameComposition.lean#L505) | accepted interval 529 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_taylor_529`](KappaCheck/AlignedFrameComposition.lean#L508) | accepted taylor 529 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`acceptedMoment`](KappaCheck/AlignedFrameComposition.lean#L511) | acceptedMoment | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`acceptedFromCounts`](KappaCheck/AlignedFrameComposition.lean#L539) | acceptedFromCounts | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_profile_link`](KappaCheck/AlignedFrameComposition.lean#L567) | accepted profile link | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_moment`](KappaCheck/AlignedFrameComposition.lean#L570) | accepted moment | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`accepted_paid_moment`](KappaCheck/AlignedFrameComposition.lean#L573) | accepted paid moment | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_1`](KappaCheck/AlignedFrameComposition.lean#L577) | rejected 1 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_1`](KappaCheck/AlignedFrameComposition.lean#L578) | rejected interval 1 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_1`](KappaCheck/AlignedFrameComposition.lean#L581) | rejected taylor 1 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_2`](KappaCheck/AlignedFrameComposition.lean#L584) | rejected 2 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_2`](KappaCheck/AlignedFrameComposition.lean#L585) | rejected interval 2 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_2`](KappaCheck/AlignedFrameComposition.lean#L588) | rejected taylor 2 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_3`](KappaCheck/AlignedFrameComposition.lean#L591) | rejected 3 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_3`](KappaCheck/AlignedFrameComposition.lean#L592) | rejected interval 3 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_3`](KappaCheck/AlignedFrameComposition.lean#L595) | rejected taylor 3 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_4`](KappaCheck/AlignedFrameComposition.lean#L598) | rejected 4 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_4`](KappaCheck/AlignedFrameComposition.lean#L599) | rejected interval 4 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_4`](KappaCheck/AlignedFrameComposition.lean#L602) | rejected taylor 4 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_5`](KappaCheck/AlignedFrameComposition.lean#L605) | rejected 5 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_5`](KappaCheck/AlignedFrameComposition.lean#L606) | rejected interval 5 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_5`](KappaCheck/AlignedFrameComposition.lean#L609) | rejected taylor 5 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_6`](KappaCheck/AlignedFrameComposition.lean#L612) | rejected 6 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_6`](KappaCheck/AlignedFrameComposition.lean#L613) | rejected interval 6 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_6`](KappaCheck/AlignedFrameComposition.lean#L616) | rejected taylor 6 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_7`](KappaCheck/AlignedFrameComposition.lean#L619) | rejected 7 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_7`](KappaCheck/AlignedFrameComposition.lean#L620) | rejected interval 7 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_7`](KappaCheck/AlignedFrameComposition.lean#L623) | rejected taylor 7 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_8`](KappaCheck/AlignedFrameComposition.lean#L626) | rejected 8 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_8`](KappaCheck/AlignedFrameComposition.lean#L627) | rejected interval 8 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_8`](KappaCheck/AlignedFrameComposition.lean#L630) | rejected taylor 8 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_9`](KappaCheck/AlignedFrameComposition.lean#L633) | rejected 9 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_9`](KappaCheck/AlignedFrameComposition.lean#L634) | rejected interval 9 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_9`](KappaCheck/AlignedFrameComposition.lean#L637) | rejected taylor 9 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_10`](KappaCheck/AlignedFrameComposition.lean#L640) | rejected 10 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_10`](KappaCheck/AlignedFrameComposition.lean#L641) | rejected interval 10 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_10`](KappaCheck/AlignedFrameComposition.lean#L644) | rejected taylor 10 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_11`](KappaCheck/AlignedFrameComposition.lean#L647) | rejected 11 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_11`](KappaCheck/AlignedFrameComposition.lean#L648) | rejected interval 11 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_11`](KappaCheck/AlignedFrameComposition.lean#L651) | rejected taylor 11 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_12`](KappaCheck/AlignedFrameComposition.lean#L654) | rejected 12 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_12`](KappaCheck/AlignedFrameComposition.lean#L655) | rejected interval 12 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_12`](KappaCheck/AlignedFrameComposition.lean#L658) | rejected taylor 12 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_13`](KappaCheck/AlignedFrameComposition.lean#L661) | rejected 13 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_13`](KappaCheck/AlignedFrameComposition.lean#L662) | rejected interval 13 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_13`](KappaCheck/AlignedFrameComposition.lean#L665) | rejected taylor 13 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_14`](KappaCheck/AlignedFrameComposition.lean#L668) | rejected 14 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_14`](KappaCheck/AlignedFrameComposition.lean#L669) | rejected interval 14 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_14`](KappaCheck/AlignedFrameComposition.lean#L672) | rejected taylor 14 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_15`](KappaCheck/AlignedFrameComposition.lean#L675) | rejected 15 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_15`](KappaCheck/AlignedFrameComposition.lean#L676) | rejected interval 15 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_15`](KappaCheck/AlignedFrameComposition.lean#L679) | rejected taylor 15 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_16`](KappaCheck/AlignedFrameComposition.lean#L682) | rejected 16 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_16`](KappaCheck/AlignedFrameComposition.lean#L683) | rejected interval 16 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_16`](KappaCheck/AlignedFrameComposition.lean#L686) | rejected taylor 16 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_17`](KappaCheck/AlignedFrameComposition.lean#L689) | rejected 17 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_17`](KappaCheck/AlignedFrameComposition.lean#L690) | rejected interval 17 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_17`](KappaCheck/AlignedFrameComposition.lean#L693) | rejected taylor 17 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_18`](KappaCheck/AlignedFrameComposition.lean#L696) | rejected 18 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_18`](KappaCheck/AlignedFrameComposition.lean#L697) | rejected interval 18 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_18`](KappaCheck/AlignedFrameComposition.lean#L700) | rejected taylor 18 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_19`](KappaCheck/AlignedFrameComposition.lean#L703) | rejected 19 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_19`](KappaCheck/AlignedFrameComposition.lean#L704) | rejected interval 19 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_19`](KappaCheck/AlignedFrameComposition.lean#L707) | rejected taylor 19 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_20`](KappaCheck/AlignedFrameComposition.lean#L710) | rejected 20 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_20`](KappaCheck/AlignedFrameComposition.lean#L711) | rejected interval 20 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_20`](KappaCheck/AlignedFrameComposition.lean#L714) | rejected taylor 20 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_21`](KappaCheck/AlignedFrameComposition.lean#L717) | rejected 21 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_21`](KappaCheck/AlignedFrameComposition.lean#L718) | rejected interval 21 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_21`](KappaCheck/AlignedFrameComposition.lean#L721) | rejected taylor 21 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_22`](KappaCheck/AlignedFrameComposition.lean#L724) | rejected 22 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_22`](KappaCheck/AlignedFrameComposition.lean#L725) | rejected interval 22 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_22`](KappaCheck/AlignedFrameComposition.lean#L728) | rejected taylor 22 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_23`](KappaCheck/AlignedFrameComposition.lean#L731) | rejected 23 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_23`](KappaCheck/AlignedFrameComposition.lean#L732) | rejected interval 23 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_23`](KappaCheck/AlignedFrameComposition.lean#L735) | rejected taylor 23 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_25`](KappaCheck/AlignedFrameComposition.lean#L738) | rejected 25 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_25`](KappaCheck/AlignedFrameComposition.lean#L739) | rejected interval 25 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_25`](KappaCheck/AlignedFrameComposition.lean#L742) | rejected taylor 25 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_481`](KappaCheck/AlignedFrameComposition.lean#L745) | rejected 481 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_481`](KappaCheck/AlignedFrameComposition.lean#L746) | rejected interval 481 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_481`](KappaCheck/AlignedFrameComposition.lean#L749) | rejected taylor 481 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_525`](KappaCheck/AlignedFrameComposition.lean#L752) | rejected 525 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_525`](KappaCheck/AlignedFrameComposition.lean#L753) | rejected interval 525 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_525`](KappaCheck/AlignedFrameComposition.lean#L756) | rejected taylor 525 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_529`](KappaCheck/AlignedFrameComposition.lean#L759) | rejected 529 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_interval_529`](KappaCheck/AlignedFrameComposition.lean#L760) | rejected interval 529 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_taylor_529`](KappaCheck/AlignedFrameComposition.lean#L763) | rejected taylor 529 | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejectedMoment`](KappaCheck/AlignedFrameComposition.lean#L766) | rejectedMoment | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejectedFromCounts`](KappaCheck/AlignedFrameComposition.lean#L794) | rejectedFromCounts | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_profile_link`](KappaCheck/AlignedFrameComposition.lean#L822) | rejected profile link | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_moment`](KappaCheck/AlignedFrameComposition.lean#L825) | rejected moment | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | +| [`rejected_paid_moment`](KappaCheck/AlignedFrameComposition.lean#L828) | rejected paid moment | — | — | [README.md:3](../../research/aligned-composition/lean/README.md#L3)
[README.md:5](../../research/aligned-composition/lean/README.md#L5) | Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses. | diff --git a/formal/lean/sources.py b/formal/lean/sources.py index eedaedad3b..ffb8241a90 100644 --- a/formal/lean/sources.py +++ b/formal/lean/sources.py @@ -410,6 +410,305 @@ def main_(*k): [], 'Non-vacuity check for `scoped_ceiling_exact`; no source line.'), ] +# Aligned finite arithmetic supplement; original historical rows remain unchanged. +ROWS += [ +('AlignedFrameComposition', ['m'], 'm', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['n'], 'n', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['roles23'], 'roles23', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['blocks23'], 'blocks23', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['roles25'], 'roles25', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['blocks25'], 'blocks25', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['width'], 'width', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['counts'], 'counts', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count'], 'count', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['mass'], 'mass', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['network_counts'], 'network counts', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rank_mass'], 'rank mass', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_1'], 'count 1', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_2'], 'count 2', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_3'], 'count 3', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_4'], 'count 4', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_5'], 'count 5', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_6'], 'count 6', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_7'], 'count 7', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_8'], 'count 8', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_9'], 'count 9', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_10'], 'count 10', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_11'], 'count 11', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_12'], 'count 12', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_13'], 'count 13', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_14'], 'count 14', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_15'], 'count 15', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_16'], 'count 16', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_17'], 'count 17', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_18'], 'count 18', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_19'], 'count 19', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_20'], 'count 20', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_21'], 'count 21', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_22'], 'count 22', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_23'], 'count 23', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_25'], 'count 25', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_481'], 'count 481', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_525'], 'count 525', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['count_529'], 'count 529', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['childSizes'], 'childSizes', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['complete_child_support'], 'complete child support', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['strict_child_contraction'], 'strict child contraction', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['a'], 'a', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['b'], 'b', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['kappa'], 'kappa', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['eta'], 'eta', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['beta'], 'beta', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['tau'], 'tau', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['sigma'], 'sigma', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['qParam'], 'qParam', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['lp'], 'lp', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['c'], 'c', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['epsilon'], 'epsilon', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['lam'], 'lam', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['g'], 'g', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['r'], 'r', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['delta'], 'delta', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['internal'], 'internal', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['leaf'], 'leaf', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['complexWidth'], 'complexWidth', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['complexRank'], 'complexRank', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['scalar'], 'scalar', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['guardE'], 'guardE', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['guardB'], 'guardB', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['literal'], 'literal', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['guardC'], 'guardC', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['literalGap'], 'literalGap', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rowGap'], 'rowGap', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['margins'], 'margins', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_a_positive'], 'slack a positive', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_a_below_b'], 'slack a below b', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_b_below_one_over32'], 'slack b below one over32', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_beta_positive'], 'slack beta positive', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_beta_below_one'], 'slack beta below one', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_phase_leaf_above_bit'], 'slack phase leaf above bit', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_q_positive'], 'slack q positive', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_q_below_internal'], 'slack q below internal', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_q_below_leaf'], 'slack q below leaf', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_c_positive'], 'slack c positive', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_c_below_one'], 'slack c below one', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_q_below_reservations'], 'slack q below reservations', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_lambda_above_tau'], 'slack lambda above tau', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_lambda_above_sigma'], 'slack lambda above sigma', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_lambda_above_internal'], 'slack lambda above internal', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_lambda_prime_above_lambda'], 'slack lambda prime above lambda', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_compact_leaf'], 'slack compact leaf', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_compact_reservations'], 'slack compact reservations', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_lambda_prime_below_one'], 'slack lambda prime below one', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_epsilon_positive'], 'slack epsilon positive', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_epsilon_below_one'], 'slack epsilon below one', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_guard_width'], 'slack guard width', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_K_geometry'], 'slack K geometry', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_K_dominates_log'], 'slack K dominates log', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_record_suffix'], 'slack record suffix', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_phase_local'], 'slack phase local', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_phase_boundary'], 'slack phase boundary', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_gamma_sublinear'], 'slack gamma sublinear', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_cell_above_band'], 'slack cell above band', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_prime_interval_packing'], 'slack prime interval packing', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_alpha_positive'], 'slack alpha positive', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_alpha_below_one'], 'slack alpha below one', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_alpha_below_one_fourth'], 'slack alpha below one fourth', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_delta_positive'], 'slack delta positive', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_delta_below_one_eighth'], 'slack delta below one eighth', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_short_record_fallback'], 'slack short record fallback', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_small_field_exposure'], 'slack small field exposure', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_artificial_boundary'], 'slack artificial boundary', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_literal_scalar_guard'], 'slack literal scalar guard', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_row_product_gap'], 'slack row product gap', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_g1_above_kappa'], 'slack g1 above kappa', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_g2_above_kappa'], 'slack g2 above kappa', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_g3_above_kappa'], 'slack g3 above kappa', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_g4_above_kappa'], 'slack g4 above kappa', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_g5_above_kappa'], 'slack g5 above kappa', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_g6_above_kappa'], 'slack g6 above kappa', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['slack_g7_above_kappa'], 'slack g7 above kappa', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['margins_strict'], 'margins strict', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['balanced_identities'], 'balanced identities', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['controlling_margin'], 'controlling margin', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['gain_over_original'], 'gain over original', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['finite_bridge'], 'finite bridge', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['taylor8'], 'taylor8', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['expUpper'], 'expUpper', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_1'], 'accepted 1', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_1'], 'accepted interval 1', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_1'], 'accepted taylor 1', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_2'], 'accepted 2', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_2'], 'accepted interval 2', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_2'], 'accepted taylor 2', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_3'], 'accepted 3', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_3'], 'accepted interval 3', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_3'], 'accepted taylor 3', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_4'], 'accepted 4', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_4'], 'accepted interval 4', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_4'], 'accepted taylor 4', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_5'], 'accepted 5', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_5'], 'accepted interval 5', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_5'], 'accepted taylor 5', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_6'], 'accepted 6', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_6'], 'accepted interval 6', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_6'], 'accepted taylor 6', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_7'], 'accepted 7', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_7'], 'accepted interval 7', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_7'], 'accepted taylor 7', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_8'], 'accepted 8', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_8'], 'accepted interval 8', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_8'], 'accepted taylor 8', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_9'], 'accepted 9', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_9'], 'accepted interval 9', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_9'], 'accepted taylor 9', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_10'], 'accepted 10', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_10'], 'accepted interval 10', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_10'], 'accepted taylor 10', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_11'], 'accepted 11', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_11'], 'accepted interval 11', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_11'], 'accepted taylor 11', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_12'], 'accepted 12', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_12'], 'accepted interval 12', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_12'], 'accepted taylor 12', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_13'], 'accepted 13', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_13'], 'accepted interval 13', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_13'], 'accepted taylor 13', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_14'], 'accepted 14', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_14'], 'accepted interval 14', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_14'], 'accepted taylor 14', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_15'], 'accepted 15', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_15'], 'accepted interval 15', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_15'], 'accepted taylor 15', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_16'], 'accepted 16', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_16'], 'accepted interval 16', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_16'], 'accepted taylor 16', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_17'], 'accepted 17', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_17'], 'accepted interval 17', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_17'], 'accepted taylor 17', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_18'], 'accepted 18', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_18'], 'accepted interval 18', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_18'], 'accepted taylor 18', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_19'], 'accepted 19', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_19'], 'accepted interval 19', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_19'], 'accepted taylor 19', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_20'], 'accepted 20', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_20'], 'accepted interval 20', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_20'], 'accepted taylor 20', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_21'], 'accepted 21', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_21'], 'accepted interval 21', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_21'], 'accepted taylor 21', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_22'], 'accepted 22', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_22'], 'accepted interval 22', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_22'], 'accepted taylor 22', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_23'], 'accepted 23', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_23'], 'accepted interval 23', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_23'], 'accepted taylor 23', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_25'], 'accepted 25', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_25'], 'accepted interval 25', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_25'], 'accepted taylor 25', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_481'], 'accepted 481', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_481'], 'accepted interval 481', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_481'], 'accepted taylor 481', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_525'], 'accepted 525', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_525'], 'accepted interval 525', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_525'], 'accepted taylor 525', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_529'], 'accepted 529', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_interval_529'], 'accepted interval 529', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_taylor_529'], 'accepted taylor 529', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['acceptedMoment'], 'acceptedMoment', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['acceptedFromCounts'], 'acceptedFromCounts', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_profile_link'], 'accepted profile link', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_moment'], 'accepted moment', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['accepted_paid_moment'], 'accepted paid moment', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_1'], 'rejected 1', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_1'], 'rejected interval 1', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_1'], 'rejected taylor 1', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_2'], 'rejected 2', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_2'], 'rejected interval 2', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_2'], 'rejected taylor 2', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_3'], 'rejected 3', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_3'], 'rejected interval 3', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_3'], 'rejected taylor 3', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_4'], 'rejected 4', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_4'], 'rejected interval 4', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_4'], 'rejected taylor 4', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_5'], 'rejected 5', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_5'], 'rejected interval 5', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_5'], 'rejected taylor 5', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_6'], 'rejected 6', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_6'], 'rejected interval 6', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_6'], 'rejected taylor 6', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_7'], 'rejected 7', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_7'], 'rejected interval 7', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_7'], 'rejected taylor 7', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_8'], 'rejected 8', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_8'], 'rejected interval 8', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_8'], 'rejected taylor 8', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_9'], 'rejected 9', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_9'], 'rejected interval 9', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_9'], 'rejected taylor 9', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_10'], 'rejected 10', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_10'], 'rejected interval 10', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_10'], 'rejected taylor 10', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_11'], 'rejected 11', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_11'], 'rejected interval 11', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_11'], 'rejected taylor 11', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_12'], 'rejected 12', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_12'], 'rejected interval 12', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_12'], 'rejected taylor 12', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_13'], 'rejected 13', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_13'], 'rejected interval 13', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_13'], 'rejected taylor 13', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_14'], 'rejected 14', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_14'], 'rejected interval 14', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_14'], 'rejected taylor 14', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_15'], 'rejected 15', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_15'], 'rejected interval 15', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_15'], 'rejected taylor 15', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_16'], 'rejected 16', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_16'], 'rejected interval 16', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_16'], 'rejected taylor 16', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_17'], 'rejected 17', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_17'], 'rejected interval 17', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_17'], 'rejected taylor 17', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_18'], 'rejected 18', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_18'], 'rejected interval 18', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_18'], 'rejected taylor 18', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_19'], 'rejected 19', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_19'], 'rejected interval 19', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_19'], 'rejected taylor 19', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_20'], 'rejected 20', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_20'], 'rejected interval 20', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_20'], 'rejected taylor 20', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_21'], 'rejected 21', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_21'], 'rejected interval 21', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_21'], 'rejected taylor 21', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_22'], 'rejected 22', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_22'], 'rejected interval 22', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_22'], 'rejected taylor 22', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_23'], 'rejected 23', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_23'], 'rejected interval 23', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_23'], 'rejected taylor 23', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_25'], 'rejected 25', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_25'], 'rejected interval 25', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_25'], 'rejected taylor 25', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_481'], 'rejected 481', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_481'], 'rejected interval 481', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_481'], 'rejected taylor 481', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_525'], 'rejected 525', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_525'], 'rejected interval 525', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_525'], 'rejected taylor 525', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_529'], 'rejected 529', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_interval_529'], 'rejected interval 529', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_taylor_529'], 'rejected taylor 529', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejectedMoment'], 'rejectedMoment', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejectedFromCounts'], 'rejectedFromCounts', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_profile_link'], 'rejected profile link', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_moment'], 'rejected moment', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +('AlignedFrameComposition', ['rejected_paid_moment'], 'rejected paid moment', [Line('research/aligned-composition/lean/README.md', 3, 3, '197 theorems'), Line('research/aligned-composition/lean/README.md', 5, 5, 'external hypotheses')], 'Frozen data and exact generator: research/aligned-composition/lean/input.json and generate.py. Rational arithmetic only; external physical/analytic/all-size hypotheses.'), +] + DECL = re.compile(r'^(?:noncomputable )?(?:theorem|def) (\S+)', re.M) STOP = re.compile(r'^(?:theorem|def|noncomputable|/-|end |namespace|section)', re.M) diff --git a/references/frame-compiler/aligned-r11/CANDIDATE_PARENT.json b/references/frame-compiler/aligned-r11/CANDIDATE_PARENT.json new file mode 100644 index 0000000000..f023a81bcd --- /dev/null +++ b/references/frame-compiler/aligned-r11/CANDIDATE_PARENT.json @@ -0,0 +1,116 @@ +{ + "23": { + "W": 131973908, + "bit_saving": "52448177993289/1000000000000000000", + "compile_seconds": 41.97542989999056, + "coordinate_permutation": [ + 1, + 2, + 4, + 3, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 20, + 19, + 21, + 22, + 0 + ], + "exact_CRT_profiles": "PASS", + "full_physical_replay": "PASS both orientations", + "groups": "444", + "h": 23, + "kappa": "6555678415753/125000000000000000", + "label": "search", + "mode": "envelope-half", + "output_mode": "baseline", + "path": "results/23-444-envelope-half-baseline-search", + "profile_seconds": 1.6327140040230006, + "replay_seconds": 1.7665091671515256, + "roles": 26620, + "seconds": 48.58395723090507, + "stats": { + "augmentations": 134, + "carry_exchanges": 1774, + "carry_two_cycles": 140, + "clearing_xors": 5682, + "live_anchor_candidates": 74199, + "live_anchor_xors": 576, + "matched": 50244, + "multi_node_regions": 8625, + "reclaimed": 2658, + "regions": 67861 + }, + "word_sha256": "a2fc7194e9190f0fa4ddeac38aa76605f1b08243a7b51642a2433a52325b98c7" + }, + "25": { + "W": 132094198, + "bit_saving": "26157624115811/500000000000000000", + "compile_seconds": 68.12840775190853, + "coordinate_permutation": [ + 2, + 1, + 4, + 3, + 6, + 5, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "exact_CRT_profiles": "PASS", + "full_physical_replay": "PASS both orientations", + "groups": "441", + "h": 25, + "kappa": "326953196809/6250000000000000", + "label": "canary", + "mode": "envelope-half", + "output_mode": "route-late", + "path": "results/25-441-envelope-half-route-late-canary", + "profile_seconds": 2.3878593081608415, + "replay_seconds": 2.661699212156236, + "roles": 35138, + "seconds": 77.2729034400545, + "stats": { + "augmentations": 166, + "carry_exchanges": 2090, + "carry_two_cycles": 266, + "clearing_xors": 7148, + "live_anchor_candidates": 97315, + "live_anchor_xors": 868, + "matched": 70124, + "multi_node_regions": 11375, + "reclaimed": 3491, + "regions": 93828 + }, + "word_sha256": "a378551e7c6511576d2ed7d0d035bf0403c4a1e5fa14b458c1de8d7b988e23fb" + } +} diff --git a/references/frame-compiler/aligned-r11/COORDINATES.json b/references/frame-compiler/aligned-r11/COORDINATES.json new file mode 100644 index 0000000000..20c55f4f0e --- /dev/null +++ b/references/frame-compiler/aligned-r11/COORDINATES.json @@ -0,0 +1,54 @@ +{ + "23": [ + 1, + 2, + 4, + 3, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 20, + 19, + 21, + 22, + 0 + ], + "25": [ + 2, + 1, + 4, + 3, + 6, + 5, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ] +} diff --git a/references/frame-compiler/aligned-r11/EXPERIMENT.txt b/references/frame-compiler/aligned-r11/EXPERIMENT.txt new file mode 100644 index 0000000000..96079838a0 --- /dev/null +++ b/references/frame-compiler/aligned-r11/EXPERIMENT.txt @@ -0,0 +1 @@ +PR74 aligned first6/first9 depth splits and hhh coarse factoring composed with R10 order, geometric pricing, three-cycles and coordinate flags. All new literal words checked. Supplied foreign baseline used as working profile; no foreign baseline reproduction gate. Own R10 canaries only. 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. 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3916, + "live_anchor_xors": 76 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "word_sha256": "3f58db33edc2059ad6ca01cf8c36dd8cd8ae12149e1072e1f42757ca4ef17b82" +} diff --git a/references/frame-compiler/aligned-r11/baseline/h25/profiles.json b/references/frame-compiler/aligned-r11/baseline/h25/profiles.json new file mode 100644 index 0000000000..2be4368700 --- /dev/null +++ b/references/frame-compiler/aligned-r11/baseline/h25/profiles.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35684,"loss":600,"rank_sum":892700,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":51168,"crt_matrices":7278,"crt_disagreements":0,"blocks":[0,491871,27309,10127,7839,5460,4947,4006,3802,2943,2456,2025,1787,1423,1124,867,560,478,221,170,46,59,0,25,0,0]} diff --git a/references/frame-compiler/aligned-r11/baseline/h25/replay.json b/references/frame-compiler/aligned-r11/baseline/h25/replay.json new file mode 100644 index 0000000000..3ec3c54dc6 --- /dev/null +++ b/references/frame-compiler/aligned-r11/baseline/h25/replay.json @@ -0,0 +1,36 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 35684, + "output_roles": 6925, + "elementary_xors": 224161, + "word_length": 928844, + "full_basis_vectors": 40284, + "rank_mass": 892700, + "histogram": { + "1": 77041, + "0": 238437, + "2": 118217, + "3": 13314, + "4": 18459, + "6": 3215, + "5": 8388, + "7": 948, + "8": 1195, + "9": 721, + "10": 828, + "12": 708, + "13": 182, + "14": 653, + "16": 2171, + "18": 506, + "19": 981, + "17": 633, + "15": 187, + "11": 15, + "20": 4464, + "21": 8405, + "24": 25, + "23": 463 + } +} diff --git a/references/frame-compiler/aligned-r11/baseline/h25/result.json b/references/frame-compiler/aligned-r11/baseline/h25/result.json new file mode 100644 index 0000000000..50b259fcd7 --- /dev/null +++ b/references/frame-compiler/aligned-r11/baseline/h25/result.json @@ -0,0 +1,19 @@ +{ + "h": 25, + "roles": 35684, + "stats": { + "augmentations": 16, + "regions": 84843, + "matched": 60971, + "multi_node_regions": 11575, + "carry_exchanges": 1000, + "carry_two_cycles": 62, + "live_anchor_candidates": 98464, + "reclaimed": 3263, + "clearing_xors": 6027, + "live_anchor_xors": 132 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "word_sha256": "7c60369042197c356dfac3516ae396d68dc92edbc5824b6078dce0e6676f7f79" +} diff --git a/references/frame-compiler/aligned-r11/batch.py b/references/frame-compiler/aligned-r11/batch.py new file mode 100644 index 0000000000..3618548092 --- /dev/null +++ b/references/frame-compiler/aligned-r11/batch.py @@ -0,0 +1,41 @@ +"""Aligned PR74 working graphs with independently audited R10 additions. +Never rerun the supplied foreign baseline as a prerequisite. Own R10 canaries +guard engine/driver preservation; all new words receive full physical checks. +""" +from pathlib import Path +from hashlib import sha256 +from fractions import Fraction as Q +from concurrent.futures import ProcessPoolExecutor,as_completed +import argparse,itertools,json,subprocess,sys,time +ROOT=Path(__file__).resolve().parent +sys.path.insert(0,str(ROOT)) +from graph_batch import generate +def run(job): + h,config=job + return generate(h,**config) +def jobs(h): + old=json.loads((ROOT/'R10_FROZEN.json').read_text())['axes'][str(h)] + new=json.loads((ROOT/'references/pr74-aligned/research/aligned-exchange-frames/selection.json').read_text())['axes'][str(h)] + configs=[] + for key,pricing,cycles,coords in itertools.product(('pr74','cover-minus-core-minus'),(False,True),(0,3),('old','new')): + if (key,pricing,cycles,coords)==('pr74',True,0,'new'):continue + configs.append(dict(groups=new['groups'],anchor_pairs=new['anchor_pairs'],coarse_word=new['coarse_word'],mode='envelope-half',output_mode=old['output_mode'],coordinate=old['coordinate_permutation'] if coords=='old' else new['coordinate_permutation'],label=f'{key}-pricing{int(pricing)}-cycles{cycles}-{coords}',pricing=pricing,three_cycle_passes=cycles,node_order=key)) + return [(h,c) for c in configs] +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--h',type=int,choices=(23,25),required=True);ap.add_argument('--workers',type=int,default=8);args=ap.parse_args();assert 1<=args.workers<=8 + manifest=json.loads((ROOT/'SOURCE.json').read_text()) + for name,digest in manifest['files'].items():assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + print('SOURCE PASS',len(manifest['files']),sha256((ROOT/'SOURCE.json').read_bytes()).hexdigest(),flush=True) + h=args.h;old=json.loads((ROOT/'R10_FROZEN.json').read_text());a=old['axes'][str(h)];rows=[];started=time.monotonic() + canary=generate(h,a['groups'],mode='envelope-half',output_mode=a['output_mode'],coordinate=a['coordinate_permutation'],label='own-r10-canary',pricing=a['oracle_coordinate_pricing'],three_cycle_passes=a['three_cycle_passes'],node_order=a['node_order']) + assert canary['word_sha256']==a['word_sha256'] and canary['kappa']==old['kappa'] + assert json.loads((ROOT/canary['path']/'profiles.json').read_text())==a['paid_profile'] + print('CANARY PASS',json.dumps(canary),flush=True) + alljobs=jobs(h) + with ProcessPoolExecutor(max_workers=args.workers) as pool: + for f in as_completed([pool.submit(run,j) for j in alljobs]): + row=f.result();rows.append(row);receipt=dict(h=h,complete=False,source_sha256=sha256((ROOT/'SOURCE.json').read_bytes()).hexdigest(),canary=canary,rows=rows,expected_cases=len(alljobs),validated_cases=len(rows),wall_seconds=time.monotonic()-started) + temp=ROOT/'progress.tmp';temp.write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');temp.replace(ROOT/'progress.json');print('RESULT',json.dumps(row),flush=True) + receipt.update(complete=True,best_axis=max(rows,key=lambda r:Q(r['kappa'])),wall_seconds=time.monotonic()-started) + (ROOT/'progress.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print('COMPLETE',h,flush=True) +if __name__=='__main__':main() diff --git a/references/frame-compiler/aligned-r11/build.sh b/references/frame-compiler/aligned-r11/build.sh new file mode 100644 index 0000000000..44cbeea56b --- /dev/null +++ b/references/frame-compiler/aligned-r11/build.sh @@ -0,0 +1,5 @@ +#!/bin/sh +set -eu +mkdir -p bin +c++ -O3 -std=c++17 -I references/frame-compiler/pr48/scripts/partial_swap scripts/experiments/profile_oracle.cpp -o bin/profile-oracle +c++ -O3 -std=c++17 -I references/frame-compiler/pr48/scripts/partial_swap scripts/experiments/binary_frame_profiles.cpp -o bin/profiles diff --git a/references/frame-compiler/aligned-r11/candidate-parent/h23/profiles.json b/references/frame-compiler/aligned-r11/candidate-parent/h23/profiles.json new file mode 100644 index 0000000000..d881b695c2 --- /dev/null +++ b/references/frame-compiler/aligned-r11/candidate-parent/h23/profiles.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":26620,"loss":506,"rank_sum":612766,"field_prime":2305843009213693951,"frames":67863,"distinct_matrices":37844,"crt_matrices":5571,"crt_disagreements":0,"blocks":[0,362191,17808,9346,4092,3667,3946,3336,2453,1663,1220,1339,814,768,525,441,247,102,108,0,92,23,0,0]} diff --git a/references/frame-compiler/aligned-r11/candidate-parent/h23/replay.json b/references/frame-compiler/aligned-r11/candidate-parent/h23/replay.json new file mode 100644 index 0000000000..174e857f58 --- /dev/null +++ b/references/frame-compiler/aligned-r11/candidate-parent/h23/replay.json @@ -0,0 +1,34 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 26620, + "output_roles": 5336, + "elementary_xors": 181432, + "word_length": 750522, + "full_basis_vectors": 30162, + "rank_mass": 612766, + "histogram": { + "1": 79271, + "0": 196941, + "2": 77528, + "4": 14036, + "3": 9524, + "6": 1494, + "5": 5451, + "8": 2029, + "7": 785, + "9": 1807, + "10": 711, + "11": 580, + "12": 707, + "13": 267, + "14": 1131, + "16": 243, + "15": 404, + "17": 629, + "18": 2574, + "19": 5438, + "22": 23, + "21": 354 + } +} diff --git a/references/frame-compiler/aligned-r11/candidate-parent/h23/result.json b/references/frame-compiler/aligned-r11/candidate-parent/h23/result.json new file mode 100644 index 0000000000..669c2d7c98 --- /dev/null +++ b/references/frame-compiler/aligned-r11/candidate-parent/h23/result.json @@ -0,0 +1,24 @@ +{ + "h": 23, + "groups": "444", + "mode": "envelope-half", + "roles": 26620, + "word_sha256": "a2fc7194e9190f0fa4ddeac38aa76605f1b08243a7b51642a2433a52325b98c7", + "stats": { + "augmentations": 134, + "regions": 67861, + "matched": 50244, + "multi_node_regions": 8625, + "carry_exchanges": 1774, + "carry_two_cycles": 140, + "live_anchor_candidates": 74199, + "live_anchor_xors": 576, + "reclaimed": 2658, + "clearing_xors": 5682 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "compile_seconds": 41.97542989999056, + "replay_seconds": 1.7665091671515256, + "profile_seconds": 1.6327140040230006 +} diff --git a/references/frame-compiler/aligned-r11/candidate-parent/h23/word.json.gz b/references/frame-compiler/aligned-r11/candidate-parent/h23/word.json.gz new file mode 100644 index 0000000000..72140140b2 Binary files /dev/null and b/references/frame-compiler/aligned-r11/candidate-parent/h23/word.json.gz differ diff --git a/references/frame-compiler/aligned-r11/candidate-parent/h25/profiles.json b/references/frame-compiler/aligned-r11/candidate-parent/h25/profiles.json new file mode 100644 index 0000000000..67f4cf0c33 --- /dev/null +++ b/references/frame-compiler/aligned-r11/candidate-parent/h25/profiles.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35138,"loss":600,"rank_sum":879050,"field_prime":2305843009213693951,"frames":93830,"distinct_matrices":53695,"crt_matrices":7335,"crt_disagreements":0,"blocks":[0,504362,27018,10748,5926,4937,5498,3818,3229,2589,2366,1865,1416,1370,1008,737,503,423,251,98,124,0,107,25,0,0]} diff --git a/references/frame-compiler/aligned-r11/candidate-parent/h25/replay.json b/references/frame-compiler/aligned-r11/candidate-parent/h25/replay.json new file mode 100644 index 0000000000..0b2dbfd701 --- /dev/null +++ b/references/frame-compiler/aligned-r11/candidate-parent/h25/replay.json @@ -0,0 +1,36 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 35138, + "output_roles": 6925, + "elementary_xors": 247252, + "word_length": 1021208, + "full_basis_vectors": 39738, + "rank_mass": 879050, + "histogram": { + "1": 101941, + "0": 266827, + "2": 108937, + "4": 22808, + "3": 12153, + "5": 7685, + "6": 1999, + "8": 2775, + "7": 826, + "9": 1016, + "10": 888, + "11": 552, + "12": 965, + "14": 478, + "13": 459, + "15": 454, + "16": 1970, + "18": 268, + "17": 661, + "19": 916, + "20": 3478, + "21": 7250, + "24": 25, + "23": 461 + } +} diff --git a/references/frame-compiler/aligned-r11/candidate-parent/h25/result.json b/references/frame-compiler/aligned-r11/candidate-parent/h25/result.json new file mode 100644 index 0000000000..373a2a5a79 --- /dev/null +++ b/references/frame-compiler/aligned-r11/candidate-parent/h25/result.json @@ -0,0 +1,24 @@ +{ + "h": 25, + "groups": "441", + "mode": "envelope-half", + "roles": 35138, + "word_sha256": "a378551e7c6511576d2ed7d0d035bf0403c4a1e5fa14b458c1de8d7b988e23fb", + "stats": { + "augmentations": 166, + "regions": 93828, + "matched": 70124, + "multi_node_regions": 11375, + "carry_exchanges": 2090, + "carry_two_cycles": 266, + "live_anchor_candidates": 97315, + "live_anchor_xors": 868, + "reclaimed": 3491, + "clearing_xors": 7148 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "compile_seconds": 68.12840775190853, + "replay_seconds": 2.661699212156236, + "profile_seconds": 2.3878593081608415 +} diff --git a/references/frame-compiler/aligned-r11/candidate-parent/h25/word.json.gz b/references/frame-compiler/aligned-r11/candidate-parent/h25/word.json.gz new file mode 100644 index 0000000000..04e196397b Binary files /dev/null and b/references/frame-compiler/aligned-r11/candidate-parent/h25/word.json.gz differ diff --git a/references/frame-compiler/aligned-r11/configs.json b/references/frame-compiler/aligned-r11/configs.json new file mode 100644 index 0000000000..56e87fd388 --- /dev/null +++ b/references/frame-compiler/aligned-r11/configs.json @@ -0,0 +1,8 @@ +[ + "111", + "112", + "411", + "171", + "141", + "181" +] diff --git a/references/frame-compiler/aligned-r11/evaluate.py b/references/frame-compiler/aligned-r11/evaluate.py new file mode 100644 index 0000000000..ad3369d6c0 --- /dev/null +++ b/references/frame-compiler/aligned-r11/evaluate.py @@ -0,0 +1,65 @@ +"""Exact high-precision comparisons, compounding verified PR65 arithmetic.""" +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +from copy import deepcopy +import importlib.util,json,sys,itertools +HERE=Path(__file__).resolve().parent +BASE=HERE +AR=BASE/'research/reordered-rank-pair/arithmetic' +sys.path.insert(0,str(AR)) +import refine +N=4073300;m=575 + +def load(path): + f=json.loads((path/'profiles.json').read_text());r=json.loads((path/'replay.json').read_text());s=json.loads((path/'result.json').read_text()) + assert f['crt_disagreements']==0 and f['R']==r['roles']==s['roles'] + return f + +def counts(profiles): + W=2*N;L=0;hist=Counter({1:19*N,21:2*N,17:2*N,481:2*N}) + for h,f in profiles.items(): + rep=N//f['v'];bank=rep*f['R'];W+=bank;L+=rep*f['loss'] + assert sum(t*n for t,n in enumerate(f['blocks']))==h*f['R']+f['loss']==f['rank_sum'] + hist.update({t:n*rep for t,n in enumerate(f['blocks']) if t and n});hist.update({h:bank,m-2*h:bank});hist.update({1:2*N,h-2:2*N}) + mass=sum(t*n for t,n in hist.items());assert mass==m*W-N+L + return dict(m=m,N=N,W=W,L=L,total_rank=mass,deficit=m*W-mass,maxchild=max(hist),child_multiplicities=dict(sorted(hist.items()))) + +def fine(profiles): + p=counts(profiles);rows=p['child_multiplicities'];den=10**18;lo=1;hi=6*10**13 + assert refine.exact_moment(m,p['W'],rows,Q(lo,den))['upper']<11:hi=mid + else:raise ArithmeticError('Enclosure inconclusive') + a=Q(lo,den);bridge=deepcopy(baseline['finite_bridge']);bridge['bit']['W']=p['W'] + bridge['bit']['wire_bits']=p['W'].bit_length() + bridge['rows']['coefficient']=sum(bridge[name]['halving_degree']*bridge[name]['wire_bits'] for name in ('bit','complex')) + bridge['rows']['degree_gap']=Q(bridge['rows']['degree'])-Q(51,25)*bridge['rows']['coefficient'] + bridge['rows']['suffix_slope']=4*bridge['rows']['degree'] + accepted=refine.exact_moment(m,p['W'],rows,a);rejected=refine.exact_moment(m,p['W'],rows,Q(hi,den));assert accepted['upper']<1prior and best['prior65_moment']['lower']>1 + for r in rows: + r['moment_at_best_bit']=refine.exact_moment(m,r['bit']['W'],r['bit']['child_multiplicities'],best['bit_saving']) + output={'verified_baseline':{'pr':65,'commit':'49e84f939d15b618b50714eb039cabf97c74256a','kappa':prior},'best':best,'rows':rows,'cases':len(rows)} + (HERE/'fine-pair-comparison.json').write_text(json.dumps(refine.arithmetic.js(output),indent=2,sort_keys=True)+'\n') + (HERE/'selected-exact-result.json').write_text(json.dumps(refine.arithmetic.js(best),indent=2,sort_keys=True)+'\n') + print('BEST',json.dumps({'pair':best['pair'],'kappa':str(best['kappa']),'bit_saving':str(best['bit_saving']),'W':best['bit']['W'],'gain_percent_vs_verified65':float(100*(best['kappa']/prior-1))},sort_keys=True),flush=True) diff --git a/references/frame-compiler/aligned-r11/frozen/h23/profiles.json b/references/frame-compiler/aligned-r11/frozen/h23/profiles.json new file mode 100644 index 0000000000..f55d353ea8 --- /dev/null +++ b/references/frame-compiler/aligned-r11/frozen/h23/profiles.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":26581,"loss":506,"rank_sum":611869,"field_prime":2305843009213693951,"frames":67863,"distinct_matrices":37862,"crt_matrices":5592,"crt_disagreements":0,"blocks":[0,362562,17799,9304,4092,3667,3941,3297,2487,1668,1210,1284,797,779,565,445,228,126,96,0,48,23,0,0]} diff --git a/references/frame-compiler/aligned-r11/frozen/h23/replay.json b/references/frame-compiler/aligned-r11/frozen/h23/replay.json new file mode 100644 index 0000000000..071902a010 --- /dev/null +++ b/references/frame-compiler/aligned-r11/frozen/h23/replay.json @@ -0,0 +1,34 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 26581, + "output_roles": 5336, + "elementary_xors": 181144, + "word_length": 749370, + "full_basis_vectors": 30123, + "rank_mass": 611869, + "histogram": { + "1": 79265, + "0": 196259, + "2": 77566, + "4": 14061, + "3": 9537, + "6": 1489, + "5": 5555, + "8": 2061, + "7": 804, + "9": 1730, + "10": 705, + "11": 564, + "12": 682, + "13": 262, + "14": 1150, + "16": 264, + "17": 623, + "15": 406, + "18": 2555, + "19": 5447, + "22": 23, + "21": 304 + } +} diff --git a/references/frame-compiler/aligned-r11/frozen/h23/result.json b/references/frame-compiler/aligned-r11/frozen/h23/result.json new file mode 100644 index 0000000000..7e26607850 --- /dev/null +++ b/references/frame-compiler/aligned-r11/frozen/h23/result.json @@ -0,0 +1,24 @@ +{ + "h": 23, + "groups": "444", + "mode": "envelope-half", + "roles": 26581, + "word_sha256": "3b6aac37d3e39d60381fa05250a4c0a88ed665cc2dccca7242e8c1ad5f9b3a66", + "stats": { + "augmentations": 138, + "regions": 67861, + "matched": 50244, + "multi_node_regions": 8625, + "carry_exchanges": 1644, + "carry_two_cycles": 95, + "live_anchor_candidates": 74185, + "reclaimed": 2697, + "clearing_xors": 5846, + "live_anchor_xors": 582 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "compile_seconds": 41.298744522966444, + "replay_seconds": 1.8352416479028761, + "profile_seconds": 1.6531089791096747 +} diff --git a/references/frame-compiler/aligned-r11/frozen/h23/word.json.gz b/references/frame-compiler/aligned-r11/frozen/h23/word.json.gz new file mode 100644 index 0000000000..3497b6461a Binary files /dev/null and b/references/frame-compiler/aligned-r11/frozen/h23/word.json.gz differ diff --git a/references/frame-compiler/aligned-r11/frozen/h25/profiles.json b/references/frame-compiler/aligned-r11/frozen/h25/profiles.json new file mode 100644 index 0000000000..cec0de6d53 --- /dev/null +++ b/references/frame-compiler/aligned-r11/frozen/h25/profiles.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35133,"loss":600,"rank_sum":878925,"field_prime":2305843009213693951,"frames":93830,"distinct_matrices":53721,"crt_matrices":7343,"crt_disagreements":0,"blocks":[0,504140,27187,10762,5913,4944,5499,3802,3244,2580,2359,1859,1424,1359,1005,738,501,428,252,98,121,0,107,25,0,0]} diff --git a/references/frame-compiler/aligned-r11/frozen/h25/replay.json b/references/frame-compiler/aligned-r11/frozen/h25/replay.json new file mode 100644 index 0000000000..9d82492a82 --- /dev/null +++ b/references/frame-compiler/aligned-r11/frozen/h25/replay.json @@ -0,0 +1,36 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 35133, + "output_roles": 6925, + "elementary_xors": 247312, + "word_length": 1021448, + "full_basis_vectors": 39733, + "rank_mass": 878925, + "histogram": { + "1": 101899, + "0": 266942, + "2": 108919, + "4": 22817, + "3": 12176, + "5": 7694, + "6": 2041, + "8": 2773, + "7": 845, + "9": 986, + "10": 898, + "11": 535, + "12": 967, + "14": 492, + "13": 461, + "15": 463, + "16": 1972, + "18": 268, + "17": 649, + "19": 908, + "20": 3476, + "21": 7248, + "24": 25, + "23": 453 + } +} diff --git a/references/frame-compiler/aligned-r11/frozen/h25/result.json b/references/frame-compiler/aligned-r11/frozen/h25/result.json new file mode 100644 index 0000000000..356d1f6471 --- /dev/null +++ b/references/frame-compiler/aligned-r11/frozen/h25/result.json @@ -0,0 +1,25 @@ +{ + "h": 25, + "groups": "441", + "mode": "envelope-half", + "roles": 35133, + "word_sha256": "81accb74c4697f5fb7569636023cd212b6995de44fe2ba862f89b80316cb3756", + "stats": { + "augmentations": 166, + "regions": 93828, + "matched": 70124, + "multi_node_regions": 11375, + "carry_exchanges": 1815, + "carry_two_cycles": 201, + "carry_three_cycles": 2, + "live_anchor_candidates": 97647, + "live_anchor_xors": 865, + "reclaimed": 3496, + "clearing_xors": 7154 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "compile_seconds": 74.8752128710039, + "replay_seconds": 3.0210618681740016, + "profile_seconds": 2.4829084710218012 +} diff --git a/references/frame-compiler/aligned-r11/frozen/h25/word.json.gz b/references/frame-compiler/aligned-r11/frozen/h25/word.json.gz new file mode 100644 index 0000000000..6064ccd1d2 Binary files /dev/null and b/references/frame-compiler/aligned-r11/frozen/h25/word.json.gz differ diff --git a/references/frame-compiler/aligned-r11/graph_batch.py b/references/frame-compiler/aligned-r11/graph_batch.py new file mode 100644 index 0000000000..266a29fa09 --- /dev/null +++ b/references/frame-compiler/aligned-r11/graph_batch.py @@ -0,0 +1,96 @@ +"""Durable independent CPU search over pinned current two-cycle construction. +Each accepted case regenerates and independently replays the literal word, +reconstructs paid frames, computes CPU CRT profiles and exact inequalities. +""" +from pathlib import Path +from hashlib import sha256 +from concurrent.futures import ProcessPoolExecutor,as_completed +import argparse,ast,cProfile,gzip,importlib.util,json,os,pstats,subprocess,sys,time,types +ROOT=Path(__file__).resolve().parent +sys.path.insert(0,str(ROOT/'scripts/experiments')) + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m + +def generate(h,groups,profile=False,mode="baseline",output_mode=None,coordinate=None,label="search",pricing=False,three_cycle_passes=0,node_order="pr74",anchor_pairs=1,coarse_word=None): + started=time.monotonic();out=ROOT/'results'/f'{h}-{groups}-{mode}-{output_mode}-{label}';out.mkdir(parents=True,exist_ok=True) + compiler=load('search_compiler',ROOT/'scripts/experiments/compiler.py') + source=(ROOT/'research/pair-assembly/pair_graph.py').read_text() + donor=ROOT/'references/pr69/balanced_coarse_compiler.py' + constants={n.targets[0].id:ast.literal_eval(n.value) for n in ast.parse(donor.read_text()).body if isinstance(n,ast.Assign) and isinstance(n.targets[0],ast.Name) and n.targets[0].id in ('BEFORE','AFTER')} + replacement=constants['AFTER'];needle='columns = [self.total([e(a,b) for a in groups[i]]) for b in groups[j]]' + orientation=mode.removeprefix('envelope-') if mode.startswith('envelope-') else ('half' if h==23 else 'row') + if orientation=='half': + replacement=replacement.replace(needle,'columns = ([self.total([e(a,b) for a in groups[i]]) for b in groups[j]] if i+j < ng-1 else [self.total([e(a,b) for b in groups[j]]) for a in groups[i]])') + elif orientation=='row':replacement=replacement.replace(needle,'columns = [self.total([e(a,b) for b in groups[j]]) for a in groups[i]]') + if coarse_word is not None: + assert coarse_word and set(coarse_word)<=set('crh') + aligned=ROOT/'references/pr74-aligned/research/aligned-exchange-frames/partition_graph.py' + replacement=next(ast.literal_eval(n.value) for n in ast.parse(aligned.read_text()).body if isinstance(n,ast.Assign) and isinstance(n.targets[0],ast.Name) and n.targets[0].id=='AFTER') + assert source.count(constants['BEFORE'])==1 + graph=types.ModuleType('balanced_graph');graph.__file__=str(ROOT/'research/pair-assembly/pair_graph.py');graph.COARSE=coarse_word;exec(compile(source.replace(constants['BEFORE'],replacement),graph.__file__,'exec'),graph.__dict__) + original=graph.circuit_class + def subclass(dim): + parent=original(dim) + class Split(parent): + def grouping(self,points): + result=super().grouping(points);choices=([int(x) for x in groups] if isinstance(groups,str) else groups);choice=choices[self._level] if self._level3 and choice: + first,mid,last=0,(len(result)-1)//2,len(result)-1 + requested=(list(range(min(int(choice[5:]),len(result)))) if isinstance(choice,str) and choice.startswith('first') and choice[5:].isdigit() else {1:[first],2:[mid],3:[last],4:[first,mid],5:[first,last],6:[mid,last],7:[first,mid,last],8:[first,first+1],9:[last-1,last]}[choice]) + chosen=[] + for k in requested: + if k not in chosen and 0<=k>common&1 and not(mask&forbidden)) + assert support[x]==expected + return {'status':'PASS all global supports, exact envelopes, disjoint additions and target outputs','nodes':len(c.active),'outputs':len(c.outputs),'sha256':digest.hexdigest()} + +# Coordinate action preserves the literal physical word under a global input relabel. +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word diff --git a/references/frame-compiler/aligned-r11/original/carry_cycle_compiler.py b/references/frame-compiler/aligned-r11/original/carry_cycle_compiler.py new file mode 100644 index 0000000000..d883cbc71d --- /dev/null +++ b/references/frame-compiler/aligned-r11/original/carry_cycle_compiler.py @@ -0,0 +1,338 @@ +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path('/Users/chafreaky/Documents/personal/integer-mult-research-20261008/joint-reclaim/references/frame-compiler/pr48') +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + diff --git a/references/frame-compiler/aligned-r11/original/output_basis_compiler.py b/references/frame-compiler/aligned-r11/original/output_basis_compiler.py new file mode 100644 index 0000000000..517e4cd5e8 --- /dev/null +++ b/references/frame-compiler/aligned-r11/original/output_basis_compiler.py @@ -0,0 +1,407 @@ +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path('/Users/chafreaky/Documents/personal/integer-mult-research-20261008/joint-reclaim/references/frame-compiler/pr48') +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000000000, + "cutoff_log2_input": { + "alpha": 5743214657, + "compact": 22972858625, + "geometry": 3999929625045871804, + "guard": 4205968, + "log_p": 25, + "normalization": 14000000000000000000, + "period": 45945717249, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000000000, + "powers": { + "alpha": { + "exponent": 738942256940779, + "rhs": 112000000000000151632, + "rhs_bits": 67 + }, + "compact": { + "exponent": 738942256940779, + "rhs": 448000000000000606464, + "rhs_bits": 69 + }, + "leaf": { + "exponent": 666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 738942256940779, + "rhs": 224000000000000303192, + "rhs_bits": 68 + }, + "rows": { + "exponent": 738942256940779, + "rhs": 112000000000000151632000, + "rhs_bits": 77 + } + } + }, + { + "log2_input": 28000000000000000000, + "powers": { + "alpha": { + "exponent": 1477884513881558, + "rhs": 224000000000000151632, + "rhs_bits": 68 + }, + "compact": { + "exponent": 1477884513881558, + "rhs": 896000000000000606464, + "rhs_bits": 70 + }, + "leaf": { + "exponent": 1333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1477884513881558, + "rhs": 448000000000000303192, + "rhs_bits": 69 + }, + "rows": { + "exponent": 1477884513881558, + "rhs": 224000000000000151632000, + "rhs_bits": 78 + } + } + }, + { + "log2_input": 56000000000000000000, + "powers": { + "alpha": { + "exponent": 2955769027763116, + "rhs": 448000000000000151632, + "rhs_bits": 69 + }, + "compact": { + "exponent": 2955769027763116, + "rhs": 1792000000000000606464, + "rhs_bits": 71 + }, + "leaf": { + "exponent": 2666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2955769027763116, + "rhs": 896000000000000303192, + "rhs_bits": 70 + }, + "rows": { + "exponent": 2955769027763116, + "rhs": 448000000000000151632000, + "rhs_bits": 79 + } + } + }, + { + "log2_input": 112000000000000000000, + "powers": { + "alpha": { + "exponent": 5911538055526232, + "rhs": 896000000000000151632, + "rhs_bits": 70 + }, + "compact": { + "exponent": 5911538055526232, + "rhs": 3584000000000000606464, + "rhs_bits": 72 + }, + "leaf": { + "exponent": 5333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5911538055526232, + "rhs": 1792000000000000303192, + "rhs_bits": 71 + }, + "rows": { + "exponent": 5911538055526232, + "rhs": 896000000000000151632000, + "rhs_bits": 80 + } + } + }, + { + "log2_input": 224000000000000000000, + "powers": { + "alpha": { + "exponent": 11823076111052464, + "rhs": 1792000000000000151632, + "rhs_bits": 71 + }, + "compact": { + "exponent": 11823076111052464, + "rhs": 7168000000000000606464, + "rhs_bits": 73 + }, + "leaf": { + "exponent": 10666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11823076111052464, + "rhs": 3584000000000000303192, + "rhs_bits": 72 + }, + "rows": { + "exponent": 11823076111052464, + "rhs": 1792000000000000151632000, + "rhs_bits": 81 + } + } + }, + { + "log2_input": 448000000000000000000, + "powers": { + "alpha": { + "exponent": 23646152222104929, + "rhs": 3584000000000000151632, + "rhs_bits": 72 + }, + "compact": { + "exponent": 23646152222104929, + "rhs": 14336000000000000606464, + "rhs_bits": 74 + }, + "leaf": { + "exponent": 21333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 23646152222104929, + "rhs": 7168000000000000303192, + "rhs_bits": 73 + }, + "rows": { + "exponent": 23646152222104929, + "rhs": 3584000000000000151632000, + "rhs_bits": 82 + } + } + } + ], + "practical_runtime_claim": false + }, + "finite_bridge": { + "bit": { + "W": 130468512, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 27 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 843, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "7007/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5278214423139/100000000000000000", + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "endpoint_copy": { + "1": 4073300 + }, + "exterior_23": { + "23": 60740700, + "529": 60740700 + }, + "exterior_25": { + "25": 61581212, + "525": 61581212 + }, + "growth_23": { + "1": 8146600, + "21": 8146600 + }, + "growth_25": { + "1": 8146600, + "23": 8146600 + }, + "internal_23": { + "1": 852147700, + "10": 2711700, + 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witness; inherited all-size transfer remains assumed" +} diff --git a/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/check.py b/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/check.py new file mode 100644 index 0000000000..74f1f8efa7 --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/check.py @@ -0,0 +1,117 @@ +#!/usr/bin/env python3 +"""Screen complete paid profiles from independently replayed axis constructions.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions required') +from pathlib import Path +from collections import Counter +from fractions import Fraction as Q +import importlib.util,argparse,json,subprocess,tempfile,hashlib,os,shlex +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +from producer import check_sources +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m +exact=load('candidate_exact',ROOT/'research/rank-pair-refinement/refine.py') +balanced=load('candidate_assembly',DEP/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') + +def profile(path): + v=json.loads(Path(path).read_text()) + return v['profile'] if 'profile' in v else v + +def calculate(first,second): + profiles=[profile(first),profile(second)] + N=4073300;m=575 + assert [p['h'] for p in profiles]==[23,25] + W=2*N+sum(N//p['v']*p['R'] for p in profiles) + parts={'data':Counter({1:18*N,21:2*N,17:2*N,481:2*N}),'endpoint_copy':Counter({1:N})} + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 + assert p['rank_sum']==h*p['R']+p['loss']==sum(t*n for t,n in enumerate(p['blocks'])) + assert p['loss']==h*(h-1) + parts[f'internal_{h}']=Counter({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + parts[f'exterior_{h}']=Counter({h:bank,m-2*h:bank}) + parts[f'growth_{h}']=Counter({1:2*N,h-2:2*N}) + rows=sum(parts.values(),Counter());assert sum(t*n for t,n in rows.items())==m*W-1846900 + lo,hi,grid=1,71700000000000,10**18 + while lo+11 + result.update(status='Verified finite conditional witness; inherited all-size transfer remains assumed', + source_manifest_sha256=hashlib.sha256((HERE/'SOURCE.json').read_bytes()).hexdigest(), + axes=axes,eventual_bounds=balanced.cutoffs(result['finite_bridge'],result['assembly']), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113',pr71_kappa=Q(previous['kappa']), + relative_gain_pr71=result['kappa']/Q(previous['kappa'])-1, + pr71_complete_profile_exclusion_lower=old_lower)) + comparisons={} + for name,relative in ( + ('previous_pr74','research/balanced-split-frames/certificate.json'), + ('pr82','references/frame-compiler/pr82/research/envelope-balanced/certificate.json'), + ('pr84','references/frame-compiler/pr84/certificates/indexed-cycle-kappa.json')): + prior=json.loads((ROOT/relative).read_text());physical=prior.get('bit',prior) + counts={int(t):n for t,n in physical['child_multiplicities'].items()} + assert sum(t*n for t,n in counts.items())==575*physical['W']-1846900 + lower=exact.moment(arithmetic,575,physical['W'],counts,result['bit_saving'])['lower'] + assert lower>1 and result['kappa']>Q(prior['kappa']) + comparisons[name]=dict(source_certificate=relative,kappa=Q(prior['kappa']),relative_gain=result['kappa']/Q(prior['kappa'])-1,complete_profile_exclusion_lower=lower) + result['additional_comparisons']=comparisons + result=arithmetic.js(result) + path=HERE/'certificate.json' + if record:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:assert result==json.loads(path.read_text()) + print('PASS exact moment, next-grid exclusions, 47 inequalities and seven margins',flush=True) + return result + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--record',action='store_true');args=parser.parse_args();generate(args.record) diff --git a/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/exchange-proof.md b/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/exchange-proof.md new file mode 100644 index 0000000000..09ccd4ed5e --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/exchange-proof.md @@ -0,0 +1,137 @@ +# Paid carried-signal exchanges + +## Scope and provenance + +The selected producer uses Chafik Boukhalfa's pinned PR #84 indexed engine, +with up to three single-edge and three two-edge exchange passes. The local +invariant proof below applies at every accepted exchange and hence through +all passes. Our independently developed one-pass reference implementation +is retained as `exchange_policy.py`; it is not the selected runtime engine. +PR #70, by Alejandro Zarzuelo Urdiales, supplied the carried-signal exchange +method, and Dominik Scholz's PR #76 supplied integer profile-entropy pricing. +This composition and its independent reference work were prepared for +Thomas DiFiore with substantial OpenAI Codex assistance. All inherited +contributors, source notices and licenses remain credited. + +This is a finite construction argument. The inherited all-size compiler, +analytic, fixed-tape, precision, routing, prime-selection and recovery +hypotheses remain assumptions. The search is bounded and makes no claim of +minimum cost or global optimality. + +## Matching invariant + +Each eligible edge has the form `(g,u,i)`: region `g` carries its input +coordinate `i` to use `u`. The inherited graph builder supplies the entire +eligible edge list. Each edge already satisfies the required signal identity, +chronology and frame containment. The exchange policy selects edges from +that list and does not add an eligibility rule. + +For region `g`, let `O_g` be the span over F2 of its independent desired +output rows. Let `C_g` contain the selected input unit rows carried out of +that region. The matching invariants are: + +1. The rows consisting of a basis of `O_g` followed by `C_g` are independent. +2. Every use `u` is assigned to at most one selected edge. +3. The total number of selected edges equals the initial matching cardinality. + +The function `can(e,drop)` recomputes the local binary basis after excluding +`drop`, when present, and checks independence of the new edge's unit row. +Removing a selected row from another region also preserves independence. + +## One-edge exchanges + +Consider an unselected edge `e=(g,u,i)`. + +If `u` is assigned to edge `f`, the policy checks that adding `e` is locally +independent after removing `f` when both edges belong to `g`. When `f` belongs +to another region, it checks independence against the unchanged selected +rows at `g`. Replacing `f` by `e` preserves the assigned use and cardinality. +The donor region either has a checked replacement or loses a row. + +If `u` is unassigned, the policy finds a selected edge `f` in the same region +such that the replacement passes the same independence check. Removing `f` +frees its use, and adding `e` assigns the previously free use `u`. Cardinality +and use uniqueness are again preserved. + +Each accepted replacement strictly lowers the fixed integer discovery cost. +The selected implementation makes three deterministic passes. + +## Two-edge cycles + +Suppose the matching contains + +- `z=(g,u_z,i_z)`, and +- `f=(g',u_f,i_f)`, with `g != g'`. + +The policy considers eligible unselected edges + +- `e=(g,u_f,i_e)`, and +- `w=(g',u_z,i_w)`. + +It checks `can(e,z)` and `can(w,f)`, and requires +`price(e)+price(w) < price(z)+price(f)`. +The two local checks concern different regions. Replacing `{z,f}` with +`{e,w}` therefore preserves local independence in both regions. Every other +region is unchanged. The set of assigned uses is exactly the same, and two +selected edges replace two selected edges. Thus all three invariants hold. + +The implementation removes both old edges before inserting either new edge. +It asserts use uniqueness during insertion, then checks total cardinality +and every region's complete output-plus-carried-row independence at the end. +Each pass is deterministic, with explicit integer and edge-ID tie breaking. +The selected engine stops after at most three passes, or an unchanged pass. +Three-edge cycles are outside the selected policy. + +## Discovery pricing and final coordinates + +The discovery oracle receives each region's core and cover after applying +the selected pricing permutation in `selection.json`. A separately recorded +final permutation can subsequently relabel the compiled word; its complete +profiles are recomputed. The oracle's integer weights are retained +from PR #76: bounded rational logarithms define reproducible approximations +to `t log(t)`. The fixed oracle profile of each eligible transition supplies +its score. Prices remain fixed during the bounded matching passes. + +These prices choose among eligible matchings. Acceptance of the construction +uses the complete physical word and its independently reconstructed paid +profile. An improvement of a discovery score alone is insufficient evidence +for an exponent improvement. + +## Literal implementation and paid cost + +After matching, the inherited compiler constructs independent output rows, +selected carried unit rows, and an independent completion to a full basis. +Its binary elimination synthesizes that invertible basis change as literal +XORs at the common frame. All selected carrying, frame growth, copied +outputs, clearing controls and cleanup are represented in the resulting +word. Changing the matching does not remove any of these charges. + +The complete word is checked on all ordinary-input and arbitrary-dirty +basis vectors in both orientations. Its literal frame transitions determine +the exact fixed-basis recursive child multiset. Copied centers, endpoint +copies, data growth, data blocks and the inherited complex costs are included +by the complete recurrence checker. The exponent is accepted only after +exact moment bounds and the full assembly checks pass. + +## A strict profile-dominance criterion + +A useful sufficient condition can be stated without a discovery score. +At fixed physical width, replace `q` size-1 children by `n_t` size-`t` +children, where every `t>1`, `n_t>=0`, and `sum(t*n_t)=q`. The rank is +unchanged. For any positive saving `a`, the replaced contribution to the +characteristic changes from a factor proportional to `q` to +`sum(t*n_t/t^a)`, which is strictly smaller when at least one child is added. +All unchanged paid terms cancel in this comparison. + +As a checked example on the fixed PR #82 graphs at commit +`3410b940aa26e5876202152dfa7c4f66451ee22c`, the additional two-edge pass produced: + +| Axis | Size-1 children removed | Larger children added | +| --- | ---: | --- | +| h23 | 147 | 63 of size 2; 7 of size 3 | +| h25 | 216 | 56 of size 2; 12 of size 3; 2 of size 7; 6 of size 9 | + +Both ranks and role counts were unchanged, and both complete words passed +independent dirty replay and exact profiles. This establishes strict moment +improvement for every positive saving for that experiment. The selected +aligned graphs have their own separately checked complete costs. diff --git a/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/exchange_policy.py b/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/exchange_policy.py new file mode 100644 index 0000000000..674f81f54e --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/exchange_policy.py @@ -0,0 +1,132 @@ +"""Composable carried-signal exchanges for an inherited frame compiler. + +PR70 exchange methodology: Alejandro Zarzuelo Urdiales. +PR76 integer profile-entropy pricing and one-edge passes: Dominik Scholz, +commit 2333abcea79793fe301b479a7c971cc2be45596c, with OpenAI assistance. +The selected two-edge cycles and factory packaging are prepared for +Thomas DiFiore with substantial OpenAI Codex assistance. Apache-2.0. +Every candidate still needs complete dirty replay and actual paid profiles. +""" +from pathlib import Path +from types import SimpleNamespace +import json,struct,subprocess,importlib.util,sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +MATH_PATH=ROOT/'references/frame-compiler/pr71/scripts/experiments/binary_frame_math.py' +_math_spec=importlib.util.spec_from_file_location('aligned_exchange_pinned_math',MATH_PATH) +_math=importlib.util.module_from_spec(_math_spec) +_math_spec.loader.exec_module(_math) +logs=_math.logs + + +def install(compiler, oracle_executable, h, work_dir, passes=3, + two_passes=1, permutation=None, record_matching=False): + """Mutate this private compiler's matching callback; leave synthesis intact.""" + a=SimpleNamespace(h=h,work_dir=Path(work_dir),passes=passes, + two_passes=two_passes,price_coordinates=permutation is not None) + assert h in (23,25) and passes==3 and two_passes==1, 'Changed selected exchange configuration' + assert permutation is not None, 'Selected policy requires explicit coordinate pricing' + a.work_dir.mkdir(parents=True,exist_ok=True) + executable=Path(oracle_executable) + if permutation is not None:assert sorted(permutation)==list(range(h)) + def permute_mask(bits):return sum(1<>i&1) + original_match=compiler.match + def exchange_match(blocks,uses,enabled): + result=original_match(blocks,uses,enabled) + edges,chosen,right,stats=result + initial_cardinality=len(chosen) + if not a.passes:return result + owner={x:g for g,b in enumerate(blocks) for x in b['nodes']} + path=a.work_dir/'matching-oracle.bin' + with path.open('wb')as stream: + h=a.h;v=h*(h-1)*(h-2)//6 + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks: + frame=tuple(permute_mask(v) for v in b['frame']) if a.price_coordinates else b['frame'] + stream.write(struct.pack('<2QI',*frame,b['rank'])) + oracle=subprocess.Popen([str(executable),str(path)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + weights=[0]+[int(t*sum(logs(t))*10**30//2)for t in range(1,h+1)];cache={} + def entropy(x,y): + if (x,y)not in cache: + oracle.stdin.write(f'{x} {y}\n');oracle.stdin.flush();line=oracle.stdout.readline();assert line + values=list(map(int,line.split()));assert len(values)==h+1 + cache[x,y]=sum(n*w for n,w in zip(values,weights)) + return cache[x,y] + def cost(edge): + g,u,i=edge;p=owner[blocks[g]['inputs'][i]];t=uses[u][1] + return -entropy(g+2,t+2)+entropy(g+2,1)+entropy(0,p+2)+entropy(p+2,t+2) + try: + prices=[] + for j,e in enumerate(edges): + prices.append(cost(e)) + if j%20000==0:print('edge prices',j,len(edges),'pairs',len(cache),flush=True) + finally: + oracle.stdin.close();assert oracle.wait(timeout=10)==0 + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e]));initial=sum(prices[e]for e in chosen) + def can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]=0:continue + if not can(e,z) or not can(w,f):continue + key=(delta,z,w) + if best is None or keystep and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1< 3: + if choice in (1,2,3): + indices=[{1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice]] + elif isinstance(choice,str): + indices=list(range(min(int(choice[5:]),len(groups)))) + selected = [i for i in sorted(set(indices)) if len(groups[i]) == 2] + # Each split adds one group. This cap leaves at least one pair. + selected = selected[:max(0, n-len(groups)-1)] + result = [] + for i, group in enumerate(groups): + result.extend([[point] for point in group] if i in selected else [group]) + assert all(len(group) in (1, 2) for group in result) + assert len(result) < n + assert [point for group in result for point in group] == list(points) + return result + return Partition + + module.circuit_class = selected_class + original_points = module.alternating_points + def anchored_points(dimension, common): + order = original_points(dimension, common) + pairs = [(a,a+1) for a in range(0, dimension-1, 2) if common not in (a,a+1)] + head = [point for pair in pairs[:count] for point in pair] + result = head + [point for point in order if point not in head] + assert sorted(result) == [point for point in range(dimension) if point != common] + return result + module.alternating_points = anchored_points + circuit = module.graph(h) + if ordered: + circuit = reorder(circuit) + assert circuit.verify()['circuit_sha256'] == config['expected_scalar_sha256'] + else: + circuit.verify() + return circuit diff --git a/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/producer.py b/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/producer.py new file mode 100644 index 0000000000..3f43c4a6ad --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/producer.py @@ -0,0 +1,105 @@ +#!/usr/bin/env python3 +"""Aligned recursive partitions, future bases, and coordinated carry exchanges. + +Composition for Thomas DiFiore with OpenAI Codex assistance. Apache-2.0. +The pinned PR71 engine and PR69 graph are retained unchanged. Future-unit +completion follows PR79; weighted carry exchanges follow PR70/76. PR84 contributes exact candidate indexes, additional exchange passes and +future-use output routing. Our multi-pair aligned partitions and pricing +composition are checked as literal +finite words, including all physical frames and arbitrary dirty inputs. +""" +import sys +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +from hashlib import sha256 +import argparse,gzip,importlib.util,json,os,shlex,subprocess,tempfile,types +from concurrent.futures import ProcessPoolExecutor +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +from binary_frame_replay import replay +from partition_graph import graph + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module);return module +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + + +def check_sources(): + for folder in (DEP,ROOT/'references/frame-compiler/pr69',ROOT/'references/frame-compiler/pr82',ROOT/'references/frame-compiler/pr84'): + manifest=json.loads((folder/'SOURCE.json').read_text()) + for name,digest in manifest['files'].items():assert sha256((folder/name).read_bytes()).hexdigest()==digest,name + manifest=json.loads((HERE/'SOURCE.json').read_text()) + required={str((HERE/name).relative_to(ROOT)) for name in ('producer.py','partition_graph.py','exchange_policy.py','future_completion.py','check.py','graph_audit.py','independent_check.py','selection.json')} + assert required<=set(manifest['files']), 'Incomplete selected source closure' + for name,digest in manifest['files'].items():assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + + +def compile_axis(h): + check_sources() + config=json.loads((HERE/'selection.json').read_text())['axes'][str(h)] + assert config['engine']=='indexed-pr84' and config['single_exchange_passes']==3 + assert config['two_exchange_passes']==3 + assert config['output_mode'] in ('baseline','route-late') + price=config['pricing_permutation'];assert sorted(price)==list(range(h)) + source_path=ROOT/'references/frame-compiler/pr84/scripts/experiments/indexed_cycle_engine.py' + source=source_path.read_text() + old="for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank']))" + new="for b in blocks:stream.write(struct.pack('<2QI',*(permute_mask(mask) for mask in b['frame']),b['rank']))" + assert source.count(old)==1;source=source.replace(old,new) + marker=' # Bounded two-donor exchanges after single-edge local optimization.' + assert source.count(marker)==1 + prefix,suffix=source.split(marker);assert suffix.count('for phase in range(3):')==1 + source=prefix+marker+suffix.replace('for phase in range(3):','for phase in range(TWO_PASSES):') + engine=types.ModuleType('aligned_private_engine') + engine.__file__=str(DEP/'scripts/experiments/split_pair_engine.py') + exec(compile(source,str(source_path)+':aligned-indexed','exec'),engine.__dict__) + engine.permute_mask=lambda bits:sum(1<>i&1) + engine.graph=graph;engine.PENDING_COST=True;engine.oracles=[] + engine.OUTPUT_MODE=config['output_mode'];engine.TWO_PASSES=config['two_exchange_passes'] + with tempfile.TemporaryDirectory(prefix='aligned-exchange-compile-') as directory: + work=Path(directory);oracle=work/'oracle' + subprocess.run([*shlex.split(os.environ.get('CXX','c++')),'-O3','-std=c++17','-I',str(DEP/'references/frame-compiler/pr48/scripts/partial_swap'),str(DEP/'references/frame-compiler/pr67/research/slot-cost-rank-pair/profile_oracle.cpp'),'-o',str(oracle)],check=True) + engine.ORACLE_EXE=str(oracle);engine.ORACLE_INPUT=str(work/'oracle.bin') + try:compiled,word=engine.compile_(h,matching=True,reclaim=True,dirty=True) + finally: + for process in engine.oracles:process.stdin.close();assert process.wait(timeout=10)==0 + compiled.pop('seconds',None) + compiled['scalar']=graph(h).verify() + compiled['graph_configuration']=config + compiled['private_engine_sha256']=sha256(source.encode()).hexdigest() + word=relabel(word,config['coordinate_permutation']) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + assert sha256(raw).hexdigest()==config['expected_word_sha256'],'Selected word differs' + path=HERE/f'word-{h}.json.gz' + with path.open('wb') as stream: + with gzip.GzipFile(filename='',fileobj=stream,mode='wb',mtime=0) as archive:archive.write(raw) + receipt=replay(path) + axis=dict(configuration=config,compiled=compiled,replay=receipt,word_sha256=sha256(raw).hexdigest(),gzip_sha256=sha256(path.read_bytes()).hexdigest()) + (HERE/f'axis-{h}.json').write_text(json.dumps(axis,indent=2)+'\n') + print(f'PASS fresh aligned/exchange word h={h}, roles={receipt["roles"]}',flush=True) + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--h',type=int,choices=(23,25));args=parser.parse_args() + if args.h:compile_axis(args.h) + else: + with ProcessPoolExecutor(max_workers=2) as pool:list(pool.map(compile_axis,(23,25))) diff --git a/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/profile-23.json b/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/profile-23.json new file mode 100644 index 0000000000..a217fee46b --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/profile-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 26409, + "loss": 506, + "rank_sum": 607913, + "field_prime": 2305843009213693951, + "frames": 78515, + "distinct_matrices": 40708, + "crt_matrices": 5083, + "crt_disagreements": 0, + "blocks": [ + 0, + 370499, + 11858, + 15932, + 4919, + 4023, + 3213, + 2140, + 1959, + 1435, + 1179, + 870, + 837, + 498, + 407, + 295, + 267, + 74, + 324, + 0, + 171, + 23, + 0, + 0 + ] +} diff --git a/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/profile-25.json b/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/profile-25.json new file mode 100644 index 0000000000..f33aaaa4ef --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/profile-25.json @@ -0,0 +1,40 @@ +{ + "h": 25, + "v": 2300, + "R": 34772, + "loss": 600, + "rank_sum": 869900, + "field_prime": 2305843009213693951, + "frames": 108758, + "distinct_matrices": 54701, + "crt_matrices": 5955, + "crt_disagreements": 0, + "blocks": [ + 0, + 504794, + 18246, + 19029, + 7745, + 4399, + 4490, + 3536, + 3135, + 2207, + 2256, + 1548, + 1493, + 910, + 909, + 469, + 581, + 263, + 210, + 59, + 387, + 101, + 169, + 25, + 0, + 0 + ] +} diff --git a/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/selection.json b/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/selection.json new file mode 100644 index 0000000000..ef0b559d02 --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74-aligned/research/aligned-exchange-frames/selection.json @@ -0,0 +1,159 @@ +{ + "axes": { + "23": { + "groups": [ + "first6", + 1, + 1 + ], + "anchor_pairs": 6, + "coarse_word": "hhh", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "engine": "indexed-pr84", + "future_unit_completion": true, + "single_exchange_passes": 3, + "two_exchange_passes": 3, + "output_mode": "baseline", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "pricing_permutation": [ + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 18, + 17, + 19, + 20, + 21, + 22, + 0, + 1, + 3, + 2, + 4 + ], + "coordinate_permutation": [ + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 18, + 17, + 19, + 20, + 21, + 22, + 0, + 1, + 3, + 2, + 4 + ], + "expected_scalar_sha256": 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Rank-first reclamation on interval-strip pair assembly, 8 October 2026 +Composition and exact profile witness: Dominik Scholz, with substantial OpenAI +GPT-6 Astra / Codex assistance. The PR #60 descending-frame-rank compiler by +Chafik Boukhalfa is reused unchanged on Avi Eisenberg's PR #62 scalar graph. +The joint frame compiler and paid reclamation are eumemic's PR #57, developed +with OpenAI Codex assistance. PR #62 records Anthropic Claude assistance. +This composition improves actual fixed-basis block profiles with unchanged +role counts; no new slot-priority rule or scalar graph is claimed. All prior +contributors, licenses, compiler arguments and conditional analytic/tape +interfaces remain credited. See research/rank-pair/PROOF.md. + +Ordered scalar frames, minimum-raise reclamation and coordinate relabeling +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. +The new finite construction and exact arithmetic certificates are in +research/ordered-frames, with an earlier parameter refinement in +research/rank-pair-refinement. These build on Dominik Scholz's PR #63 +composition, Chafik Boukhalfa's PR #60 reclamation compiler, Avi Eisenberg's +PR #62 scalar graph and eumemic's PR #57 reversible frame compiler. +Concurrent PR #65/#67 work is acknowledged in the proof. All inherited +licenses, author notices and conditional proof boundaries remain in force. + +Balanced split frames with core node ordering and coordinate relabeling +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. +This composition combines eumemic's PR69 coarse column sums, Chafik Boukhalfa's +PR71 anchored split/next-use-live compiler, and the earlier PR74 node ordering +and coordinate relabeling. Rohan Garg's PR59 split operation, Avi Eisenberg's +PR62 scalar graph, Rohan Arun's PR65/67 schedules and profile-cost selection, +Dominik Scholz's PR63/68 composition and pending controls, and eumemic's PR57 +compiler remain credited. Original source closures and notices are preserved +under references/frame-compiler/pr69 and pr71; all preceding licenses apply. +See research/balanced-split-frames/PROOF.md for the finite conditional scope. diff --git a/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/PROOF.md b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/PROOF.md new file mode 100644 index 0000000000..7244811413 --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/PROOF.md @@ -0,0 +1,145 @@ +# A paid composition of balanced coarse sums, split recursion and frame order + +## Statement and boundary + +The complete finite profile below certifies + +`kappa = 10366199626713/200000000000000000` + +for the inherited conditional bound `T(n)=O(n(log n)^(1-kappa))`. +The all-size compiler, analytic transfer, fixed-alphabet tape simulation, +precision, routing, prime selection and exact recovery hypotheses are inherited. +Finite source checks and arithmetic do not establish those general hypotheses. + +## 1. Pinned ingredients + +PR #71 is frozen at `1bef94fd40a746452548c84a4a8f8834670a3113` in +`references/frame-compiler/pr71/`, including its complete consumed source +closure, selected words, data interfaces, licenses, notices and root documents. +Its own source manifest is preserved without re-pinning. PR #69's original +coarse-sum compiler and notices are frozen at +`91aa1f17e6e3fc063241686a41a34ddd0dc24c50` in the adjacent `pr69/` archive. + +The new producer reads PR #69's literal BEFORE/AFTER replacement, applies it +exactly once to the archived PR #62 scalar graph consumed by PR #71, and keeps +PR #71's `[1,1,2]` split choices and lowest-intact-pair anchoring. The original +source files are unchanged. After reordering, it uses the archived PR #71 +compiler and its next-use profile-cost selection unchanged. + +## 2. Shared intermediate sums preserve the scalar map + +For two disjoint groups A and B, replace the chain forming +`sum_{a in A,b in B} e(a,b)` by +`sum_{b in B} (sum_{a in A} e(a,b))`. +Each operand support occurs exactly once. The nested sums are disjoint, +so this is an equality over the inherited scalar field. Existing node +interning shares the column intermediates with later strip computations. +The singleton cases and strictly decreasing recursive partitions retain the +same identity. No negative coefficient or cancellation is introduced. + +`graph_audit.py` reconstructs dense global triple-coordinate supports using +its own recurrence. For each dimension it checks every input, addition, +core, cover and prescribed output, and compares the complete output support +inventory with original PR #71. This checks 67,460 / 94,993 additions and +5,336 / 6,925 outputs. Original PR #71 has 68,771 / 96,718 additions. + +## 3. Legal node order and fully charged live reclamation + +Keep source IDs fixed. Group remaining active nodes by their original +(core, cover), retaining their original order within each group. Sort groups +lexicographically by + +`(popcount(cover)-popcount(core), -core, cover, first_original_node)`. + +Remap every operand and output ID, clear support caches indexed by old IDs, +and verify again. The independent audit proves that each literal edge and +output is preserved, every operand precedes its consumer, every envelope is +unchanged, and this is exactly the selected renumbering. Matching is recomputed +on the resulting graph and the compiler uses its natural region order. + +PR #71's unchanged pending live controls enter a clearing basis only when +their current frame is contained in the present frame and that frame is +contained in their next-use frame. Controls retain their values. The complete +word contains every chosen clearing XOR and every required frame raise. +The discovery score is never substituted for the actual charged profile. + +Both complete words are regenerated with dirty-basis checks enabled. A +separate serialized-word checker replays every input and arbitrary dirty +basis column in both orientations. The final roles are 27,136 / 35,744. + +## 4. Coordinate relabeling and the data family + +Apply each selected permutation to the frame core/cover masks, source-triple +indices, scatter target-triple indices, output common points and output +triples. Literal XORs, scratch IDs and frame IDs remain unchanged. The complete +permutations are frozen in `selection.json`; both relabeled words are replayed. + +For permutation matrix P, both fixed bases `I+J` and the inverse metric +`I-J/9` commute with P. Envelope projectors therefore transform by conjugation. +Containment and every legal incidence remain valid. Ordered contiguous child +profiles can change, and every one is regenerated from the literal word +using the inherited exact bounded-minor/CRT profiler, with zero disagreements. + +Each coordinate permutation induces a bijection on the complete triple set. +Consequently the complete two-axis data-block family is only reindexed: its +aggregate inherited profile and rational recovery cases remain valid. Copied +centers, endpoints and data growth remain explicitly charged. + +## 5. Complete recurrence and assembly + +Let `N=4073300`, `m=575`, and let `R_h` and `b_{h,t}` be the verified role count +and exact internal profile. The physical width is + +`W = 2N + (N/1771)R_23 + (N/2300)R_25 = 133862024`. + +The complete child multiset includes: + +- data: `18N` children of size 1 and `2N` each of sizes 21, 17 and 481; +- paid endpoint copies: `N` additional size-1 children; +- internal axis h: `(N/binom(h,3))*b_{h,t}` children of size t; +- exterior axis h: `(N/binom(h,3))*R_h` each of sizes h and `m-2h`; +- data growth per axis: `2N` each of sizes 1 and `h-2`. + +The total rank is `76968816900 = mW-1846900`; maximum child size is 529. +The exact characteristic is +`M(a)=sum_t (t*n_t/(mW))*exp(a*log(m/t))`. +At `a=25916842362591/500000000000000000`, a rigorous upper bound is below 1. +At `a+10^-18`, a rigorous lower bound is above 1. Positive logarithms make +the characteristic increasing. The complete original PR #71 profile is +separately excluded at the new accepted saving. + +Production arithmetic uses the retained rational logarithm/exponential +helper. The independent checker derives the complete paid multiset and uses +40 exact atanh terms for logarithms and Taylor degree 10 with a geometric +exponential tail. It imports no production arithmetic and checks each of the +47 assembly slacks and seven margins independently. The next kappa grid value +is rejected. Negative controls reject omitted paid children, fabricated slacks +and incorrect source hashes. + +Use positive backoff `10^-18`. Since W is below `2^27`, its `bit_length()` is +27. The product-row coefficient becomes `9*27+20*30=843`. Keeping degree 2000 +and suffix slope 8000 gives degree gap `2000-(51/25)*843=7007/25`. +These values are derived and checked; no stale predecessor constants remain. +Arithmetic cutoff bounds are not complete operational runtime thresholds. + +## Credits + +The composition, core-order continuation, coordinate choices, packaging and +independent audits were prepared for Thomas DiFiore with substantial OpenAI +Codex assistance. Coarse-sum reassociation is eumemic's PR #69. Anchored split +frames and next-use-aware live selection are Chafik Boukhalfa's PR #71. +Rohan Garg supplied the split operation (#59); Avi Eisenberg supplied interval +strips and core-aware pair assembly (#62); Rohan Arun supplied region schedules +and profile-cost selection (#65/#67); Dominik Scholz supplied ranked composition +and pending live controls (#63/#68); eumemic supplied the reversible compiler +and physical/profile checking interfaces (#57). Our earlier PR #74 supplied the +core node ordering and coordinate-relabeling continuation used here. + +The preserved archives retain all earlier credits, including RaD/hipotures, +icekylinx, James Chang, Zhihao Chen, Aurel Prosz, Swapnil Jain, Alejandro Zarzuelo +Urdiales, Douglas Colkitt, OpenAI and Harvey–van der Hoeven, and predecessor +AI-assistance disclosures. No predecessor authorship or endorsement of this +composition is implied. Existing licenses and notices remain in force. + +Concurrent PR #75–#79 contributions, including carry exchanges, balanced split +constructions and coordinate flags, are acknowledged. No priority claim is made. diff --git a/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/README.md b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/README.md new file mode 100644 index 0000000000..5784b8b928 --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/README.md @@ -0,0 +1,70 @@ +# Balanced split frames with shared sums and reusable live controls + +**κ = 10366199626713 / 200000000000000000 = 0.000051830998133565** + +The conditional bound is `T(n) = O(n (log n)^(1-kappa))`. +This is **0.9788258% above our original PR #74 result**, **0.8097927% above +pinned PR #71**, and **0.8082664% above PR #75's claim observed on 8 October +2026**. The later PR #79 claim `5.1745625472866e-5`, observed at 19:55 UTC on the same +date, is also below this result by **0.1649853%**. These compare asymptotic exponent savings; they are not measured +multiplication speedups. + +| Quantity | Original PR #74 | Pinned PR #71 | This composition | +| --- | ---: | ---: | ---: | +| h23 auxiliary roles | 27,698 | 27,455 | 27,136 | +| h25 auxiliary roles | 36,310 | 36,015 | 35,744 | +| Physical width | 136,157,010 | 135,075,665 | 133,862,024 | +| Conditional κ | 5.132858076595e-5 | 5.1414646104039e-5 | 5.1830998133565e-5 | + +## Construction + +Compose eumemic's PR #69 column-balanced coarse sums with Chafik Boukhalfa's +PR #71 anchored split recursion and next-use-aware live reclamation. Apply +our original-envelope node order before carrier matching, then relabel the +geometric coordinates and recompute the actual fixed-basis profiles. + +The balanced graph has 67,460 / 94,993 active additions, compared with +PR #71's 68,771 / 96,718. Every prescribed output is unchanged. The complete +physical words pay for all XORs, frame raises, copied centers and data blocks. +The width now lies below `2^27`; its role-logarithm and product-row constants +are recomputed in the exact certificate. + +## Evidence and reproduction + +- [Proof, scope and contributor credits](PROOF.md) +- [Exact certificate](certificate.json) +- [Selected graph and coordinate choices](selection.json) +- [Immutable source manifest](SOURCE.json) +- [Independent dense scalar audit](graph-audit.json) +- [Independent exact arithmetic audit](independent-audit.json) +- [Verification receipt](validation.json) and [raw log](verification.log) + +Use Python 3.11 or newer and a C++17 compiler with unsigned 128-bit support: + +```sh +make balanced-split-frames-verify +``` + +This regenerates both words from pinned sources, checks their selected raw +hashes, audits the complete scalar graph, independently replays every input +and dirty basis vector in both orientations, reconstructs every literal frame +transition and exact profile, and checks the full paid recurrence and assembly. +The two replay dimensions contain 30,678 / 40,344 basis coordinates. +Both profiles have zero CRT disagreements. Independent arithmetic verifies +all 47 strict inequalities, seven margins, adjacent-grid rejection, and +exclusion of the complete pinned PR #71 profile at the new bit saving. + +The earlier full-suite receipt in `../ordered-frames/validation.json` covers +that historical source state. Current upstream checks and formal packages +remain separate CI jobs. The new source archives retain original notices +and original root documentation so predecessor pins remain unchanged. + +All inherited analytic, all-size compiler, fixed-tape, precision, routing, +prime-selection and recovery hypotheses remain assumed. This is a verified +finite conditional witness, with no global-optimality or practical-speed claim. + +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. Original +PR #74 remains available in `../ordered-frames/`; all predecessor credits and +licenses remain applicable. + +Concurrent PR #75–#79 work is acknowledged; no priority claim is made. diff --git a/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/SOURCE.json b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/SOURCE.json new file mode 100644 index 0000000000..06404d9283 --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/SOURCE.json @@ -0,0 +1,21 @@ +{ + "files": { + "references/frame-compiler/pr69/SOURCE.json": "928fa8cce0964a6894af3f40cbde6d983aac395336e5277f751c9cbf1b07957f", + "references/frame-compiler/pr71/SOURCE.json": "1c79309362044dd386f72946ccb2e258e98d07d7239ea89d8a8646338d24228a", + "research/balanced-split-frames/check.py": "45fb95cb2a6b0573efbe37938c149936f4aa4fff1a88425380af7bc59239b4ae", + "research/balanced-split-frames/graph_audit.py": "b95cf9269fbcaf7f7b9732b28d7a8b790feefc262e86a36de33a92ab7906a8b3", + "research/balanced-split-frames/independent_check.py": "02dd998ebe68f111a42657e1591416b28b618a8d58bbd4fb0686d3afd929db1a", + "research/balanced-split-frames/producer.py": "ec94e4b7af370f7e921fffa3679e80d081a672dbd3ff198043edfb0dc7a9cc9d", + "research/balanced-split-frames/profile-23.json": "7f61525499f56ccc3a183a2741ef823cce30423475fa586ba7d36610b5b66844", + "research/balanced-split-frames/profile-25.json": "9b4d0647e3667af963c164c048c6ea750d90397b046336ede5a5b6902a9f6473", + "research/balanced-split-frames/selection.json": "cbc616540af0ff5b63a90a920c70acd660fbb67052e4dc19889fe0443f2129f4", + "research/balanced-split-frames/transitions-23.json": "0e9b6bbb1f9f08b34077bb93a60b39c2d61cf8f1329c884fd47326bf32bfac60", + "research/balanced-split-frames/transitions-25.json": "3bffd56836edefb309825f4ba303dc27ae88455aa7c8fc918af3ef24d82caee3", + "research/balanced-split-frames/word-23.json.gz": "956b886339ccbd3d599c5e0ec403b870958d052f3442067e8f12a56318e9525d", + "research/balanced-split-frames/word-25.json.gz": "ea090af1c4b56b7dae31d1f0d3fece4417677160f07c372e0455d7f8ac31c7b0", + "research/rank-pair-refinement/refine.py": "a19a79ea064fe66cb5f4e2971d6ab277cdfd452975c539e23066174533430691" + }, + "pr69_commit": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "pr71_commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "scope": "Selected sources and finite inputs. The archived PR69 and PR71 manifests bind the complete inherited source closure; generated axis receipts and arithmetic/audit certificates are checked outputs." +} diff --git a/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/certificate.json b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/certificate.json new file mode 100644 index 0000000000..6a3cfa48df --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/certificate.json @@ -0,0 +1,740 @@ +{ + "W": 133862024, + "accepted": { + "lower": "99999999999999999979924873504956311258242134978917/100000000000000000000000000000000000000000000000000", + "strict_gap": "20075126495043683558076755370663/100000000000000000000000000000000000000000000000000", + "terms": { + "1": { + "lower": "578243869104998674370968149468068831065643870861/25000000000000000000000000000000000000000000000000", + "upper": 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"94434876046990177945341754110010142349456588841/100000000000000000000000000000000000000000000000000", + "upper": "94434876046990177945341754110010147244624766813/100000000000000000000000000000000000000000000000000" + } + }, + "upper": "100000000000000000026221541888937804027773835325287/100000000000000000000000000000000000000000000000000" + }, + "roles": [ + 27136, + 35744 + ], + "source_manifest_sha256": "c933a96c636f1e22e02be6fb775a9da2cd14c11fa2d07ba75af17c7e99f00049", + "status": "Verified finite conditional witness; inherited all-size transfer remains assumed" +} diff --git a/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/check.py b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/check.py new file mode 100644 index 0000000000..0630cfc19a --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/check.py @@ -0,0 +1,104 @@ +#!/usr/bin/env python3 +"""Screen complete paid profiles from independently replayed axis constructions.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions required') +from pathlib import Path +from collections import Counter +from fractions import Fraction as Q +import importlib.util,argparse,json,subprocess,tempfile,hashlib,os,shlex +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +from producer import check_sources +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m +exact=load('candidate_exact',ROOT/'research/rank-pair-refinement/refine.py') +balanced=load('candidate_assembly',DEP/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') + +def profile(path): + v=json.loads(Path(path).read_text()) + return v['profile'] if 'profile' in v else v + +def calculate(first,second): + profiles=[profile(first),profile(second)] + N=4073300;m=575 + assert [p['h'] for p in profiles]==[23,25] + W=2*N+sum(N//p['v']*p['R'] for p in profiles) + parts={'data':Counter({1:18*N,21:2*N,17:2*N,481:2*N}),'endpoint_copy':Counter({1:N})} + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 + assert p['rank_sum']==h*p['R']+p['loss']==sum(t*n for t,n in enumerate(p['blocks'])) + assert p['loss']==h*(h-1) + parts[f'internal_{h}']=Counter({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + parts[f'exterior_{h}']=Counter({h:bank,m-2*h:bank}) + parts[f'growth_{h}']=Counter({1:2*N,h-2:2*N}) + rows=sum(parts.values(),Counter());assert sum(t*n for t,n in rows.items())==m*W-1846900 + lo,hi,grid=1,71700000000000,10**18 + while lo+11 + result.update(status='Verified finite conditional witness; inherited all-size transfer remains assumed', + source_manifest_sha256=hashlib.sha256((HERE/'SOURCE.json').read_bytes()).hexdigest(), + axes=axes,eventual_bounds=balanced.cutoffs(result['finite_bridge'],result['assembly']), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113',pr71_kappa=Q(previous['kappa']), + relative_gain_pr71=result['kappa']/Q(previous['kappa'])-1, + pr71_complete_profile_exclusion_lower=old_lower)) + result=arithmetic.js(result) + path=HERE/'certificate.json' + if record:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:assert result==json.loads(path.read_text()) + print('PASS exact moment, next-grid exclusions, 47 inequalities and seven margins',flush=True) + return result + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--record',action='store_true');args=parser.parse_args();generate(args.record) diff --git a/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/producer.py b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/producer.py new file mode 100644 index 0000000000..8d68303a3b --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/producer.py @@ -0,0 +1,132 @@ +#!/usr/bin/env python3 +"""Balanced coarse sums + anchored split/live frames + core ordering and coordinates. + +Composition for Thomas DiFiore with OpenAI Codex assistance. Apache-2.0. +PR69 coarse sums: eumemic. PR71 split/live composition: Chafik Boukhalfa. +Graph: Avi Eisenberg PR62; split operation: Rohan Garg PR59; reclamation: +Rohan Arun PR65/67, Dominik Scholz PR63/68, eumemic PR57. Original notices +and exact sources are retained under references/frame-compiler/pr69 and pr71. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +from hashlib import sha256 +import argparse,ast,gzip,importlib.util,json,types +from concurrent.futures import ProcessPoolExecutor +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +import split_pair_graph as provider +import split_pair_compiler as ancestor +from binary_frame_replay import replay + + +def check_sources(): + for folder in (DEP,ROOT/'references/frame-compiler/pr69'): + manifest=json.loads((folder/'SOURCE.json').read_text()) + for name,digest in manifest['files'].items(): + assert sha256((folder/name).read_bytes()).hexdigest()==digest,name + manifest=json.loads((HERE/'SOURCE.json').read_text()) + required={str((HERE/name).relative_to(ROOT)) for name in ('producer.py','check.py','graph_audit.py','independent_check.py','selection.json')} + assert required <= set(manifest['files']), 'Incomplete selected source closure' + for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + + +def reorder(c): + groups={} + for x in sorted(c.active): + if c.args[x]: groups.setdefault((c.core[x],c.union[x]),[]).append(x) + def key(item): + (core,cover),nodes=item + return cover.bit_count()-core.bit_count(),-core,cover,min(nodes) + ids=list(range(len(c.inputs)+1))+[x for _,nodes in sorted(groups.items(),key=key) for x in nodes] + mapping={x:i for i,x in enumerate(ids)} + args,core,cover,provenance=c.args,c.core,c.union,c.provenance + c.args=[tuple(mapping[y] for y in args[x]) if args[x] else None for x in ids] + c.core=[core[x] for x in ids];c.union=[cover[x] for x in ids] + c.provenance=[provenance[x] for x in ids] + c.active={mapping[x] for x in c.active};c.outputs={k:mapping[v] for k,v in c.outputs.items()} + c.support_in.cache_clear() + c.verify() + return c + + +def graph(h,ordered=True): + source=Path(provider._graph.__file__).read_text() + original=ROOT/'references/frame-compiler/pr69/scripts/experiments/balanced_coarse_compiler.py' + replacements={} + for node in ast.parse(original.read_text()).body: + if isinstance(node,ast.Assign): + for target in node.targets: + if isinstance(target,ast.Name) and target.id in ('BEFORE','AFTER'): + replacements[target.id]=ast.literal_eval(node.value) + assert source.count(replacements['BEFORE'])==1 + module=types.ModuleType('balanced_split_private_graph');module.__file__=provider._graph.__file__ + exec(compile(source.replace(replacements['BEFORE'],replacements['AFTER']),module.__file__+':balanced-coarse','exec'),module.__dict__) + previous=provider._graph + try: + provider._graph=module + c=provider.graph(h) + finally: + provider._graph=previous + return reorder(c) if ordered else c + + +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + +def compile_axis(h): + check_sources() + config=json.loads((HERE/'selection.json').read_text())['axes'][str(h)] + previous_graph,previous_order=provider.graph,provider.ordered_build + # graph() calls the original provider; keep that callable private while + # the inherited driver resolves the selected composed graph dynamically. + original_graph=previous_graph + def selected_graph(dimension): + provider.graph=original_graph + try:return graph(dimension) + finally:provider.graph=selected_graph + try: + provider.graph=selected_graph + provider.ordered_build=lambda original,dimension:original + compiled,word=ancestor.compile_axis(h) + finally: + provider.graph,provider.ordered_build=previous_graph,previous_order + compiled['graph_configuration']=config + word=relabel(word,config['coordinate_permutation']) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + path=HERE/f'word-{h}.json.gz' + with path.open('wb') as stream: + with gzip.GzipFile(filename='',fileobj=stream,mode='wb',mtime=0) as archive:archive.write(raw) + receipt=replay(path) + assert sha256(raw).hexdigest()==config['expected_word_sha256'] + axis=dict(configuration=config,compiled=compiled,replay=receipt, + word_sha256=sha256(raw).hexdigest(),gzip_sha256=sha256(path.read_bytes()).hexdigest()) + (HERE/f'axis-{h}.json').write_text(json.dumps(axis,indent=2)+'\n') + print(f'PASS fresh balanced/split/core word h={h}, roles={receipt["roles"]}',flush=True) + + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--h',type=int,choices=(23,25));args=parser.parse_args() + if args.h:compile_axis(args.h) + else: + with ProcessPoolExecutor(max_workers=2) as pool:list(pool.map(compile_axis,(23,25))) diff --git a/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/profile-23.json b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/profile-23.json new file mode 100644 index 0000000000..013f4e59c7 --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/profile-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27136,"loss":506,"rank_sum":624634,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38292,"crt_matrices":5488,"crt_disagreements":0,"blocks":[0,355721,21666,6948,6524,3093,4314,2400,3266,1501,2094,1008,1374,586,732,353,307,139,62,16,0,23,0,0]} diff --git a/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/profile-25.json b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/profile-25.json new file mode 100644 index 0000000000..1e3b6b89aa --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/profile-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35744,"loss":600,"rank_sum":894200,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52202,"crt_matrices":7623,"crt_disagreements":0,"blocks":[0,490052,26188,13531,7191,4637,5355,4229,3705,2610,2620,2080,1814,1357,1070,868,612,463,233,56,141,0,71,25,0,0]} diff --git a/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/selection.json b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/selection.json new file mode 100644 index 0000000000..57cf3b6b65 --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr74/research/balanced-split-frames/selection.json @@ -0,0 +1,86 @@ +{ + "source_pr71": "1bef94fd40a746452548c84a4a8f8834670a3113", + "source_pr69": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "axes": { + "23": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 22, + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 20, + 19, + 21 + ], + "expected_word_sha256": "8dc6696a274e70ca0af3fc49c4bdede362adaedc8dc322f335e3dab499f1ed48" + }, + "25": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 2, + 1, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "expected_word_sha256": "2c923afe366219ee3fffc9db063c91e44cdf7cbbdb62246b8e6a297dc440b577" + } + } +} diff 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"ede836ef555e700601810f4beea31057af88ce7ff4dae21fceba44918be26551" + }, + "research/envelope-balanced/compiler.py": { + "git_blob": "b4d43e88aaa65aad4b3d83decd3f34947b4b6962", + "sha256": "1716168a06fa5385c41232b40f343a98b322dec3718cb641f0042aa8f5610738" + }, + "research/envelope-balanced/flag_engine.py": { + "git_blob": "d210d9336bf92edf03eb9b6d89b9e66b22a15a54", + "sha256": "e42a43947c8d575b764683d88ddc26a290618ac79028337b3b50daedc8475183" + }, + "research/envelope-balanced/order-23.json": { + "git_blob": "035f01df59be3312e30ec692754d3a331a766799", + "sha256": "def92cd69f3fba2986c7a230ece45f9eb63fd38fef512d055bf0adffe9edfa82" + }, + "research/envelope-balanced/order-25.json": { + "git_blob": "ec2a8aa14c0b0c07de47b7314b535aa1385c0756", + "sha256": "47632a745319452f4237754ccb1793e7d0ae455654b68c6a31eb2a79a0f98b9f" + }, + "research/envelope-balanced/verify.py": { + "git_blob": "e74b03c41417c914bcf0e4e8fd0150a27e61aaef", + "sha256": "bd767d460a85414ca320a449705860a376bee42cb8ce0734233a8e9706ad4fc5" + } + }, + "repo": "rohanarun/integer-mult-bounds", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/82" +} diff --git a/references/frame-compiler/aligned-r11/references/pr82/LICENSE b/references/frame-compiler/aligned-r11/references/pr82/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr82/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Balanced coarse split composition (2026-10-08) +--------------------------------------------- +Eumemic / @eumemic supplied PR69's balanced coarse sums, with OpenAI Codex +assistance. Alejandro Zarzuelo Urdiales / @alejandrozu supplied PR70's bounded +carry-exchange strategy with the AI disclosures retained in the source archive. +Chafik Boukhalfa / @chafreaky, with OpenAI Codex assistance, selected the row/ +half-plane coarse rules, future-compatible unit completion, exact integer-price +carry adaptation, composition and this certificate package. The PR71 anchored +split vector, schedules, arithmetic, pending controls and their contributor +chain are retained as credited above. Original PR69/70 sources, licenses and +notices and the complete published PR71 baseline are preserved under +references/frame-compiler. All earlier notices remain applicable. diff --git a/references/frame-compiler/aligned-r11/references/pr82/research/envelope-balanced/README.md b/references/frame-compiler/aligned-r11/references/pr82/research/envelope-balanced/README.md new file mode 100644 index 0000000000..77486a38c2 --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr82/research/envelope-balanced/README.md @@ -0,0 +1,127 @@ +# Envelope ordering inside balanced split compilation + +The finite conditional witness gives **kappa = 5203279888519/100000000000000000 = 5.2032798885190e-05**, +0.49049670% above PR80. Bit saving is 13008876609597/250000000000000000. +This is a draft pending the full expanded repository verification. + +PR80 selected already-compiled axes from PR76 and PR79. Here we compose +their construction methods before compilation on both axes: PR79's balanced +coarse graph and future-compatible unit completion; PR76/PR74's envelope +node ordering; three passes of PR79/PR70's bounded carry exchanges; and +PR78's geometric coordinate flags. h23 uses the half-plane coarse choice +and cover-core schedule; h25 uses row coarse sums and reverse-node schedule. +Both retain the anchored [1,1,2] split vector and exact next-use profile costs. +All archived sources are unchanged. `compiler.py` is the portable composition. +At h25 the discovery oracle receives coordinate-permuted frame masks, so its +costs refer to the final flag rather than the original coordinate order. +`flag_engine.py` differs from PR79's engine only in that oracle frame writer +and an attribution comment; operations, eligibility, independence and dirty +checks are unchanged. This changes only heuristic selection among legal +choices. Its final word is still independently replayed and exactly priced. +At h23 oracle pricing retains the original coordinate order. + +| Quantity | PR80 | This witness | +|---|---:|---:| +| h23 auxiliary roles | 27256 | 27075 | +| h25 auxiliary roles | 35684 | 35500 | +| Physical width | 134031764 | 133289600 | +| Total recursive rank | 77066417400 | 76639673100 | +| Deficit | 1846900 | 1846900 | + +## General compatibility argument + +Balanced coarse parenthesization changes only how the same Cartesian-product +edge sums are evaluated. The weighted scalar identities and recursively +contracting anchored partition are inherited from PR79's proof. Envelope +ordering then applies a bijection to non-source scalar node IDs, grouping +nodes by (core, cover), preserving the order inside each group and every +argument, output and provenance reference. It changes no scalar linear form +or frame. The graph verifier is rerun after this relabeling. Dependency and +carrier-eligibility checks in the compiler remain enabled. + +Future-compatible completion chooses independent unit rows after the desired +outputs and retained carriers. Any accepted independent completion is a full +invertible basis; the unchanged synthesis emits its literal XOR operations. +Bounded carrier exchanges preserve matching cardinality, unique uses and +independence of the output-plus-retained-input rows. These choices can change +each other's costs, so the words are recompiled and every profile recomputed; +we do not add reported savings or assume independent numerical gains. + +All clearing targets and controls remain charged. Both frame-containment +checks for pending controls remain enabled. The compiler and independent +replay verify the full arbitrary-dirty-role wrapper in both orientations. +Independent axis implementations expose the same source triple lines, fixed +I+J basis, terminal frames and scatter identity. Hence the complete tensor/data +construction is unchanged. Every endpoint/copy/data-growth/complex term is +retained exactly once. The fixed-width bridge is derived from the actual W. + +## General relabeling argument + +Let P be a permutation matrix on the h coordinates. It commutes with J, +so P commutes with the fixed basis L = I+J and preserves the form I-J/9. +For a core/cover frame F(C,U), the relabeled projector is +P F(C,U) P^-1 = F(P C,P U). Consequently, every frame inclusion, rank, +nondegeneracy condition, projector denominator bound and elementary role +operation is preserved. The existing exact CRT bounds apply unchanged. + +Relabel each input triple T to P T, each output (c,T) to (P c,P T), +each frame mask by P, and each scatter row by the induced triple permutation. +The role slots and literal XOR operations do not change. This conjugates +the complete linear word by the input/output permutation and therefore +preserves its identity on every ordinary input and arbitrary dirty role. +The verifier independently replays that identity in both orientations. + +The data component sums over every pair of source triples. Independent +coordinate permutations on the two axes induce a bijection on that complete +Cartesian product. Hence its existing complete histogram, copied-center +costs and endpoint corrections are unchanged. This argument uses the full +case set; it would not justify retaining a selected subset's histogram. + +North-east corner rank profiles depend on the fixed coordinate order. +Conjugating by P can change which adjacent pivots form a recursive block, +even though total rank is unchanged. We regenerate these profiles from the +actual relabeled words rather than assuming their costs are invariant. +Both dimensions use the selected orders in order-23.json and order-25.json. + +## Reproduction and validation + +From the repository root with assert-enabled Python 3.11+ and C++17: + +```sh +python3 research/envelope-balanced/verify.py --regenerate +(cd research/envelope-balanced && python3 -m unittest test_controls -v) +make verify +``` + +The regeneration option launches two isolated compiler processes and requires +both original words to reproduce byte-for-byte. The verifier then regenerates +the coordinate-permuted words, performs independent full input/dirty replay, +reconstructs all transitions, and regenerates exact bounded-minor/CRT profiles. +The complete paid child list is reconstructed; independent rational moment +bounds, 47 strict inequalities, seven margins and both next-grid exclusions +are checked. The complete PR76, PR79 and PR80 child lists are each excluded at +the new bit saving using their own width. Six physical/coordinate failure +controls and three stale bridge controls run separately. A dedicated +three-version CI workflow retains every inherited workflow. + +The bounded searches are not proofs of global optimality. All inherited +all-size residual compiler, routing, recovery, prime selection, finite +alphabet/tape, precision and analytic transfer interfaces remain hypotheses. +No unconditional multiplication theorem or practical speedup is claimed. + +## Attribution + +Thomas DiFiore (PR74) introduced the envelope ordering; Dominik Scholz +(PR76) composed it with carried exchanges; Chafik Boukhalfa (PR79/71) +provided balanced/future/exchange and anchored split compilation; eumemic +(PR69/57) provided balanced coarse sums and reversible compilation; +Alejandro Zarzuelo Urdiales (PR70) supplied the carry-exchange strategy; +Rohan Arun (PR78/80/65/67) supplied coordinate flags, axis selection, +schedules and profile-cost reclamation. This new pre-compilation composition +and finite selection were prepared by Rohan Arun with OpenAI Codex assistance. + +Credit also Rohan Garg, Avi Eisenberg, icekylinx, James Chang, Zhihao Chen, +Aurel Prosz/Paureel, Swapnil Jain, RaD/hipotures, Douglas Colkitt, OpenAI, +Harvey–van der Hoeven and all inherited contributors. Original licenses, +author and AI-assistance notices remain preserved. Tested PR75 zero-circuit +variants were not selected for this witness and are not claimed as its method. diff --git a/references/frame-compiler/aligned-r11/references/pr82/research/envelope-balanced/SOURCE.json b/references/frame-compiler/aligned-r11/references/pr82/research/envelope-balanced/SOURCE.json new file mode 100644 index 0000000000..6b7fbca6d0 --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr82/research/envelope-balanced/SOURCE.json @@ -0,0 +1,304 @@ +{ + "parent_pr80": "a9ed157ff106fd35557b5896197f66a1272f7f13", + "files": { + ".gitattributes": "5f257f4e9e574ad5767f902242f519dad19cc455d6858f49234d0ccc345cabf1", + ".github/workflows/combined-flags.yml": "53d0f33c83356b2764f3cb332892690ff74ffa0e68b9ae1203fe837979c15396", + ".github/workflows/envelope-balanced.yml": "d658c2f91e1377eac5288cff7725ae1e573efdff70dac5472e6a4060085ab7fc", + ".github/workflows/verify.yml": "1a9cccd742ba2a5aa5a5ac38c1b7559bc0dec46b23d3ce3ff3e26c3137e6c3a2", + "Makefile": 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Composition by Rohan Arun +with OpenAI Codex assistance. Apache-2.0; finite conditional witness only. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2] +sys.path.insert(0,str(ROOT/'scripts/experiments')) +import balanced_split_graph as graph +import balanced_split_exchange_engine as baseline_engine +import flag_engine +sys.path.insert(0,str(ROOT/'references/frame-compiler/pr76/research/round7-scheduling')) +from schedule_variant import reorder +import argparse,gzip,json,subprocess,os,shlex + +def check_flag_engine(): + original=(ROOT/'scripts/experiments/balanced_split_exchange_engine.py').read_text() + before="for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank']))" + after="for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank']))" + assert original.count(before)==1 + expected='# Coordinate-conjugated oracle pricing by Rohan Arun with OpenAI Codex.\n'+original.replace(before,after) + assert (Path(__file__).parent/'flag_engine.py').read_text()==expected,'Flag engine contains changes beyond oracle coordinate pricing' + +def compile_axis(h,work): + check_flag_engine() + engine=flag_engine if h==25 else baseline_engine + if h==25: + cfg=json.loads((ROOT/f'research/envelope-balanced/order-{h}.json').read_text()) + assert sorted(cfg['order'])==list(range(h)) + engine.COORD_MAP={int(k):v for k,v in cfg['mapping'].items()} + assert engine.COORD_MAP=={old:new for new,old in enumerate(cfg['order'])} + work.mkdir(parents=True,exist_ok=True) + oracle=work/'oracle' + subprocess.run([*shlex.split(os.environ.get('CXX','c++')),'-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/profile_oracle.cpp'),'-o',str(oracle)],check=True) + engine.graph=lambda dimension:reorder(graph.graph(dimension)) + engine.build=graph.ordered_build(engine.build,h) + engine.ORACLE_EXE=str(oracle);engine.ORACLE_INPUT=str(work/'oracle.bin');engine.PENDING_COST=True;engine.oracles=[] + try:result,word=engine.compile_(h,matching=True,reclaim=True,dirty=True) + finally: + for process in engine.oracles: + process.stdin.close();assert process.wait(timeout=10)==0 + result.pop('seconds',None);result['scalar']=engine.graph(h).verify() + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + (work/'word.json.gz').write_bytes(gzip.compress(raw,mtime=0)) + (work/'compiler.json').write_text(json.dumps(result,indent=2)+'\n') + print('PASS compiled envelope-balanced axis',h,result['roles'],flush=True) + +if __name__=='__main__': + p=argparse.ArgumentParser();p.add_argument('--h',type=int,choices=(23,25),required=True);p.add_argument('--work',type=Path,required=True);args=p.parse_args();compile_axis(args.h,args.work) diff --git a/references/frame-compiler/aligned-r11/references/pr82/research/envelope-balanced/flag_engine.py b/references/frame-compiler/aligned-r11/references/pr82/research/envelope-balanced/flag_engine.py new file mode 100644 index 0000000000..d210d9336b --- /dev/null +++ b/references/frame-compiler/aligned-r11/references/pr82/research/envelope-balanced/flag_engine.py @@ -0,0 +1,312 @@ +# Coordinate-conjugated oracle pricing by Rohan Arun with OpenAI Codex. +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(index[int(i)]):s for i,s in word['sources'].items()} + v=word['v'];word['scatter']=[[v+index[a-v],b] for a,b in word['scatter']] + word['outputs']=[[s,g,perm[c],sorted(perm[x] for x in triple)] for s,g,c,triple in word['outputs']] + return word + +def exact(profiles): + cert=json.loads((HERE/'certificate.json').read_text()) + N=comb(23,3)*comb(25,3);m=575;W=2*N+sum(N//p['v']*p['R'] for p in profiles) + L=sum(N//p['v']*p['loss'] for p in profiles) + rows=Counter({1:19*N,21:2*N,17:2*N,481:2*N}) + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 and p['v']==comb(h,3) + assert sum(t*n for t,n in enumerate(p['blocks']))==h*p['R']+h*(h-1)==p['rank_sum'] + rows.update({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + rows[h]+=bank;rows[m-2*h]+=bank;rows[1]+=2*N;rows[h-2]+=2*N + bit=dict(m=m,N=N,W=W,L=L,total_rank=sum(t*n for t,n in rows.items()),child_multiplicities=dict(sorted(rows.items()))) + assert bit['total_rank']==m*W-N+L + assert arithmetic.js(bit)==cert['bit'] + saving=Q(cert['bit_saving']);moment=refine.exact_moment(m,W,rows,saving) + rejected=refine.exact_moment(m,W,rows,saving+Q(1,10**18)) + assert moment['upper']<11 + assert Q(cert['kappa'])>Q(old['kappa']) + print('PASS exact conditional kappa',result['kappa'],'47 constraints, seven margins, independent bounds and next-grid controls') + +def verify(regenerate=False): + sources();profiles=[] + with tempfile.TemporaryDirectory(prefix='coordinate-flags-') as directory: + work=Path(directory);exe=work/'profiles' + subprocess.run(['c++','-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'scripts/experiments/binary_frame_profiles.cpp'),'-o',str(exe)],check=True) + if regenerate: + jobs=[] + for h in (23,25): + axis=work/str(h);axis.mkdir() + jobs.append(subprocess.Popen([sys.executable,str(HERE/'compiler.py'),'--h',str(h),'--work',str(axis)])) + for job in jobs:assert job.wait()==0,'Portable compiler regeneration failed' + for h in (23,25): + assert gzip.decompress((work/str(h)/'word.json.gz').read_bytes())==gzip.decompress(original_path(h).read_bytes()),'Regenerated physical word changed' + print('PASS portable deterministic regeneration of both unpermuted words',flush=True) + for h in (23,25): + original=json.loads(gzip.decompress((original_path(h)).read_bytes())) + config=json.loads((HERE/f'order-{h}.json').read_text());word=relabel(original,config) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + assert raw==gzip.decompress((HERE/f'word-{h}.json.gz').read_bytes()) + path=work/f'word-{h}.json';path.write_bytes(raw);checked=replay(path) + stored=json.loads((HERE/f'replay-{h}.json').read_text());assert arithmetic.js(checked)==stored['replay'] + trans=work/f'transitions-{h}.bin';receipt=prepare(path,trans);assert arithmetic.js(receipt)==stored['transitions'] + subprocess.run([str(exe),str(trans)],check=True) + profile=json.loads(Path(str(trans)+'.profiles.json').read_text());assert profile==json.loads((HERE/f'profiles-{h}.json').read_text()) + profiles.append(profile);print('PASS complete relabelled physical word and profile',h,flush=True) + exact(profiles) +if __name__=='__main__': + import argparse + parser=argparse.ArgumentParser();parser.add_argument('--regenerate',action='store_true');args=parser.parse_args();verify(args.regenerate) diff --git a/references/frame-compiler/aligned-r11/research/pair-assembly/pair_graph.py b/references/frame-compiler/aligned-r11/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/aligned-r11/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/aligned-r11/research/reordered-rank-pair/arithmetic/refine.py b/references/frame-compiler/aligned-r11/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/aligned-r11/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/aligned-r11/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/aligned-r11/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/aligned-r11/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/aligned-r11/research/reordered-rank-pair/verify.py b/references/frame-compiler/aligned-r11/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/aligned-r11/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/aligned-r11/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/aligned-r11/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/aligned-r11/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/aligned-r11/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/aligned-r11/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/aligned-r11/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<0 and carry_can(x,f) and carry_can(other,y): + options.append((-gain,z,x,y,other)) + if not options:continue + _,z,x,y,other=min(options) + old=(f,z,y);new=(e,x,other) + assert len(set(old))==len(set(new))==3 and not set(old)&set(new) + assert {edges[t][1] for t in old}=={edges[t][1] for t in new} + assert len({edges[t][0] for t in old})==len({edges[t][0] for t in new})==3 + for t in old: + tg,tu,ti=edges[t];chosen.remove(t);blocks[tg]['selected'].remove(t);del right[tu] + for t in new: + tg,tu,ti=edges[t];assert tu not in right;chosen.add(t);blocks[tg]['selected'].add(t);right[tu]=t + changes+=1 + return changes + + +def compile_(h,matching=True,reclaim=False,dirty=True): + t0=time.time();c,blocks,uses,value_uses,owner,signal,order,contains=build(h);v=len(c.inputs);position={g:i for i,g in enumerate(order)} + print('built',h,len(blocks),'regions',flush=True,file=sys.stderr) + mode=globals().get('OUTPUT_MODE','baseline') + edges,chosen,right,stats=match(blocks,uses,matching) + print('matched',len(chosen),'seconds',time.time()-t0,flush=True,file=sys.stderr) + slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();retired_index=RetiredIndex(h);pending={};pending_index=PendingIndex(h);stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + oracle_map=globals().get('ORACLE_COORDINATES',list(range(h))) + assert sorted(oracle_map)==list(range(h)), 'Invalid oracle coordinate permutation' + for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + for phase in range(globals().get('THREE_CYCLE_PASSES',0)): + changes=improve_three_cycles(blocks,edges,chosen,right,prices,priority,carry_can) + stats['carry_three_cycles']+=changes + print('carry three-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=3 or result[0]==0 +assert accepted>0 +print(json.dumps({'status':'PASS','actual_source':str(ROOT/'scripts/experiments/compiler.py'),'fixtures':1604,'accepted_three_cycles':accepted,'checks':['strict-cycle-only fixture','equal and worsening cost rejected','dependent replacement rejected','cardinality','one use per choice','local vector independence','exact integer descent','determinism','distinct block requirement']})) diff --git a/references/frame-compiler/final-r10/CANDIDATE_PARENT.json b/references/frame-compiler/final-r10/CANDIDATE_PARENT.json new file mode 100644 index 0000000000..f023a81bcd --- /dev/null +++ b/references/frame-compiler/final-r10/CANDIDATE_PARENT.json @@ -0,0 +1,116 @@ +{ + "23": { + "W": 131973908, + "bit_saving": "52448177993289/1000000000000000000", + "compile_seconds": 41.97542989999056, + "coordinate_permutation": [ + 1, + 2, + 4, + 3, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 20, + 19, + 21, + 22, + 0 + ], + "exact_CRT_profiles": "PASS", + "full_physical_replay": "PASS both orientations", + "groups": "444", + "h": 23, + "kappa": "6555678415753/125000000000000000", + "label": "search", + "mode": "envelope-half", + "output_mode": "baseline", + "path": "results/23-444-envelope-half-baseline-search", + "profile_seconds": 1.6327140040230006, + "replay_seconds": 1.7665091671515256, + "roles": 26620, + "seconds": 48.58395723090507, + "stats": { + "augmentations": 134, + "carry_exchanges": 1774, + "carry_two_cycles": 140, + "clearing_xors": 5682, + "live_anchor_candidates": 74199, + "live_anchor_xors": 576, + "matched": 50244, + "multi_node_regions": 8625, + "reclaimed": 2658, + "regions": 67861 + }, + "word_sha256": "a2fc7194e9190f0fa4ddeac38aa76605f1b08243a7b51642a2433a52325b98c7" + }, + "25": { + "W": 132094198, + "bit_saving": "26157624115811/500000000000000000", + "compile_seconds": 68.12840775190853, + "coordinate_permutation": [ + 2, + 1, + 4, + 3, + 6, + 5, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "exact_CRT_profiles": "PASS", + "full_physical_replay": "PASS both orientations", + "groups": "441", + "h": 25, + "kappa": "326953196809/6250000000000000", + "label": "canary", + "mode": "envelope-half", + "output_mode": "route-late", + "path": "results/25-441-envelope-half-route-late-canary", + "profile_seconds": 2.3878593081608415, + "replay_seconds": 2.661699212156236, + "roles": 35138, + "seconds": 77.2729034400545, + "stats": { + "augmentations": 166, + "carry_exchanges": 2090, + "carry_two_cycles": 266, + "clearing_xors": 7148, + "live_anchor_candidates": 97315, + "live_anchor_xors": 868, + "matched": 70124, + "multi_node_regions": 11375, + "reclaimed": 3491, + "regions": 93828 + }, + "word_sha256": "a378551e7c6511576d2ed7d0d035bf0403c4a1e5fa14b458c1de8d7b988e23fb" + } +} diff --git a/references/frame-compiler/final-r10/COORDINATES.json b/references/frame-compiler/final-r10/COORDINATES.json new file mode 100644 index 0000000000..20c55f4f0e --- /dev/null +++ b/references/frame-compiler/final-r10/COORDINATES.json @@ -0,0 +1,54 @@ +{ + "23": [ + 1, + 2, + 4, + 3, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 20, + 19, + 21, + 22, + 0 + ], + "25": [ + 2, + 1, + 4, + 3, + 6, + 5, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ] +} diff --git a/references/frame-compiler/final-r10/EXPERIMENT.txt b/references/frame-compiler/final-r10/EXPERIMENT.txt new file mode 100644 index 0000000000..ad05de15b5 --- /dev/null +++ b/references/frame-compiler/final-r10/EXPERIMENT.txt @@ -0,0 +1 @@ +Final bounded composition before the next publication freeze. Independently compare original74 versus best-tested rank-preserving order; exact original versus coordinate-aware heuristic pricing fromPR82; zero versus three passes of improving three-donor cycles. Selected R9 grouping/output policy and R6 map fixed peraxis. First reproduce R9 winning words/profiles as canaries. Full independent dense scalar/support check, dirty physical replay both orientations, exact CRT profiles and complete47+7 assembly on everycase. No source edits during a run. diff --git a/references/frame-compiler/final-r10/FROZEN.json b/references/frame-compiler/final-r10/FROZEN.json new file mode 100644 index 0000000000..74d58ee763 --- /dev/null +++ b/references/frame-compiler/final-r10/FROZEN.json @@ -0,0 +1,178 @@ +{ + "PR74_commit": "3f78d8967c009153f2df5c6a6577b6ab1d37e2ca", + "PR78_commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf", + "R5_SOURCE_sha256": "57d9a8742b3870e8899f46b43f62654b2fbd1daab62d6c7f4fff4496e64af900", + "W": 132466108, + "axes": { + "23": { + "coarse": "half", + "coordinate_permutation": [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 22, + 0 + ], + "groups": "411", + "node_order": "PR74 rank,-core,cover,minnode; natural execution", + "output_mode": "baseline", + "paid_profile": { + "R": 26834, + "blocks": [ + 0, + 360947, + 18308, + 10287, + 5376, + 3976, + 3779, + 2686, + 2296, + 1754, + 1371, + 1322, + 902, + 790, + 495, + 433, + 233, + 96, + 102, + 0, + 90, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 5567, + "distinct_matrices": 38555, + "field_prime": 2305843009213693951, + "frames": 65728, + "h": 23, + "loss": 506, + "rank_sum": 617688, + "v": 1771 + }, + "parent": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/spark-results/spark/envelope-r5/results/23-411-envelope-half", + "parent_word_sha256": "18cf81638085c4851d0346d8398fc8ea50a5be84b40aa85a5478b51a5264e25d", + "profiles_sha256": "263c516190c53723bf103dd603309efbbceac1e30193ed1781f92df19e0e08bc", + "roles": 26834, + "selected": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/coordinate-r5-search/h23-shift1", + "word_sha256": "c67fb6efa490db56814c743a48044c99397f3067f0038ce80673930c2f0ed829" + }, + "25": { + "coarse": "half", + "coordinate_permutation": [ + 2, + 1, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "groups": "141", + "node_order": "PR74 rank,-core,cover,minnode; natural execution", + "output_mode": "route-late", + "paid_profile": { + "R": 35348, + "blocks": [ + 0, + 492700, + 23012, + 12086, + 6121, + 4924, + 5649, + 4980, + 3550, + 2660, + 2408, + 2123, + 1685, + 1370, + 958, + 775, + 544, + 438, + 260, + 97, + 130, + 0, + 126, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 7465, + "distinct_matrices": 48221, + "field_prime": 2305843009213693951, + "frames": 86507, + "h": 25, + "loss": 600, + "rank_sum": 884300, + "v": 2300 + }, + "parent": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/spark-results/spark2/envelope-r5/results/25-141-envelope-half", + "parent_word_sha256": "7a5b52058bcc4b3923914e8633764f75f0b9214909c8f72f6e153121cc7e9070", + "profiles_sha256": "a74d3c0bccfbfb96b8e416536d3c52a2e9c0d99faa5f1c35b90d4d5647153ddb", + "roles": 35348, + "selected": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/coordinate-r5-search/h25-pr74", + "word_sha256": "ec153b2cd0ef6edeb626dbb2831abc5ce7a59c99870ec6a5e08afb5a1530c845" + } + }, + "bit_saving": "408390793141/7812500000000000", + "coordinate_driver_sha256": "acd52c55a9c4e43833d0d81ff952d2882336ed188f5857bc1dbb2866fdbfb082", + "equivalent_best_pairs": [ + [ + "coordinate-r5-search:shift1", + "coordinate-r5-search:pr74" + ] + ], + "kappa": "261356445457/5000000000000000", + "portfolio": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/spark-results/final-portfolio.json", + "portfolio_pairs": 7569, + "portfolio_sha256": "1631e97c3a58dd28f7a0b8aee732c739a7be82566159070bf460ee9f83775166", + "rank_mass": 76166165200, + "relabel_source_sha256": "9476e799b86aca3f6941acdd4d57779ba5bb5f4f29ed89247569daa9e88c1600", + "reported_pr74_kappa": "10366199626713/200000000000000000", + "status": "FROZEN pending independent physical/arithmetic final clearance" +} diff --git a/references/frame-compiler/final-r10/LICENSE b/references/frame-compiler/final-r10/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/final-r10/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. 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a/references/frame-compiler/final-r10/baseline/h23/profiles.json b/references/frame-compiler/final-r10/baseline/h23/profiles.json new file mode 100644 index 0000000000..7baddf40c6 --- /dev/null +++ b/references/frame-compiler/final-r10/baseline/h23/profiles.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27285,"loss":506,"rank_sum":628061,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38513,"crt_matrices":5538,"crt_disagreements":0,"blocks":[0,356669,20912,7996,5407,4043,3702,3146,2579,1990,1706,1444,980,839,542,483,239,205,49,97,0,23,0,0]} diff --git a/references/frame-compiler/final-r10/baseline/h23/replay.json b/references/frame-compiler/final-r10/baseline/h23/replay.json new file mode 100644 index 0000000000..d37ffd1add --- /dev/null +++ b/references/frame-compiler/final-r10/baseline/h23/replay.json @@ -0,0 +1,34 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27285, + "output_roles": 5336, + "elementary_xors": 160435, + "word_length": 666534, + "full_basis_vectors": 30827, + "rank_mass": 628061, + "histogram": { + "1": 58281, + "0": 171307, + "2": 80793, + "4": 14511, + "3": 10007, + "5": 6429, + "6": 2036, + "8": 1110, + "10": 535, + "9": 471, + "12": 661, + "14": 1868, + "13": 193, + "16": 431, + "11": 120, + "17": 574, + "18": 3412, + "15": 334, + "19": 6482, + "22": 23, + "21": 393, + "7": 627 + } +} diff --git a/references/frame-compiler/final-r10/baseline/h23/result.json b/references/frame-compiler/final-r10/baseline/h23/result.json new file mode 100644 index 0000000000..349e949822 --- /dev/null +++ b/references/frame-compiler/final-r10/baseline/h23/result.json @@ -0,0 +1,19 @@ +{ + "h": 23, + "roles": 27285, + "stats": { + "augmentations": 13, + "regions": 59801, + "matched": 41730, + "multi_node_regions": 8694, + "carry_exchanges": 644, + "carry_two_cycles": 52, + "live_anchor_candidates": 72361, + "reclaimed": 2125, + "clearing_xors": 3916, + "live_anchor_xors": 76 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "word_sha256": "3f58db33edc2059ad6ca01cf8c36dd8cd8ae12149e1072e1f42757ca4ef17b82" +} diff --git a/references/frame-compiler/final-r10/baseline/h25/profiles.json b/references/frame-compiler/final-r10/baseline/h25/profiles.json new file mode 100644 index 0000000000..2be4368700 --- /dev/null +++ b/references/frame-compiler/final-r10/baseline/h25/profiles.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35684,"loss":600,"rank_sum":892700,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":51168,"crt_matrices":7278,"crt_disagreements":0,"blocks":[0,491871,27309,10127,7839,5460,4947,4006,3802,2943,2456,2025,1787,1423,1124,867,560,478,221,170,46,59,0,25,0,0]} diff --git a/references/frame-compiler/final-r10/baseline/h25/replay.json b/references/frame-compiler/final-r10/baseline/h25/replay.json new file mode 100644 index 0000000000..3ec3c54dc6 --- /dev/null +++ b/references/frame-compiler/final-r10/baseline/h25/replay.json @@ -0,0 +1,36 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 35684, + "output_roles": 6925, + "elementary_xors": 224161, + "word_length": 928844, + "full_basis_vectors": 40284, + "rank_mass": 892700, + "histogram": { + "1": 77041, + "0": 238437, + "2": 118217, + "3": 13314, + "4": 18459, + "6": 3215, + "5": 8388, + "7": 948, + "8": 1195, + "9": 721, + "10": 828, + "12": 708, + "13": 182, + "14": 653, + "16": 2171, + "18": 506, + "19": 981, + "17": 633, + "15": 187, + "11": 15, + "20": 4464, + "21": 8405, + "24": 25, + "23": 463 + } +} diff --git a/references/frame-compiler/final-r10/baseline/h25/result.json b/references/frame-compiler/final-r10/baseline/h25/result.json new file mode 100644 index 0000000000..50b259fcd7 --- /dev/null +++ b/references/frame-compiler/final-r10/baseline/h25/result.json @@ -0,0 +1,19 @@ +{ + "h": 25, + "roles": 35684, + "stats": { + "augmentations": 16, + "regions": 84843, + "matched": 60971, + "multi_node_regions": 11575, + "carry_exchanges": 1000, + "carry_two_cycles": 62, + "live_anchor_candidates": 98464, + "reclaimed": 3263, + "clearing_xors": 6027, + "live_anchor_xors": 132 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "word_sha256": "7c60369042197c356dfac3516ae396d68dc92edbc5824b6078dce0e6676f7f79" +} diff --git a/references/frame-compiler/final-r10/batch.py b/references/frame-compiler/final-r10/batch.py new file mode 100644 index 0000000000..eb46375f78 --- /dev/null +++ b/references/frame-compiler/final-r10/batch.py @@ -0,0 +1,32 @@ +"""Final bounded factorial composition with exact parent canaries.""" +from pathlib import Path +from hashlib import sha256 +from fractions import Fraction as Q +from concurrent.futures import ProcessPoolExecutor,as_completed +import argparse,json,subprocess,sys,time +ROOT=Path(__file__).resolve().parent +sys.path.insert(0,str(ROOT)) +from graph_batch import generate,load + +def run(job): + h,node_order,pricing,passes,label=job + parent=json.loads((ROOT/'CANDIDATE_PARENT.json').read_text())[str(h)] + return generate(h,parent['groups'],mode='envelope-half',output_mode=parent['output_mode'],coordinate=parent['coordinate_permutation'],label=label,pricing=pricing,three_cycle_passes=passes,node_order=node_order) + +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--h',type=int,choices=(23,25),required=True);ap.add_argument('--workers',type=int,default=8);args=ap.parse_args();assert 1<=args.workers<=8 + manifest=json.loads((ROOT/'SOURCE.json').read_text()) + for path,digest in manifest['files'].items():assert sha256((ROOT/path).read_bytes()).hexdigest()==digest,path + print('SOURCE PASS',len(manifest['files']),sha256((ROOT/'SOURCE.json').read_bytes()).hexdigest(),flush=True) + subprocess.run([sys.executable,str(ROOT/'test_order.py')],check=True) + subprocess.run([sys.executable,str(ROOT/'test_three_cycles.py')],check=True) + parent=json.loads((ROOT/'CANDIDATE_PARENT.json').read_text())[str(args.h)];rows=[];started=time.monotonic();h=args.h + row=run((h,'pr74',False,0,'canary'));assert row['word_sha256']==parent['word_sha256'];assert row['kappa']==parent['kappa'];assert json.loads((ROOT/row['path']/'profiles.json').read_text())==json.loads((ROOT/f'candidate-parent/h{h}/profiles.json').read_text());rows.append(row);print('CANARY',json.dumps(row),flush=True) + jobs=[(h,key,pricing,passes,f'{key}-pricing{int(pricing)}-cycles{passes}') for key in ('pr74','cover-minus-core-minus') for pricing in (False,True) for passes in (0,3) if (key,pricing,passes)!=('pr74',False,0)] + with ProcessPoolExecutor(max_workers=args.workers) as pool: + for future in as_completed([pool.submit(run,job) for job in jobs]): + row=future.result();rows.append(row);receipt={'h':h,'complete':False,'validated_cases':len(rows),'expected_cases':8,'rows':rows,'wall_seconds':time.monotonic()-started} + temp=ROOT/'progress.tmp';temp.write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');temp.replace(ROOT/'progress.json');print('RESULT',json.dumps(row),flush=True) + best=max(rows,key=lambda row:Q(row['kappa']));receipt.update(complete=True,best_axis=best,wall_seconds=time.monotonic()-started) + (ROOT/'progress.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print('COMPLETE',json.dumps({k:v for k,v in receipt.items() if k not in ('rows','best_axis')}),flush=True) +if __name__=='__main__':main() diff --git a/references/frame-compiler/final-r10/build.sh b/references/frame-compiler/final-r10/build.sh new file mode 100644 index 0000000000..44cbeea56b --- /dev/null +++ b/references/frame-compiler/final-r10/build.sh @@ -0,0 +1,5 @@ +#!/bin/sh +set -eu +mkdir -p bin +c++ -O3 -std=c++17 -I references/frame-compiler/pr48/scripts/partial_swap scripts/experiments/profile_oracle.cpp -o bin/profile-oracle +c++ -O3 -std=c++17 -I references/frame-compiler/pr48/scripts/partial_swap scripts/experiments/binary_frame_profiles.cpp -o bin/profiles diff --git a/references/frame-compiler/final-r10/candidate-parent/h23/profiles.json b/references/frame-compiler/final-r10/candidate-parent/h23/profiles.json new file mode 100644 index 0000000000..d881b695c2 --- /dev/null +++ b/references/frame-compiler/final-r10/candidate-parent/h23/profiles.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":26620,"loss":506,"rank_sum":612766,"field_prime":2305843009213693951,"frames":67863,"distinct_matrices":37844,"crt_matrices":5571,"crt_disagreements":0,"blocks":[0,362191,17808,9346,4092,3667,3946,3336,2453,1663,1220,1339,814,768,525,441,247,102,108,0,92,23,0,0]} diff --git a/references/frame-compiler/final-r10/candidate-parent/h23/replay.json b/references/frame-compiler/final-r10/candidate-parent/h23/replay.json new file mode 100644 index 0000000000..174e857f58 --- /dev/null +++ b/references/frame-compiler/final-r10/candidate-parent/h23/replay.json @@ -0,0 +1,34 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 26620, + "output_roles": 5336, + "elementary_xors": 181432, + "word_length": 750522, + "full_basis_vectors": 30162, + "rank_mass": 612766, + "histogram": { + "1": 79271, + "0": 196941, + "2": 77528, + "4": 14036, + "3": 9524, + "6": 1494, + "5": 5451, + "8": 2029, + "7": 785, + "9": 1807, + "10": 711, + "11": 580, + "12": 707, + "13": 267, + "14": 1131, + "16": 243, + "15": 404, + "17": 629, + "18": 2574, + "19": 5438, + "22": 23, + "21": 354 + } +} diff --git a/references/frame-compiler/final-r10/candidate-parent/h23/result.json b/references/frame-compiler/final-r10/candidate-parent/h23/result.json new file mode 100644 index 0000000000..669c2d7c98 --- /dev/null +++ b/references/frame-compiler/final-r10/candidate-parent/h23/result.json @@ -0,0 +1,24 @@ +{ + "h": 23, + "groups": "444", + "mode": "envelope-half", + "roles": 26620, + "word_sha256": "a2fc7194e9190f0fa4ddeac38aa76605f1b08243a7b51642a2433a52325b98c7", + "stats": { + "augmentations": 134, + "regions": 67861, + "matched": 50244, + "multi_node_regions": 8625, + "carry_exchanges": 1774, + "carry_two_cycles": 140, + "live_anchor_candidates": 74199, + "live_anchor_xors": 576, + "reclaimed": 2658, + "clearing_xors": 5682 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "compile_seconds": 41.97542989999056, + "replay_seconds": 1.7665091671515256, + "profile_seconds": 1.6327140040230006 +} diff --git a/references/frame-compiler/final-r10/candidate-parent/h23/word.json.gz b/references/frame-compiler/final-r10/candidate-parent/h23/word.json.gz new file mode 100644 index 0000000000..72140140b2 Binary files /dev/null and b/references/frame-compiler/final-r10/candidate-parent/h23/word.json.gz differ diff --git a/references/frame-compiler/final-r10/candidate-parent/h25/profiles.json b/references/frame-compiler/final-r10/candidate-parent/h25/profiles.json new file mode 100644 index 0000000000..67f4cf0c33 --- /dev/null +++ b/references/frame-compiler/final-r10/candidate-parent/h25/profiles.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35138,"loss":600,"rank_sum":879050,"field_prime":2305843009213693951,"frames":93830,"distinct_matrices":53695,"crt_matrices":7335,"crt_disagreements":0,"blocks":[0,504362,27018,10748,5926,4937,5498,3818,3229,2589,2366,1865,1416,1370,1008,737,503,423,251,98,124,0,107,25,0,0]} diff --git a/references/frame-compiler/final-r10/candidate-parent/h25/replay.json b/references/frame-compiler/final-r10/candidate-parent/h25/replay.json new file mode 100644 index 0000000000..0b2dbfd701 --- /dev/null +++ b/references/frame-compiler/final-r10/candidate-parent/h25/replay.json @@ -0,0 +1,36 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 35138, + "output_roles": 6925, + "elementary_xors": 247252, + "word_length": 1021208, + "full_basis_vectors": 39738, + "rank_mass": 879050, + "histogram": { + "1": 101941, + "0": 266827, + "2": 108937, + "4": 22808, + "3": 12153, + "5": 7685, + "6": 1999, + "8": 2775, + "7": 826, + "9": 1016, + "10": 888, + "11": 552, + "12": 965, + "14": 478, + "13": 459, + "15": 454, + "16": 1970, + "18": 268, + "17": 661, + "19": 916, + "20": 3478, + "21": 7250, + "24": 25, + "23": 461 + } +} diff --git a/references/frame-compiler/final-r10/candidate-parent/h25/result.json b/references/frame-compiler/final-r10/candidate-parent/h25/result.json new file mode 100644 index 0000000000..373a2a5a79 --- /dev/null +++ b/references/frame-compiler/final-r10/candidate-parent/h25/result.json @@ -0,0 +1,24 @@ +{ + "h": 25, + "groups": "441", + "mode": "envelope-half", + "roles": 35138, + "word_sha256": "a378551e7c6511576d2ed7d0d035bf0403c4a1e5fa14b458c1de8d7b988e23fb", + "stats": { + "augmentations": 166, + "regions": 93828, + "matched": 70124, + "multi_node_regions": 11375, + "carry_exchanges": 2090, + "carry_two_cycles": 266, + "live_anchor_candidates": 97315, + "live_anchor_xors": 868, + "reclaimed": 3491, + "clearing_xors": 7148 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "compile_seconds": 68.12840775190853, + "replay_seconds": 2.661699212156236, + "profile_seconds": 2.3878593081608415 +} diff --git a/references/frame-compiler/final-r10/candidate-parent/h25/word.json.gz b/references/frame-compiler/final-r10/candidate-parent/h25/word.json.gz new file mode 100644 index 0000000000..04e196397b Binary files /dev/null and b/references/frame-compiler/final-r10/candidate-parent/h25/word.json.gz differ diff --git a/references/frame-compiler/final-r10/configs.json b/references/frame-compiler/final-r10/configs.json new file mode 100644 index 0000000000..56e87fd388 --- /dev/null +++ b/references/frame-compiler/final-r10/configs.json @@ -0,0 +1,8 @@ +[ + "111", + "112", + "411", + "171", + "141", + "181" +] diff --git a/references/frame-compiler/final-r10/evaluate.py b/references/frame-compiler/final-r10/evaluate.py new file mode 100644 index 0000000000..ad3369d6c0 --- /dev/null +++ b/references/frame-compiler/final-r10/evaluate.py @@ -0,0 +1,65 @@ +"""Exact high-precision comparisons, compounding verified PR65 arithmetic.""" +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +from copy import deepcopy +import importlib.util,json,sys,itertools +HERE=Path(__file__).resolve().parent +BASE=HERE +AR=BASE/'research/reordered-rank-pair/arithmetic' +sys.path.insert(0,str(AR)) +import refine +N=4073300;m=575 + +def load(path): + f=json.loads((path/'profiles.json').read_text());r=json.loads((path/'replay.json').read_text());s=json.loads((path/'result.json').read_text()) + assert f['crt_disagreements']==0 and f['R']==r['roles']==s['roles'] + return f + +def counts(profiles): + W=2*N;L=0;hist=Counter({1:19*N,21:2*N,17:2*N,481:2*N}) + for h,f in profiles.items(): + rep=N//f['v'];bank=rep*f['R'];W+=bank;L+=rep*f['loss'] + assert sum(t*n for t,n in enumerate(f['blocks']))==h*f['R']+f['loss']==f['rank_sum'] + hist.update({t:n*rep for t,n in enumerate(f['blocks']) if t and n});hist.update({h:bank,m-2*h:bank});hist.update({1:2*N,h-2:2*N}) + mass=sum(t*n for t,n in hist.items());assert mass==m*W-N+L + return dict(m=m,N=N,W=W,L=L,total_rank=mass,deficit=m*W-mass,maxchild=max(hist),child_multiplicities=dict(sorted(hist.items()))) + +def fine(profiles): + p=counts(profiles);rows=p['child_multiplicities'];den=10**18;lo=1;hi=6*10**13 + assert refine.exact_moment(m,p['W'],rows,Q(lo,den))['upper']<11:hi=mid + else:raise ArithmeticError('Enclosure inconclusive') + a=Q(lo,den);bridge=deepcopy(baseline['finite_bridge']);bridge['bit']['W']=p['W'] + bridge['bit']['wire_bits']=p['W'].bit_length() + bridge['rows']['coefficient']=sum(bridge[name]['halving_degree']*bridge[name]['wire_bits'] for name in ('bit','complex')) + bridge['rows']['degree_gap']=Q(bridge['rows']['degree'])-Q(51,25)*bridge['rows']['coefficient'] + bridge['rows']['suffix_slope']=4*bridge['rows']['degree'] + accepted=refine.exact_moment(m,p['W'],rows,a);rejected=refine.exact_moment(m,p['W'],rows,Q(hi,den));assert accepted['upper']<1prior and best['prior65_moment']['lower']>1 + for r in rows: + r['moment_at_best_bit']=refine.exact_moment(m,r['bit']['W'],r['bit']['child_multiplicities'],best['bit_saving']) + output={'verified_baseline':{'pr':65,'commit':'49e84f939d15b618b50714eb039cabf97c74256a','kappa':prior},'best':best,'rows':rows,'cases':len(rows)} + (HERE/'fine-pair-comparison.json').write_text(json.dumps(refine.arithmetic.js(output),indent=2,sort_keys=True)+'\n') + (HERE/'selected-exact-result.json').write_text(json.dumps(refine.arithmetic.js(best),indent=2,sort_keys=True)+'\n') + print('BEST',json.dumps({'pair':best['pair'],'kappa':str(best['kappa']),'bit_saving':str(best['bit_saving']),'W':best['bit']['W'],'gain_percent_vs_verified65':float(100*(best['kappa']/prior-1))},sort_keys=True),flush=True) diff --git a/references/frame-compiler/final-r10/frozen/h23/profiles.json b/references/frame-compiler/final-r10/frozen/h23/profiles.json new file mode 100644 index 0000000000..51adafc2f2 --- /dev/null +++ b/references/frame-compiler/final-r10/frozen/h23/profiles.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":26834,"loss":506,"rank_sum":617688,"field_prime":2305843009213693951,"frames":65728,"distinct_matrices":38555,"crt_matrices":5567,"crt_disagreements":0,"blocks":[0,360947,18308,10287,5376,3976,3779,2686,2296,1754,1371,1322,902,790,495,433,233,96,102,0,90,23,0,0]} diff --git a/references/frame-compiler/final-r10/frozen/h23/replay.json b/references/frame-compiler/final-r10/frozen/h23/replay.json new file mode 100644 index 0000000000..22be4b8d75 --- /dev/null +++ b/references/frame-compiler/final-r10/frozen/h23/replay.json @@ -0,0 +1,34 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 26834, + "output_roles": 5336, + "elementary_xors": 176951, + "word_length": 732598, + "full_basis_vectors": 30376, + "rank_mass": 617688, + "histogram": { + "1": 73048, + "0": 192243, + "2": 78597, + "4": 14768, + "3": 9345, + "6": 2630, + "5": 5655, + "7": 906, + "8": 1692, + "9": 1014, + "10": 793, + "11": 207, + "12": 370, + "13": 104, + "14": 1219, + "15": 400, + "16": 493, + "17": 1036, + "18": 2643, + "19": 5609, + "22": 23, + "21": 384 + } +} diff --git a/references/frame-compiler/final-r10/frozen/h23/result.json b/references/frame-compiler/final-r10/frozen/h23/result.json new file mode 100644 index 0000000000..ab84bad553 --- /dev/null +++ b/references/frame-compiler/final-r10/frozen/h23/result.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "label": "shift1", + "permutation": [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 22, + 0 + ], + "parent_word_sha256": "18cf81638085c4851d0346d8398fc8ea50a5be84b40aa85a5478b51a5264e25d", + "word_sha256": "c67fb6efa490db56814c743a48044c99397f3067f0038ce80673930c2f0ed829", + "roles": 26834, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "seconds": 7.054715915990528 +} diff --git a/references/frame-compiler/final-r10/frozen/h23/word.json.gz b/references/frame-compiler/final-r10/frozen/h23/word.json.gz new file mode 100644 index 0000000000..3260f9aef6 Binary files /dev/null and b/references/frame-compiler/final-r10/frozen/h23/word.json.gz differ diff --git a/references/frame-compiler/final-r10/frozen/h25/profiles.json b/references/frame-compiler/final-r10/frozen/h25/profiles.json new file mode 100644 index 0000000000..1b7e20ff3a --- /dev/null +++ b/references/frame-compiler/final-r10/frozen/h25/profiles.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35348,"loss":600,"rank_sum":884300,"field_prime":2305843009213693951,"frames":86507,"distinct_matrices":48221,"crt_matrices":7465,"crt_disagreements":0,"blocks":[0,492700,23012,12086,6121,4924,5649,4980,3550,2660,2408,2123,1685,1370,958,775,544,438,260,97,130,0,126,25,0,0]} diff --git a/references/frame-compiler/final-r10/frozen/h25/replay.json b/references/frame-compiler/final-r10/frozen/h25/replay.json new file mode 100644 index 0000000000..2aed6f7d02 --- /dev/null +++ b/references/frame-compiler/final-r10/frozen/h25/replay.json @@ -0,0 +1,36 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 35348, + "output_roles": 6925, + "elementary_xors": 234549, + "word_length": 970396, + "full_basis_vectors": 39948, + "rank_mass": 884300, + "histogram": { + "1": 78977, + "0": 255645, + "2": 122604, + "4": 15384, + "3": 13298, + "5": 8687, + "6": 1876, + "8": 2952, + "10": 987, + "9": 849, + "12": 1101, + "11": 156, + "13": 318, + "14": 575, + "15": 208, + "16": 1351, + "18": 673, + "17": 472, + "19": 779, + "20": 4243, + "21": 8332, + "24": 25, + "7": 609, + "23": 495 + } +} diff --git a/references/frame-compiler/final-r10/frozen/h25/result.json b/references/frame-compiler/final-r10/frozen/h25/result.json new file mode 100644 index 0000000000..e4e4ef2705 --- /dev/null +++ b/references/frame-compiler/final-r10/frozen/h25/result.json @@ -0,0 +1,37 @@ +{ + "h": 25, + "label": "pr74", + "permutation": [ + 2, + 1, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "parent_word_sha256": "7a5b52058bcc4b3923914e8633764f75f0b9214909c8f72f6e153121cc7e9070", + "word_sha256": "ec153b2cd0ef6edeb626dbb2831abc5ce7a59c99870ec6a5e08afb5a1530c845", + "roles": 35348, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "seconds": 9.73521841596812 +} diff --git a/references/frame-compiler/final-r10/frozen/h25/word.json.gz b/references/frame-compiler/final-r10/frozen/h25/word.json.gz new file mode 100644 index 0000000000..074ec5c508 Binary files /dev/null and b/references/frame-compiler/final-r10/frozen/h25/word.json.gz differ diff --git a/references/frame-compiler/final-r10/graph_batch.py b/references/frame-compiler/final-r10/graph_batch.py new file mode 100644 index 0000000000..12192418a9 --- /dev/null +++ b/references/frame-compiler/final-r10/graph_batch.py @@ -0,0 +1,92 @@ +"""Durable independent CPU search over pinned current two-cycle construction. +Each accepted case regenerates and independently replays the literal word, +reconstructs paid frames, computes CPU CRT profiles and exact inequalities. +""" +from pathlib import Path +from hashlib import sha256 +from concurrent.futures import ProcessPoolExecutor,as_completed +import argparse,ast,cProfile,gzip,importlib.util,json,os,pstats,subprocess,sys,time,types +ROOT=Path(__file__).resolve().parent +sys.path.insert(0,str(ROOT/'scripts/experiments')) + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m + +def generate(h,groups,profile=False,mode="baseline",output_mode=None,coordinate=None,label="search",pricing=False,three_cycle_passes=0,node_order="pr74"): + started=time.monotonic();out=ROOT/'results'/f'{h}-{groups}-{mode}-{output_mode}-{label}';out.mkdir(parents=True,exist_ok=True) + compiler=load('search_compiler',ROOT/'scripts/experiments/compiler.py') + source=(ROOT/'research/pair-assembly/pair_graph.py').read_text() + donor=ROOT/'references/pr69/balanced_coarse_compiler.py' + constants={n.targets[0].id:ast.literal_eval(n.value) for n in ast.parse(donor.read_text()).body if isinstance(n,ast.Assign) and isinstance(n.targets[0],ast.Name) and n.targets[0].id in ('BEFORE','AFTER')} + replacement=constants['AFTER'];needle='columns = [self.total([e(a,b) for a in groups[i]]) for b in groups[j]]' + orientation=mode.removeprefix('envelope-') if mode.startswith('envelope-') else ('half' if h==23 else 'row') + if orientation=='half': + replacement=replacement.replace(needle,'columns = ([self.total([e(a,b) for a in groups[i]]) for b in groups[j]] if i+j < ng-1 else [self.total([e(a,b) for b in groups[j]]) for a in groups[i]])') + elif orientation=='row':replacement=replacement.replace(needle,'columns = [self.total([e(a,b) for b in groups[j]]) for a in groups[i]]') + assert source.count(constants['BEFORE'])==1 + graph=types.ModuleType('balanced_graph');graph.__file__=str(ROOT/'research/pair-assembly/pair_graph.py');exec(compile(source.replace(constants['BEFORE'],replacement),graph.__file__,'exec'),graph.__dict__) + original=graph.circuit_class + def subclass(dim): + parent=original(dim) + class Split(parent): + def grouping(self,points): + result=super().grouping(points);choices=[int(x) for x in groups];choice=choices[self._level] if self._level3 and choice: + first,mid,last=0,(len(result)-1)//2,len(result)-1 + requested={1:[first],2:[mid],3:[last],4:[first,mid],5:[first,last],6:[mid,last],7:[first,mid,last],8:[first,first+1],9:[last-1,last]}[choice] + chosen=[] + for k in requested: + if k not in chosen and 0<=k>common&1 and not(mask&forbidden)) + assert support[x]==expected + return {'status':'PASS all global supports, exact envelopes, disjoint additions and target outputs','nodes':len(c.active),'outputs':len(c.outputs),'sha256':digest.hexdigest()} + +# Coordinate action preserves the literal physical word under a global input relabel. +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word diff --git a/references/frame-compiler/final-r10/original/carry_cycle_compiler.py b/references/frame-compiler/final-r10/original/carry_cycle_compiler.py new file mode 100644 index 0000000000..d883cbc71d --- /dev/null +++ b/references/frame-compiler/final-r10/original/carry_cycle_compiler.py @@ -0,0 +1,338 @@ +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path('/Users/chafreaky/Documents/personal/integer-mult-research-20261008/joint-reclaim/references/frame-compiler/pr48') +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + diff --git a/references/frame-compiler/final-r10/original/output_basis_compiler.py b/references/frame-compiler/final-r10/original/output_basis_compiler.py new file mode 100644 index 0000000000..517e4cd5e8 --- /dev/null +++ b/references/frame-compiler/final-r10/original/output_basis_compiler.py @@ -0,0 +1,407 @@ +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path('/Users/chafreaky/Documents/personal/integer-mult-research-20261008/joint-reclaim/references/frame-compiler/pr48') +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": 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OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": 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0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000000000, + "cutoff_log2_input": { + "alpha": 5956134977, + "compact": 23824539905, + "geometry": 3999930893196446780, + "guard": 4283152, + "log_p": 25, + "normalization": 14000000000000000000, + "period": 47649079809, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000000000, + "powers": { + "alpha": { + "exponent": 725614180574271, + "rhs": 112000000000000154416, + "rhs_bits": 67 + }, + "compact": { + "exponent": 725614180574271, + "rhs": 448000000000000617600, + "rhs_bits": 69 + }, + "leaf": { + "exponent": 666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 725614180574271, + "rhs": 224000000000000308760, + "rhs_bits": 68 + }, + "rows": { + "exponent": 725614180574271, + "rhs": 112000000000000154416000, + "rhs_bits": 77 + } + } + }, + { + "log2_input": 28000000000000000000, + "powers": { + "alpha": { + "exponent": 1451228361148543, + "rhs": 224000000000000154416, + "rhs_bits": 68 + }, + "compact": { + "exponent": 1451228361148543, + "rhs": 896000000000000617600, + "rhs_bits": 70 + }, + "leaf": { + "exponent": 1333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1451228361148543, + "rhs": 448000000000000308760, + "rhs_bits": 69 + }, + "rows": { + "exponent": 1451228361148543, + "rhs": 224000000000000154416000, + "rhs_bits": 78 + } + } + }, + { + "log2_input": 56000000000000000000, + "powers": { + "alpha": { + "exponent": 2902456722297087, + "rhs": 448000000000000154416, + "rhs_bits": 69 + }, + "compact": { + "exponent": 2902456722297087, + "rhs": 1792000000000000617600, + "rhs_bits": 71 + }, + "leaf": { + "exponent": 2666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2902456722297087, + "rhs": 896000000000000308760, + "rhs_bits": 70 + }, + "rows": { + "exponent": 2902456722297087, + "rhs": 448000000000000154416000, + "rhs_bits": 79 + } + } + }, + { + "log2_input": 112000000000000000000, + "powers": { + "alpha": { + "exponent": 5804913444594174, + "rhs": 896000000000000154416, + "rhs_bits": 70 + }, + "compact": { + "exponent": 5804913444594174, + "rhs": 3584000000000000617600, + "rhs_bits": 72 + }, + "leaf": { + "exponent": 5333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5804913444594174, + "rhs": 1792000000000000308760, + "rhs_bits": 71 + }, + "rows": { + "exponent": 5804913444594174, + "rhs": 896000000000000154416000, + "rhs_bits": 80 + } + } + }, + { + "log2_input": 224000000000000000000, + "powers": { + "alpha": { + "exponent": 11609826889188348, + "rhs": 1792000000000000154416, + "rhs_bits": 71 + }, + "compact": { + "exponent": 11609826889188348, + "rhs": 7168000000000000617600, + "rhs_bits": 73 + }, + "leaf": { + "exponent": 10666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11609826889188348, + "rhs": 3584000000000000308760, + "rhs_bits": 72 + }, + "rows": { + "exponent": 11609826889188348, + "rhs": 1792000000000000154416000, + "rhs_bits": 81 + } + } + }, + { + "log2_input": 448000000000000000000, + "powers": { + "alpha": { + "exponent": 23219653778376697, + "rhs": 3584000000000000154416, + "rhs_bits": 72 + }, + "compact": { + "exponent": 23219653778376697, + "rhs": 14336000000000000617600, + "rhs_bits": 74 + }, + "leaf": { + "exponent": 21333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 23219653778376697, + "rhs": 7168000000000000308760, + "rhs_bits": 73 + }, + "rows": { + "exponent": 23219653778376697, + "rhs": 3584000000000000154416000, + "rhs_bits": 82 + } + } + } + ], + "practical_runtime_claim": false + }, + "finite_bridge": { + "bit": { + "W": 133862024, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 27 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 843, + "contract": 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witness; inherited all-size transfer remains assumed" +} diff --git a/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/check.py b/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/check.py new file mode 100644 index 0000000000..0630cfc19a --- /dev/null +++ b/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/check.py @@ -0,0 +1,104 @@ +#!/usr/bin/env python3 +"""Screen complete paid profiles from independently replayed axis constructions.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions required') +from pathlib import Path +from collections import Counter +from fractions import Fraction as Q +import importlib.util,argparse,json,subprocess,tempfile,hashlib,os,shlex +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +from producer import check_sources +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m +exact=load('candidate_exact',ROOT/'research/rank-pair-refinement/refine.py') +balanced=load('candidate_assembly',DEP/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') + +def profile(path): + v=json.loads(Path(path).read_text()) + return v['profile'] if 'profile' in v else v + +def calculate(first,second): + profiles=[profile(first),profile(second)] + N=4073300;m=575 + assert [p['h'] for p in profiles]==[23,25] + W=2*N+sum(N//p['v']*p['R'] for p in profiles) + parts={'data':Counter({1:18*N,21:2*N,17:2*N,481:2*N}),'endpoint_copy':Counter({1:N})} + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 + assert p['rank_sum']==h*p['R']+p['loss']==sum(t*n for t,n in enumerate(p['blocks'])) + assert p['loss']==h*(h-1) + parts[f'internal_{h}']=Counter({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + parts[f'exterior_{h}']=Counter({h:bank,m-2*h:bank}) + parts[f'growth_{h}']=Counter({1:2*N,h-2:2*N}) + rows=sum(parts.values(),Counter());assert sum(t*n for t,n in rows.items())==m*W-1846900 + lo,hi,grid=1,71700000000000,10**18 + while lo+11 + result.update(status='Verified finite conditional witness; inherited all-size transfer remains assumed', + source_manifest_sha256=hashlib.sha256((HERE/'SOURCE.json').read_bytes()).hexdigest(), + axes=axes,eventual_bounds=balanced.cutoffs(result['finite_bridge'],result['assembly']), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113',pr71_kappa=Q(previous['kappa']), + relative_gain_pr71=result['kappa']/Q(previous['kappa'])-1, + pr71_complete_profile_exclusion_lower=old_lower)) + result=arithmetic.js(result) + path=HERE/'certificate.json' + if record:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:assert result==json.loads(path.read_text()) + print('PASS exact moment, next-grid exclusions, 47 inequalities and seven margins',flush=True) + return result + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--record',action='store_true');args=parser.parse_args();generate(args.record) diff --git a/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/producer.py b/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/producer.py new file mode 100644 index 0000000000..8d68303a3b --- /dev/null +++ b/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/producer.py @@ -0,0 +1,132 @@ +#!/usr/bin/env python3 +"""Balanced coarse sums + anchored split/live frames + core ordering and coordinates. + +Composition for Thomas DiFiore with OpenAI Codex assistance. Apache-2.0. +PR69 coarse sums: eumemic. PR71 split/live composition: Chafik Boukhalfa. +Graph: Avi Eisenberg PR62; split operation: Rohan Garg PR59; reclamation: +Rohan Arun PR65/67, Dominik Scholz PR63/68, eumemic PR57. Original notices +and exact sources are retained under references/frame-compiler/pr69 and pr71. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +from hashlib import sha256 +import argparse,ast,gzip,importlib.util,json,types +from concurrent.futures import ProcessPoolExecutor +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +import split_pair_graph as provider +import split_pair_compiler as ancestor +from binary_frame_replay import replay + + +def check_sources(): + for folder in (DEP,ROOT/'references/frame-compiler/pr69'): + manifest=json.loads((folder/'SOURCE.json').read_text()) + for name,digest in manifest['files'].items(): + assert sha256((folder/name).read_bytes()).hexdigest()==digest,name + manifest=json.loads((HERE/'SOURCE.json').read_text()) + required={str((HERE/name).relative_to(ROOT)) for name in ('producer.py','check.py','graph_audit.py','independent_check.py','selection.json')} + assert required <= set(manifest['files']), 'Incomplete selected source closure' + for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + + +def reorder(c): + groups={} + for x in sorted(c.active): + if c.args[x]: groups.setdefault((c.core[x],c.union[x]),[]).append(x) + def key(item): + (core,cover),nodes=item + return cover.bit_count()-core.bit_count(),-core,cover,min(nodes) + ids=list(range(len(c.inputs)+1))+[x for _,nodes in sorted(groups.items(),key=key) for x in nodes] + mapping={x:i for i,x in enumerate(ids)} + args,core,cover,provenance=c.args,c.core,c.union,c.provenance + c.args=[tuple(mapping[y] for y in args[x]) if args[x] else None for x in ids] + c.core=[core[x] for x in ids];c.union=[cover[x] for x in ids] + c.provenance=[provenance[x] for x in ids] + c.active={mapping[x] for x in c.active};c.outputs={k:mapping[v] for k,v in c.outputs.items()} + c.support_in.cache_clear() + c.verify() + return c + + +def graph(h,ordered=True): + source=Path(provider._graph.__file__).read_text() + original=ROOT/'references/frame-compiler/pr69/scripts/experiments/balanced_coarse_compiler.py' + replacements={} + for node in ast.parse(original.read_text()).body: + if isinstance(node,ast.Assign): + for target in node.targets: + if isinstance(target,ast.Name) and target.id in ('BEFORE','AFTER'): + replacements[target.id]=ast.literal_eval(node.value) + assert source.count(replacements['BEFORE'])==1 + module=types.ModuleType('balanced_split_private_graph');module.__file__=provider._graph.__file__ + exec(compile(source.replace(replacements['BEFORE'],replacements['AFTER']),module.__file__+':balanced-coarse','exec'),module.__dict__) + previous=provider._graph + try: + provider._graph=module + c=provider.graph(h) + finally: + provider._graph=previous + return reorder(c) if ordered else c + + +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + +def compile_axis(h): + check_sources() + config=json.loads((HERE/'selection.json').read_text())['axes'][str(h)] + previous_graph,previous_order=provider.graph,provider.ordered_build + # graph() calls the original provider; keep that callable private while + # the inherited driver resolves the selected composed graph dynamically. + original_graph=previous_graph + def selected_graph(dimension): + provider.graph=original_graph + try:return graph(dimension) + finally:provider.graph=selected_graph + try: + provider.graph=selected_graph + provider.ordered_build=lambda original,dimension:original + compiled,word=ancestor.compile_axis(h) + finally: + provider.graph,provider.ordered_build=previous_graph,previous_order + compiled['graph_configuration']=config + word=relabel(word,config['coordinate_permutation']) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + path=HERE/f'word-{h}.json.gz' + with path.open('wb') as stream: + with gzip.GzipFile(filename='',fileobj=stream,mode='wb',mtime=0) as archive:archive.write(raw) + receipt=replay(path) + assert sha256(raw).hexdigest()==config['expected_word_sha256'] + axis=dict(configuration=config,compiled=compiled,replay=receipt, + word_sha256=sha256(raw).hexdigest(),gzip_sha256=sha256(path.read_bytes()).hexdigest()) + (HERE/f'axis-{h}.json').write_text(json.dumps(axis,indent=2)+'\n') + print(f'PASS fresh balanced/split/core word h={h}, roles={receipt["roles"]}',flush=True) + + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--h',type=int,choices=(23,25));args=parser.parse_args() + if args.h:compile_axis(args.h) + else: + with ProcessPoolExecutor(max_workers=2) as pool:list(pool.map(compile_axis,(23,25))) diff --git a/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/profile-23.json b/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/profile-23.json new file mode 100644 index 0000000000..013f4e59c7 --- /dev/null +++ b/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/profile-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27136,"loss":506,"rank_sum":624634,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38292,"crt_matrices":5488,"crt_disagreements":0,"blocks":[0,355721,21666,6948,6524,3093,4314,2400,3266,1501,2094,1008,1374,586,732,353,307,139,62,16,0,23,0,0]} diff --git a/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/profile-25.json b/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/profile-25.json new file mode 100644 index 0000000000..1e3b6b89aa --- /dev/null +++ b/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/profile-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35744,"loss":600,"rank_sum":894200,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52202,"crt_matrices":7623,"crt_disagreements":0,"blocks":[0,490052,26188,13531,7191,4637,5355,4229,3705,2610,2620,2080,1814,1357,1070,868,612,463,233,56,141,0,71,25,0,0]} diff --git a/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/selection.json b/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/selection.json new file mode 100644 index 0000000000..57cf3b6b65 --- /dev/null +++ b/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/selection.json @@ -0,0 +1,86 @@ +{ + "source_pr71": "1bef94fd40a746452548c84a4a8f8834670a3113", + "source_pr69": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "axes": { + "23": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 22, + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 20, + 19, + 21 + ], + "expected_word_sha256": "8dc6696a274e70ca0af3fc49c4bdede362adaedc8dc322f335e3dab499f1ed48" + }, + "25": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 2, + 1, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "expected_word_sha256": "2c923afe366219ee3fffc9db063c91e44cdf7cbbdb62246b8e6a297dc440b577" + } + } +} diff --git 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"bd767d460a85414ca320a449705860a376bee42cb8ce0734233a8e9706ad4fc5" + } + }, + "repo": "rohanarun/integer-mult-bounds", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/82" +} diff --git a/references/frame-compiler/final-r10/references/pr82/LICENSE b/references/frame-compiler/final-r10/references/pr82/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/final-r10/references/pr82/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Balanced coarse split composition (2026-10-08) +--------------------------------------------- +Eumemic / @eumemic supplied PR69's balanced coarse sums, with OpenAI Codex +assistance. Alejandro Zarzuelo Urdiales / @alejandrozu supplied PR70's bounded +carry-exchange strategy with the AI disclosures retained in the source archive. +Chafik Boukhalfa / @chafreaky, with OpenAI Codex assistance, selected the row/ +half-plane coarse rules, future-compatible unit completion, exact integer-price +carry adaptation, composition and this certificate package. The PR71 anchored +split vector, schedules, arithmetic, pending controls and their contributor +chain are retained as credited above. Original PR69/70 sources, licenses and +notices and the complete published PR71 baseline are preserved under +references/frame-compiler. All earlier notices remain applicable. diff --git a/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/README.md b/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/README.md new file mode 100644 index 0000000000..77486a38c2 --- /dev/null +++ b/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/README.md @@ -0,0 +1,127 @@ +# Envelope ordering inside balanced split compilation + +The finite conditional witness gives **kappa = 5203279888519/100000000000000000 = 5.2032798885190e-05**, +0.49049670% above PR80. Bit saving is 13008876609597/250000000000000000. +This is a draft pending the full expanded repository verification. + +PR80 selected already-compiled axes from PR76 and PR79. Here we compose +their construction methods before compilation on both axes: PR79's balanced +coarse graph and future-compatible unit completion; PR76/PR74's envelope +node ordering; three passes of PR79/PR70's bounded carry exchanges; and +PR78's geometric coordinate flags. h23 uses the half-plane coarse choice +and cover-core schedule; h25 uses row coarse sums and reverse-node schedule. +Both retain the anchored [1,1,2] split vector and exact next-use profile costs. +All archived sources are unchanged. `compiler.py` is the portable composition. +At h25 the discovery oracle receives coordinate-permuted frame masks, so its +costs refer to the final flag rather than the original coordinate order. +`flag_engine.py` differs from PR79's engine only in that oracle frame writer +and an attribution comment; operations, eligibility, independence and dirty +checks are unchanged. This changes only heuristic selection among legal +choices. Its final word is still independently replayed and exactly priced. +At h23 oracle pricing retains the original coordinate order. + +| Quantity | PR80 | This witness | +|---|---:|---:| +| h23 auxiliary roles | 27256 | 27075 | +| h25 auxiliary roles | 35684 | 35500 | +| Physical width | 134031764 | 133289600 | +| Total recursive rank | 77066417400 | 76639673100 | +| Deficit | 1846900 | 1846900 | + +## General compatibility argument + +Balanced coarse parenthesization changes only how the same Cartesian-product +edge sums are evaluated. The weighted scalar identities and recursively +contracting anchored partition are inherited from PR79's proof. Envelope +ordering then applies a bijection to non-source scalar node IDs, grouping +nodes by (core, cover), preserving the order inside each group and every +argument, output and provenance reference. It changes no scalar linear form +or frame. The graph verifier is rerun after this relabeling. Dependency and +carrier-eligibility checks in the compiler remain enabled. + +Future-compatible completion chooses independent unit rows after the desired +outputs and retained carriers. Any accepted independent completion is a full +invertible basis; the unchanged synthesis emits its literal XOR operations. +Bounded carrier exchanges preserve matching cardinality, unique uses and +independence of the output-plus-retained-input rows. These choices can change +each other's costs, so the words are recompiled and every profile recomputed; +we do not add reported savings or assume independent numerical gains. + +All clearing targets and controls remain charged. Both frame-containment +checks for pending controls remain enabled. The compiler and independent +replay verify the full arbitrary-dirty-role wrapper in both orientations. +Independent axis implementations expose the same source triple lines, fixed +I+J basis, terminal frames and scatter identity. Hence the complete tensor/data +construction is unchanged. Every endpoint/copy/data-growth/complex term is +retained exactly once. The fixed-width bridge is derived from the actual W. + +## General relabeling argument + +Let P be a permutation matrix on the h coordinates. It commutes with J, +so P commutes with the fixed basis L = I+J and preserves the form I-J/9. +For a core/cover frame F(C,U), the relabeled projector is +P F(C,U) P^-1 = F(P C,P U). Consequently, every frame inclusion, rank, +nondegeneracy condition, projector denominator bound and elementary role +operation is preserved. The existing exact CRT bounds apply unchanged. + +Relabel each input triple T to P T, each output (c,T) to (P c,P T), +each frame mask by P, and each scatter row by the induced triple permutation. +The role slots and literal XOR operations do not change. This conjugates +the complete linear word by the input/output permutation and therefore +preserves its identity on every ordinary input and arbitrary dirty role. +The verifier independently replays that identity in both orientations. + +The data component sums over every pair of source triples. Independent +coordinate permutations on the two axes induce a bijection on that complete +Cartesian product. Hence its existing complete histogram, copied-center +costs and endpoint corrections are unchanged. This argument uses the full +case set; it would not justify retaining a selected subset's histogram. + +North-east corner rank profiles depend on the fixed coordinate order. +Conjugating by P can change which adjacent pivots form a recursive block, +even though total rank is unchanged. We regenerate these profiles from the +actual relabeled words rather than assuming their costs are invariant. +Both dimensions use the selected orders in order-23.json and order-25.json. + +## Reproduction and validation + +From the repository root with assert-enabled Python 3.11+ and C++17: + +```sh +python3 research/envelope-balanced/verify.py --regenerate +(cd research/envelope-balanced && python3 -m unittest test_controls -v) +make verify +``` + +The regeneration option launches two isolated compiler processes and requires +both original words to reproduce byte-for-byte. The verifier then regenerates +the coordinate-permuted words, performs independent full input/dirty replay, +reconstructs all transitions, and regenerates exact bounded-minor/CRT profiles. +The complete paid child list is reconstructed; independent rational moment +bounds, 47 strict inequalities, seven margins and both next-grid exclusions +are checked. The complete PR76, PR79 and PR80 child lists are each excluded at +the new bit saving using their own width. Six physical/coordinate failure +controls and three stale bridge controls run separately. A dedicated +three-version CI workflow retains every inherited workflow. + +The bounded searches are not proofs of global optimality. All inherited +all-size residual compiler, routing, recovery, prime selection, finite +alphabet/tape, precision and analytic transfer interfaces remain hypotheses. +No unconditional multiplication theorem or practical speedup is claimed. + +## Attribution + +Thomas DiFiore (PR74) introduced the envelope ordering; Dominik Scholz +(PR76) composed it with carried exchanges; Chafik Boukhalfa (PR79/71) +provided balanced/future/exchange and anchored split compilation; eumemic +(PR69/57) provided balanced coarse sums and reversible compilation; +Alejandro Zarzuelo Urdiales (PR70) supplied the carry-exchange strategy; +Rohan Arun (PR78/80/65/67) supplied coordinate flags, axis selection, +schedules and profile-cost reclamation. This new pre-compilation composition +and finite selection were prepared by Rohan Arun with OpenAI Codex assistance. + +Credit also Rohan Garg, Avi Eisenberg, icekylinx, James Chang, Zhihao Chen, +Aurel Prosz/Paureel, Swapnil Jain, RaD/hipotures, Douglas Colkitt, OpenAI, +Harvey–van der Hoeven and all inherited contributors. Original licenses, +author and AI-assistance notices remain preserved. Tested PR75 zero-circuit +variants were not selected for this witness and are not claimed as its method. diff --git a/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/SOURCE.json b/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/SOURCE.json new file mode 100644 index 0000000000..6b7fbca6d0 --- /dev/null +++ b/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/SOURCE.json @@ -0,0 +1,304 @@ +{ + "parent_pr80": "a9ed157ff106fd35557b5896197f66a1272f7f13", + "files": { + ".gitattributes": "5f257f4e9e574ad5767f902242f519dad19cc455d6858f49234d0ccc345cabf1", + ".github/workflows/combined-flags.yml": "53d0f33c83356b2764f3cb332892690ff74ffa0e68b9ae1203fe837979c15396", + ".github/workflows/envelope-balanced.yml": "d658c2f91e1377eac5288cff7725ae1e573efdff70dac5472e6a4060085ab7fc", + ".github/workflows/verify.yml": "1a9cccd742ba2a5aa5a5ac38c1b7559bc0dec46b23d3ce3ff3e26c3137e6c3a2", + "Makefile": 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Composition by Rohan Arun +with OpenAI Codex assistance. Apache-2.0; finite conditional witness only. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2] +sys.path.insert(0,str(ROOT/'scripts/experiments')) +import balanced_split_graph as graph +import balanced_split_exchange_engine as baseline_engine +import flag_engine +sys.path.insert(0,str(ROOT/'references/frame-compiler/pr76/research/round7-scheduling')) +from schedule_variant import reorder +import argparse,gzip,json,subprocess,os,shlex + +def check_flag_engine(): + original=(ROOT/'scripts/experiments/balanced_split_exchange_engine.py').read_text() + before="for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank']))" + after="for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank']))" + assert original.count(before)==1 + expected='# Coordinate-conjugated oracle pricing by Rohan Arun with OpenAI Codex.\n'+original.replace(before,after) + assert (Path(__file__).parent/'flag_engine.py').read_text()==expected,'Flag engine contains changes beyond oracle coordinate pricing' + +def compile_axis(h,work): + check_flag_engine() + engine=flag_engine if h==25 else baseline_engine + if h==25: + cfg=json.loads((ROOT/f'research/envelope-balanced/order-{h}.json').read_text()) + assert sorted(cfg['order'])==list(range(h)) + engine.COORD_MAP={int(k):v for k,v in cfg['mapping'].items()} + assert engine.COORD_MAP=={old:new for new,old in enumerate(cfg['order'])} + work.mkdir(parents=True,exist_ok=True) + oracle=work/'oracle' + subprocess.run([*shlex.split(os.environ.get('CXX','c++')),'-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/profile_oracle.cpp'),'-o',str(oracle)],check=True) + engine.graph=lambda dimension:reorder(graph.graph(dimension)) + engine.build=graph.ordered_build(engine.build,h) + engine.ORACLE_EXE=str(oracle);engine.ORACLE_INPUT=str(work/'oracle.bin');engine.PENDING_COST=True;engine.oracles=[] + try:result,word=engine.compile_(h,matching=True,reclaim=True,dirty=True) + finally: + for process in engine.oracles: + process.stdin.close();assert process.wait(timeout=10)==0 + result.pop('seconds',None);result['scalar']=engine.graph(h).verify() + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + (work/'word.json.gz').write_bytes(gzip.compress(raw,mtime=0)) + (work/'compiler.json').write_text(json.dumps(result,indent=2)+'\n') + print('PASS compiled envelope-balanced axis',h,result['roles'],flush=True) + +if __name__=='__main__': + p=argparse.ArgumentParser();p.add_argument('--h',type=int,choices=(23,25),required=True);p.add_argument('--work',type=Path,required=True);args=p.parse_args();compile_axis(args.h,args.work) diff --git a/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/flag_engine.py b/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/flag_engine.py new file mode 100644 index 0000000000..d210d9336b --- /dev/null +++ b/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/flag_engine.py @@ -0,0 +1,312 @@ +# Coordinate-conjugated oracle pricing by Rohan Arun with OpenAI Codex. +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(index[int(i)]):s for i,s in word['sources'].items()} + v=word['v'];word['scatter']=[[v+index[a-v],b] for a,b in word['scatter']] + word['outputs']=[[s,g,perm[c],sorted(perm[x] for x in triple)] for s,g,c,triple in word['outputs']] + return word + +def exact(profiles): + cert=json.loads((HERE/'certificate.json').read_text()) + N=comb(23,3)*comb(25,3);m=575;W=2*N+sum(N//p['v']*p['R'] for p in profiles) + L=sum(N//p['v']*p['loss'] for p in profiles) + rows=Counter({1:19*N,21:2*N,17:2*N,481:2*N}) + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 and p['v']==comb(h,3) + assert sum(t*n for t,n in enumerate(p['blocks']))==h*p['R']+h*(h-1)==p['rank_sum'] + rows.update({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + rows[h]+=bank;rows[m-2*h]+=bank;rows[1]+=2*N;rows[h-2]+=2*N + bit=dict(m=m,N=N,W=W,L=L,total_rank=sum(t*n for t,n in rows.items()),child_multiplicities=dict(sorted(rows.items()))) + assert bit['total_rank']==m*W-N+L + assert arithmetic.js(bit)==cert['bit'] + saving=Q(cert['bit_saving']);moment=refine.exact_moment(m,W,rows,saving) + rejected=refine.exact_moment(m,W,rows,saving+Q(1,10**18)) + assert moment['upper']<11 + assert Q(cert['kappa'])>Q(old['kappa']) + print('PASS exact conditional kappa',result['kappa'],'47 constraints, seven margins, independent bounds and next-grid controls') + +def verify(regenerate=False): + sources();profiles=[] + with tempfile.TemporaryDirectory(prefix='coordinate-flags-') as directory: + work=Path(directory);exe=work/'profiles' + subprocess.run(['c++','-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'scripts/experiments/binary_frame_profiles.cpp'),'-o',str(exe)],check=True) + if regenerate: + jobs=[] + for h in (23,25): + axis=work/str(h);axis.mkdir() + jobs.append(subprocess.Popen([sys.executable,str(HERE/'compiler.py'),'--h',str(h),'--work',str(axis)])) + for job in jobs:assert job.wait()==0,'Portable compiler regeneration failed' + for h in (23,25): + assert gzip.decompress((work/str(h)/'word.json.gz').read_bytes())==gzip.decompress(original_path(h).read_bytes()),'Regenerated physical word changed' + print('PASS portable deterministic regeneration of both unpermuted words',flush=True) + for h in (23,25): + original=json.loads(gzip.decompress((original_path(h)).read_bytes())) + config=json.loads((HERE/f'order-{h}.json').read_text());word=relabel(original,config) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + assert raw==gzip.decompress((HERE/f'word-{h}.json.gz').read_bytes()) + path=work/f'word-{h}.json';path.write_bytes(raw);checked=replay(path) + stored=json.loads((HERE/f'replay-{h}.json').read_text());assert arithmetic.js(checked)==stored['replay'] + trans=work/f'transitions-{h}.bin';receipt=prepare(path,trans);assert arithmetic.js(receipt)==stored['transitions'] + subprocess.run([str(exe),str(trans)],check=True) + profile=json.loads(Path(str(trans)+'.profiles.json').read_text());assert profile==json.loads((HERE/f'profiles-{h}.json').read_text()) + profiles.append(profile);print('PASS complete relabelled physical word and profile',h,flush=True) + exact(profiles) +if __name__=='__main__': + import argparse + parser=argparse.ArgumentParser();parser.add_argument('--regenerate',action='store_true');args=parser.parse_args();verify(args.regenerate) diff --git a/references/frame-compiler/final-r10/research/pair-assembly/pair_graph.py b/references/frame-compiler/final-r10/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/final-r10/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/final-r10/research/reordered-rank-pair/arithmetic/refine.py b/references/frame-compiler/final-r10/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/final-r10/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/final-r10/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/final-r10/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/final-r10/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/final-r10/research/reordered-rank-pair/verify.py b/references/frame-compiler/final-r10/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/final-r10/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/final-r10/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/final-r10/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/final-r10/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/final-r10/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/final-r10/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/final-r10/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<0 and carry_can(x,f) and carry_can(other,y): + options.append((-gain,z,x,y,other)) + if not options:continue + _,z,x,y,other=min(options) + old=(f,z,y);new=(e,x,other) + assert len(set(old))==len(set(new))==3 and not set(old)&set(new) + assert {edges[t][1] for t in old}=={edges[t][1] for t in new} + assert len({edges[t][0] for t in old})==len({edges[t][0] for t in new})==3 + for t in old: + tg,tu,ti=edges[t];chosen.remove(t);blocks[tg]['selected'].remove(t);del right[tu] + for t in new: + tg,tu,ti=edges[t];assert tu not in right;chosen.add(t);blocks[tg]['selected'].add(t);right[tu]=t + changes+=1 + return changes + + +def compile_(h,matching=True,reclaim=False,dirty=True): + t0=time.time();c,blocks,uses,value_uses,owner,signal,order,contains=build(h);v=len(c.inputs);position={g:i for i,g in enumerate(order)} + print('built',h,len(blocks),'regions',flush=True,file=sys.stderr) + mode=globals().get('OUTPUT_MODE','baseline') + edges,chosen,right,stats=match(blocks,uses,matching) + print('matched',len(chosen),'seconds',time.time()-t0,flush=True,file=sys.stderr) + slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();retired_index=RetiredIndex(h);pending={};pending_index=PendingIndex(h);stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + oracle_map=globals().get('ORACLE_COORDINATES',list(range(h))) + assert sorted(oracle_map)==list(range(h)), 'Invalid oracle coordinate permutation' + for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + for phase in range(globals().get('THREE_CYCLE_PASSES',0)): + changes=improve_three_cycles(blocks,edges,chosen,right,prices,priority,carry_can) + stats['carry_three_cycles']+=changes + print('carry three-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=3 or result[0]==0 +assert accepted>0 +print(json.dumps({'status':'PASS','actual_source':str(ROOT/'scripts/experiments/compiler.py'),'fixtures':1604,'accepted_three_cycles':accepted,'checks':['strict-cycle-only fixture','equal and worsening cost rejected','dependent replacement rejected','cardinality','one use per choice','local vector independence','exact integer descent','determinism','distinct block requirement']})) diff --git a/references/frame-compiler/indexed-r5/EXPERIMENT.txt b/references/frame-compiler/indexed-r5/EXPERIMENT.txt new file mode 100644 index 0000000000..ad69d585b0 --- /dev/null +++ b/references/frame-compiler/indexed-r5/EXPERIMENT.txt @@ -0,0 +1 @@ +Compose Thomas DiFiore PR74 exact node-envelope renumbering with independently audited two-cycle matching, future completion, exact indexed reclamation, and selected h25 late output-use routing. Test six grouping structures and three coarse-sum orientations per dimension. Canary retains unchanged earlier cycles112 graph/schedule and hashes. Every new scalar graph and dirty physical word is independently checked and CPU CRT profiles/certificates are rebuilt. Imported PR74 functions and source/credits are preserved exactly. No imported claim is re-verified as a gate. diff --git a/references/frame-compiler/indexed-r5/LICENSE b/references/frame-compiler/indexed-r5/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/indexed-r5/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. diff --git a/references/frame-compiler/indexed-r5/SOURCE.json b/references/frame-compiler/indexed-r5/SOURCE.json new file mode 100644 index 0000000000..1f208b3942 --- /dev/null +++ b/references/frame-compiler/indexed-r5/SOURCE.json @@ -0,0 +1,61 @@ +{ + "experiment": "envelope-r5", + "files": { + "EXPERIMENT.txt": "7547e7255fc629a6887398c6b68d5432fdf8f6c8325db1b73e0616a02ee54eaa", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "62d9c3390f8c61fcc5efcdbeb4cd60ceb7b31aaf75c4ac214288fd72c86a5890", + "baseline/exact-results.json": "3e7e34ff9a3b61540de9c834bc393e6430972f5adfb549c9fafa15bd52ad3bbd", + "baseline/h23/profiles.json": "1764c61542871447ed5604d8b4a93f8d9bf542d5a3ffee8ee30cf4b2ed5a1feb", + "baseline/h23/replay.json": "209ba40e8ad00526cbd4e83097d14d8fbe85d3d0f30435dee50fcf3fde0142b3", + 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a/references/frame-compiler/indexed-r5/baseline/h23/profiles.json b/references/frame-compiler/indexed-r5/baseline/h23/profiles.json new file mode 100644 index 0000000000..7baddf40c6 --- /dev/null +++ b/references/frame-compiler/indexed-r5/baseline/h23/profiles.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27285,"loss":506,"rank_sum":628061,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38513,"crt_matrices":5538,"crt_disagreements":0,"blocks":[0,356669,20912,7996,5407,4043,3702,3146,2579,1990,1706,1444,980,839,542,483,239,205,49,97,0,23,0,0]} diff --git a/references/frame-compiler/indexed-r5/baseline/h23/replay.json b/references/frame-compiler/indexed-r5/baseline/h23/replay.json new file mode 100644 index 0000000000..d37ffd1add --- /dev/null +++ b/references/frame-compiler/indexed-r5/baseline/h23/replay.json @@ -0,0 +1,34 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27285, + "output_roles": 5336, + "elementary_xors": 160435, + "word_length": 666534, + "full_basis_vectors": 30827, + "rank_mass": 628061, + "histogram": { + "1": 58281, + "0": 171307, + "2": 80793, + "4": 14511, + "3": 10007, + "5": 6429, + "6": 2036, + "8": 1110, + "10": 535, + "9": 471, + "12": 661, + "14": 1868, + "13": 193, + "16": 431, + "11": 120, + "17": 574, + "18": 3412, + "15": 334, + "19": 6482, + "22": 23, + "21": 393, + "7": 627 + } +} diff --git a/references/frame-compiler/indexed-r5/baseline/h23/result.json b/references/frame-compiler/indexed-r5/baseline/h23/result.json new file mode 100644 index 0000000000..349e949822 --- /dev/null +++ b/references/frame-compiler/indexed-r5/baseline/h23/result.json @@ -0,0 +1,19 @@ +{ + "h": 23, + "roles": 27285, + "stats": { + "augmentations": 13, + "regions": 59801, + "matched": 41730, + "multi_node_regions": 8694, + "carry_exchanges": 644, + "carry_two_cycles": 52, + "live_anchor_candidates": 72361, + "reclaimed": 2125, + "clearing_xors": 3916, + "live_anchor_xors": 76 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "word_sha256": "3f58db33edc2059ad6ca01cf8c36dd8cd8ae12149e1072e1f42757ca4ef17b82" +} diff --git a/references/frame-compiler/indexed-r5/baseline/h25/profiles.json b/references/frame-compiler/indexed-r5/baseline/h25/profiles.json new file mode 100644 index 0000000000..2be4368700 --- /dev/null +++ b/references/frame-compiler/indexed-r5/baseline/h25/profiles.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35684,"loss":600,"rank_sum":892700,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":51168,"crt_matrices":7278,"crt_disagreements":0,"blocks":[0,491871,27309,10127,7839,5460,4947,4006,3802,2943,2456,2025,1787,1423,1124,867,560,478,221,170,46,59,0,25,0,0]} diff --git a/references/frame-compiler/indexed-r5/baseline/h25/replay.json b/references/frame-compiler/indexed-r5/baseline/h25/replay.json new file mode 100644 index 0000000000..3ec3c54dc6 --- /dev/null +++ b/references/frame-compiler/indexed-r5/baseline/h25/replay.json @@ -0,0 +1,36 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 35684, + "output_roles": 6925, + "elementary_xors": 224161, + "word_length": 928844, + "full_basis_vectors": 40284, + "rank_mass": 892700, + "histogram": { + "1": 77041, + "0": 238437, + "2": 118217, + "3": 13314, + "4": 18459, + "6": 3215, + "5": 8388, + "7": 948, + "8": 1195, + "9": 721, + "10": 828, + "12": 708, + "13": 182, + "14": 653, + "16": 2171, + "18": 506, + "19": 981, + "17": 633, + "15": 187, + "11": 15, + "20": 4464, + "21": 8405, + "24": 25, + "23": 463 + } +} diff --git a/references/frame-compiler/indexed-r5/baseline/h25/result.json b/references/frame-compiler/indexed-r5/baseline/h25/result.json new file mode 100644 index 0000000000..50b259fcd7 --- /dev/null +++ b/references/frame-compiler/indexed-r5/baseline/h25/result.json @@ -0,0 +1,19 @@ +{ + "h": 25, + "roles": 35684, + "stats": { + "augmentations": 16, + "regions": 84843, + "matched": 60971, + "multi_node_regions": 11575, + "carry_exchanges": 1000, + "carry_two_cycles": 62, + "live_anchor_candidates": 98464, + "reclaimed": 3263, + "clearing_xors": 6027, + "live_anchor_xors": 132 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "word_sha256": "7c60369042197c356dfac3516ae396d68dc92edbc5824b6078dce0e6676f7f79" +} diff --git a/references/frame-compiler/indexed-r5/batch.py b/references/frame-compiler/indexed-r5/batch.py new file mode 100644 index 0000000000..1f994fa396 --- /dev/null +++ b/references/frame-compiler/indexed-r5/batch.py @@ -0,0 +1,113 @@ +"""Durable independent CPU search over pinned current two-cycle construction. +Each accepted case regenerates and independently replays the literal word, +reconstructs paid frames, computes CPU CRT profiles and exact inequalities. +""" +from pathlib import Path +from hashlib import sha256 +from concurrent.futures import ProcessPoolExecutor,as_completed +import argparse,ast,cProfile,gzip,importlib.util,json,os,pstats,subprocess,sys,time,types +ROOT=Path(__file__).resolve().parent +sys.path.insert(0,str(ROOT/'scripts/experiments')) + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m + +def generate(h,groups,profile=False,mode="baseline"): + started=time.monotonic();out=ROOT/'results'/f'{h}-{groups}-{mode}';out.mkdir(parents=True,exist_ok=True) + compiler=load('search_compiler',ROOT/'scripts/experiments/compiler.py') + source=(ROOT/'research/pair-assembly/pair_graph.py').read_text() + donor=ROOT/'references/pr69/balanced_coarse_compiler.py' + constants={n.targets[0].id:ast.literal_eval(n.value) for n in ast.parse(donor.read_text()).body if isinstance(n,ast.Assign) and isinstance(n.targets[0],ast.Name) and n.targets[0].id in ('BEFORE','AFTER')} + replacement=constants['AFTER'];needle='columns = [self.total([e(a,b) for a in groups[i]]) for b in groups[j]]' + orientation=mode.removeprefix('envelope-') if mode.startswith('envelope-') else ('half' if h==23 else 'row') + if orientation=='half': + replacement=replacement.replace(needle,'columns = ([self.total([e(a,b) for a in groups[i]]) for b in groups[j]] if i+j < ng-1 else [self.total([e(a,b) for b in groups[j]]) for a in groups[i]])') + elif orientation=='row':replacement=replacement.replace(needle,'columns = [self.total([e(a,b) for b in groups[j]]) for a in groups[i]]') + assert source.count(constants['BEFORE'])==1 + graph=types.ModuleType('balanced_graph');graph.__file__=str(ROOT/'research/pair-assembly/pair_graph.py');exec(compile(source.replace(constants['BEFORE'],replacement),graph.__file__,'exec'),graph.__dict__) + original=graph.circuit_class + def subclass(dim): + parent=original(dim) + class Split(parent): + def grouping(self,points): + result=super().grouping(points);choices=[int(x) for x in groups];choice=choices[self._level] if self._level3 and choice: + first,mid,last=0,(len(result)-1)//2,len(result)-1 + requested={1:[first],2:[mid],3:[last],4:[first,mid],5:[first,last],6:[mid,last],7:[first,mid,last],8:[first,first+1],9:[last-1,last]}[choice] + chosen=[] + for k in requested: + if k not in chosen and 0<=k1:hi=mid + else:raise ArithmeticError('Enclosure inconclusive') + a=Q(lo,den);bridge=deepcopy(baseline['finite_bridge']);bridge['bit']['W']=p['W'] + bridge['bit']['wire_bits']=p['W'].bit_length() + bridge['rows']['coefficient']=sum(bridge[name]['halving_degree']*bridge[name]['wire_bits'] for name in ('bit','complex')) + bridge['rows']['degree_gap']=Q(bridge['rows']['degree'])-Q(51,25)*bridge['rows']['coefficient'] + bridge['rows']['suffix_slope']=4*bridge['rows']['degree'] + accepted=refine.exact_moment(m,p['W'],rows,a);rejected=refine.exact_moment(m,p['W'],rows,Q(hi,den));assert accepted['upper']<1prior and best['prior65_moment']['lower']>1 + for r in rows: + r['moment_at_best_bit']=refine.exact_moment(m,r['bit']['W'],r['bit']['child_multiplicities'],best['bit_saving']) + output={'verified_baseline':{'pr':65,'commit':'49e84f939d15b618b50714eb039cabf97c74256a','kappa':prior},'best':best,'rows':rows,'cases':len(rows)} + (HERE/'fine-pair-comparison.json').write_text(json.dumps(refine.arithmetic.js(output),indent=2,sort_keys=True)+'\n') + (HERE/'selected-exact-result.json').write_text(json.dumps(refine.arithmetic.js(best),indent=2,sort_keys=True)+'\n') + print('BEST',json.dumps({'pair':best['pair'],'kappa':str(best['kappa']),'bit_saving':str(best['bit_saving']),'W':best['bit']['W'],'gain_percent_vs_verified65':float(100*(best['kappa']/prior-1))},sort_keys=True),flush=True) diff --git a/references/frame-compiler/indexed-r5/nodeops.py b/references/frame-compiler/indexed-r5/nodeops.py new file mode 100644 index 0000000000..fa6164310d --- /dev/null +++ b/references/frame-compiler/indexed-r5/nodeops.py @@ -0,0 +1,40 @@ +# Exact function extracts from Thomas DiFiore PR74,3f78d8967c009153f2df5c6a6577b6ab1d37e2ca. Apache-2.0; original source and notices retained. + +def reorder(c): + groups={} + for x in sorted(c.active): + if c.args[x]: groups.setdefault((c.core[x],c.union[x]),[]).append(x) + def key(item): + (core,cover),nodes=item + return cover.bit_count()-core.bit_count(),-core,cover,min(nodes) + ids=list(range(len(c.inputs)+1))+[x for _,nodes in sorted(groups.items(),key=key) for x in nodes] + mapping={x:i for i,x in enumerate(ids)} + args,core,cover,provenance=c.args,c.core,c.union,c.provenance + c.args=[tuple(mapping[y] for y in args[x]) if args[x] else None for x in ids] + c.core=[core[x] for x in ids];c.union=[cover[x] for x in ids] + c.provenance=[provenance[x] for x in ids] + c.active={mapping[x] for x in c.active};c.outputs={k:mapping[v] for k,v in c.outputs.items()} + c.support_in.cache_clear() + c.verify() + return c + + +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + diff --git a/references/frame-compiler/indexed-r5/original/carry_cycle_compiler.py b/references/frame-compiler/indexed-r5/original/carry_cycle_compiler.py new file mode 100644 index 0000000000..d883cbc71d --- /dev/null +++ b/references/frame-compiler/indexed-r5/original/carry_cycle_compiler.py @@ -0,0 +1,338 @@ +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path('/Users/chafreaky/Documents/personal/integer-mult-research-20261008/joint-reclaim/references/frame-compiler/pr48') +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": "41187950749917624099/1000000000000000000000000", + "cell_above_band": "666666666665666652937349833360791967/1333388250600666556832132000000000000", + "compact_leaf": "26927049500082375901/1000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "13729317166639208033/333347062650166639208033", + "epsilon_positive": "333333333333000000000000/333347062650166639208033", + "g1_above_kappa": "3408408254232349301008147/3333470626501666392080330000000000000", + "g2_above_kappa": "4241/2500000000000", + "g3_above_kappa": "74937627730682908927817/3333470626501666392080330000000000000", + "g4_above_kappa": "4241/2500000000000", + "g5_above_kappa": "5299956450675231223831763/13333882506006665568321320000000000000", + "g6_above_kappa": "11966897703678564007992423/13333882506006665568321320000000000000", + "g7_above_kappa": "3333196040161742016173902349301008147/3333470626501666392080330000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "13729317166639208033/333347062650166639208033", + "lambda_above_internal": "82375901/2000000000000000000000000", + "lambda_above_sigma": "61024099000082375901/2000000000000000000000000", + "lambda_above_tau": "82375901/2000000000000000000000000", + "lambda_prime_above_lambda": "82375901/2000000000000000000000000", + "lambda_prime_below_one": "41187950499917624099/1000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "21966907133275670202633360791967/533355300240266622732852800000000000", + "phase_leaf_above_bit": "53854099/2000000000000", + "phase_local": "109834536999766601613833360791967/2666776501201333113664264000000000000", + "prime_interval_packing": "13729317166639208033/333347062650166639208033", + "q_below_internal": "82375901/1000000000000000000000000", + "q_below_leaf": "26927049500082375901/1000000000000000000000000", + "q_below_reservations": "1/4000000000000", + "q_positive": "41187950499917624099/1000000000000000000000000", + "record_suffix": "13729317166639208033/333347062650166639208033", + "row_product_gap": "6548/25", + "short_record_fallback": "666639206901368489075295096355187267/666694125300333278416066000000000000", + "small_field_exposure": "1/1000000000000" + }, + "finite_bridge": { + "bit": { + "W": 177530859, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "margins": { + "g1": "13729317166639208033/333347062650166639208033", + "g2": "82375901/2000000000000", + "g3": "13729316833292145382833360791967/333347062650166639208033000000000000", + "g4": "82375901/2000000000000", + "g5": "21966907133275670202633360791967/533355300240266622732852800000000000", + "g6": "109834536999766601613833360791967/2666776501201333113664264000000000000", + "g7": "333333333333000000000000/333347062650166639208033" + }, + "minimum_margin": "13729316833292145382833360791967/333347062650166639208033000000000000", + "parameters": { + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": "1", + "a_bit": "82375901/2000000000000", + "a_complex": "717/10000000", + "alpha_squared_power": "27458633999931353415833360791967/666694125300333278416066000000000000", + "beta": "1/20", + "c": "41187950749917624099/1000000000000000000000000", + "delta": "1/8000000000000", + "epsilon": "333333333333000000000000/333347062650166639208033", + "h": 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000000000, + "cutoff_log2_input": { + "alpha": 5956134977, + "compact": 23824539905, + "geometry": 3999930893196446780, + "guard": 4283152, + "log_p": 25, + "normalization": 14000000000000000000, + "period": 47649079809, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000000000, + "powers": { + "alpha": { + "exponent": 725614180574271, + "rhs": 112000000000000154416, + "rhs_bits": 67 + }, + "compact": { + "exponent": 725614180574271, + "rhs": 448000000000000617600, + "rhs_bits": 69 + }, + "leaf": { + "exponent": 666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 725614180574271, + "rhs": 224000000000000308760, + "rhs_bits": 68 + }, + "rows": { + "exponent": 725614180574271, + "rhs": 112000000000000154416000, + "rhs_bits": 77 + } + } + }, + { + "log2_input": 28000000000000000000, + "powers": { + "alpha": { + "exponent": 1451228361148543, + "rhs": 224000000000000154416, + "rhs_bits": 68 + }, + "compact": { + "exponent": 1451228361148543, + "rhs": 896000000000000617600, + "rhs_bits": 70 + }, + "leaf": { + "exponent": 1333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1451228361148543, + "rhs": 448000000000000308760, + "rhs_bits": 69 + }, + "rows": { + "exponent": 1451228361148543, + "rhs": 224000000000000154416000, + "rhs_bits": 78 + } + } + }, + { + "log2_input": 56000000000000000000, + "powers": { + "alpha": { + "exponent": 2902456722297087, + "rhs": 448000000000000154416, + "rhs_bits": 69 + }, + "compact": { + "exponent": 2902456722297087, + "rhs": 1792000000000000617600, + "rhs_bits": 71 + }, + "leaf": { + "exponent": 2666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2902456722297087, + "rhs": 896000000000000308760, + "rhs_bits": 70 + }, + "rows": { + "exponent": 2902456722297087, + "rhs": 448000000000000154416000, + "rhs_bits": 79 + } + } + }, + { + "log2_input": 112000000000000000000, + "powers": { + "alpha": { + "exponent": 5804913444594174, + "rhs": 896000000000000154416, + "rhs_bits": 70 + }, + "compact": { + "exponent": 5804913444594174, + "rhs": 3584000000000000617600, + "rhs_bits": 72 + }, + "leaf": { + "exponent": 5333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5804913444594174, + "rhs": 1792000000000000308760, + "rhs_bits": 71 + }, + "rows": { + "exponent": 5804913444594174, + "rhs": 896000000000000154416000, + "rhs_bits": 80 + } + } + }, + { + "log2_input": 224000000000000000000, + "powers": { + "alpha": { + "exponent": 11609826889188348, + "rhs": 1792000000000000154416, + "rhs_bits": 71 + }, + "compact": { + "exponent": 11609826889188348, + "rhs": 7168000000000000617600, + "rhs_bits": 73 + }, + "leaf": { + "exponent": 10666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11609826889188348, + "rhs": 3584000000000000308760, + "rhs_bits": 72 + }, + "rows": { + "exponent": 11609826889188348, + "rhs": 1792000000000000154416000, + "rhs_bits": 81 + } + } + }, + { + "log2_input": 448000000000000000000, + "powers": { + "alpha": { + "exponent": 23219653778376697, + "rhs": 3584000000000000154416, + "rhs_bits": 72 + }, + "compact": { + "exponent": 23219653778376697, + "rhs": 14336000000000000617600, + 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witness; inherited all-size transfer remains assumed" +} diff --git a/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/check.py b/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/check.py new file mode 100644 index 0000000000..0630cfc19a --- /dev/null +++ b/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/check.py @@ -0,0 +1,104 @@ +#!/usr/bin/env python3 +"""Screen complete paid profiles from independently replayed axis constructions.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions required') +from pathlib import Path +from collections import Counter +from fractions import Fraction as Q +import importlib.util,argparse,json,subprocess,tempfile,hashlib,os,shlex +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +from producer import check_sources +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m +exact=load('candidate_exact',ROOT/'research/rank-pair-refinement/refine.py') +balanced=load('candidate_assembly',DEP/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') + +def profile(path): + v=json.loads(Path(path).read_text()) + return v['profile'] if 'profile' in v else v + +def calculate(first,second): + profiles=[profile(first),profile(second)] + N=4073300;m=575 + assert [p['h'] for p in profiles]==[23,25] + W=2*N+sum(N//p['v']*p['R'] for p in profiles) + parts={'data':Counter({1:18*N,21:2*N,17:2*N,481:2*N}),'endpoint_copy':Counter({1:N})} + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 + assert p['rank_sum']==h*p['R']+p['loss']==sum(t*n for t,n in enumerate(p['blocks'])) + assert p['loss']==h*(h-1) + parts[f'internal_{h}']=Counter({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + parts[f'exterior_{h}']=Counter({h:bank,m-2*h:bank}) + parts[f'growth_{h}']=Counter({1:2*N,h-2:2*N}) + rows=sum(parts.values(),Counter());assert sum(t*n for t,n in rows.items())==m*W-1846900 + lo,hi,grid=1,71700000000000,10**18 + while lo+11 + result.update(status='Verified finite conditional witness; inherited all-size transfer remains assumed', + source_manifest_sha256=hashlib.sha256((HERE/'SOURCE.json').read_bytes()).hexdigest(), + axes=axes,eventual_bounds=balanced.cutoffs(result['finite_bridge'],result['assembly']), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113',pr71_kappa=Q(previous['kappa']), + relative_gain_pr71=result['kappa']/Q(previous['kappa'])-1, + pr71_complete_profile_exclusion_lower=old_lower)) + result=arithmetic.js(result) + path=HERE/'certificate.json' + if record:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:assert result==json.loads(path.read_text()) + print('PASS exact moment, next-grid exclusions, 47 inequalities and seven margins',flush=True) + return result + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--record',action='store_true');args=parser.parse_args();generate(args.record) diff --git a/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/producer.py b/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/producer.py new file mode 100644 index 0000000000..8d68303a3b --- /dev/null +++ b/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/producer.py @@ -0,0 +1,132 @@ +#!/usr/bin/env python3 +"""Balanced coarse sums + anchored split/live frames + core ordering and coordinates. + +Composition for Thomas DiFiore with OpenAI Codex assistance. Apache-2.0. +PR69 coarse sums: eumemic. PR71 split/live composition: Chafik Boukhalfa. +Graph: Avi Eisenberg PR62; split operation: Rohan Garg PR59; reclamation: +Rohan Arun PR65/67, Dominik Scholz PR63/68, eumemic PR57. Original notices +and exact sources are retained under references/frame-compiler/pr69 and pr71. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +from hashlib import sha256 +import argparse,ast,gzip,importlib.util,json,types +from concurrent.futures import ProcessPoolExecutor +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +import split_pair_graph as provider +import split_pair_compiler as ancestor +from binary_frame_replay import replay + + +def check_sources(): + for folder in (DEP,ROOT/'references/frame-compiler/pr69'): + manifest=json.loads((folder/'SOURCE.json').read_text()) + for name,digest in manifest['files'].items(): + assert sha256((folder/name).read_bytes()).hexdigest()==digest,name + manifest=json.loads((HERE/'SOURCE.json').read_text()) + required={str((HERE/name).relative_to(ROOT)) for name in ('producer.py','check.py','graph_audit.py','independent_check.py','selection.json')} + assert required <= set(manifest['files']), 'Incomplete selected source closure' + for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + + +def reorder(c): + groups={} + for x in sorted(c.active): + if c.args[x]: groups.setdefault((c.core[x],c.union[x]),[]).append(x) + def key(item): + (core,cover),nodes=item + return cover.bit_count()-core.bit_count(),-core,cover,min(nodes) + ids=list(range(len(c.inputs)+1))+[x for _,nodes in sorted(groups.items(),key=key) for x in nodes] + mapping={x:i for i,x in enumerate(ids)} + args,core,cover,provenance=c.args,c.core,c.union,c.provenance + c.args=[tuple(mapping[y] for y in args[x]) if args[x] else None for x in ids] + c.core=[core[x] for x in ids];c.union=[cover[x] for x in ids] + c.provenance=[provenance[x] for x in ids] + c.active={mapping[x] for x in c.active};c.outputs={k:mapping[v] for k,v in c.outputs.items()} + c.support_in.cache_clear() + c.verify() + return c + + +def graph(h,ordered=True): + source=Path(provider._graph.__file__).read_text() + original=ROOT/'references/frame-compiler/pr69/scripts/experiments/balanced_coarse_compiler.py' + replacements={} + for node in ast.parse(original.read_text()).body: + if isinstance(node,ast.Assign): + for target in node.targets: + if isinstance(target,ast.Name) and target.id in ('BEFORE','AFTER'): + replacements[target.id]=ast.literal_eval(node.value) + assert source.count(replacements['BEFORE'])==1 + module=types.ModuleType('balanced_split_private_graph');module.__file__=provider._graph.__file__ + exec(compile(source.replace(replacements['BEFORE'],replacements['AFTER']),module.__file__+':balanced-coarse','exec'),module.__dict__) + previous=provider._graph + try: + provider._graph=module + c=provider.graph(h) + finally: + provider._graph=previous + return reorder(c) if ordered else c + + +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + +def compile_axis(h): + check_sources() + config=json.loads((HERE/'selection.json').read_text())['axes'][str(h)] + previous_graph,previous_order=provider.graph,provider.ordered_build + # graph() calls the original provider; keep that callable private while + # the inherited driver resolves the selected composed graph dynamically. + original_graph=previous_graph + def selected_graph(dimension): + provider.graph=original_graph + try:return graph(dimension) + finally:provider.graph=selected_graph + try: + provider.graph=selected_graph + provider.ordered_build=lambda original,dimension:original + compiled,word=ancestor.compile_axis(h) + finally: + provider.graph,provider.ordered_build=previous_graph,previous_order + compiled['graph_configuration']=config + word=relabel(word,config['coordinate_permutation']) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + path=HERE/f'word-{h}.json.gz' + with path.open('wb') as stream: + with gzip.GzipFile(filename='',fileobj=stream,mode='wb',mtime=0) as archive:archive.write(raw) + receipt=replay(path) + assert sha256(raw).hexdigest()==config['expected_word_sha256'] + axis=dict(configuration=config,compiled=compiled,replay=receipt, + word_sha256=sha256(raw).hexdigest(),gzip_sha256=sha256(path.read_bytes()).hexdigest()) + (HERE/f'axis-{h}.json').write_text(json.dumps(axis,indent=2)+'\n') + print(f'PASS fresh balanced/split/core word h={h}, roles={receipt["roles"]}',flush=True) + + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--h',type=int,choices=(23,25));args=parser.parse_args() + if args.h:compile_axis(args.h) + else: + with ProcessPoolExecutor(max_workers=2) as pool:list(pool.map(compile_axis,(23,25))) diff --git a/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-23.json b/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-23.json new file mode 100644 index 0000000000..013f4e59c7 --- /dev/null +++ b/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27136,"loss":506,"rank_sum":624634,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38292,"crt_matrices":5488,"crt_disagreements":0,"blocks":[0,355721,21666,6948,6524,3093,4314,2400,3266,1501,2094,1008,1374,586,732,353,307,139,62,16,0,23,0,0]} diff --git a/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-25.json b/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-25.json new file mode 100644 index 0000000000..1e3b6b89aa --- /dev/null +++ b/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35744,"loss":600,"rank_sum":894200,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52202,"crt_matrices":7623,"crt_disagreements":0,"blocks":[0,490052,26188,13531,7191,4637,5355,4229,3705,2610,2620,2080,1814,1357,1070,868,612,463,233,56,141,0,71,25,0,0]} diff --git a/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/selection.json b/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/selection.json new file mode 100644 index 0000000000..57cf3b6b65 --- /dev/null +++ b/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/selection.json @@ -0,0 +1,86 @@ +{ + "source_pr71": "1bef94fd40a746452548c84a4a8f8834670a3113", + "source_pr69": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "axes": { + "23": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 22, + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 20, + 19, + 21 + ], + "expected_word_sha256": "8dc6696a274e70ca0af3fc49c4bdede362adaedc8dc322f335e3dab499f1ed48" + }, + "25": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 2, + 1, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "expected_word_sha256": "2c923afe366219ee3fffc9db063c91e44cdf7cbbdb62246b8e6a297dc440b577" + } + } +} diff --git a/references/frame-compiler/indexed-r5/research/pair-assembly/pair_graph.py b/references/frame-compiler/indexed-r5/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/indexed-r5/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/indexed-r5/research/reordered-rank-pair/arithmetic/refine.py b/references/frame-compiler/indexed-r5/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/indexed-r5/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/indexed-r5/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/indexed-r5/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/indexed-r5/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/indexed-r5/research/reordered-rank-pair/verify.py b/references/frame-compiler/indexed-r5/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/indexed-r5/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": 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0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "PR48": { + "author": "Chafik Boukhalfa", + "commit": "b7194b8586844956904b33e9fe18f0c75606c11b", + "contribution": "research/copied-fixed pipeline (weighted-matching replay, exact data recovery, verification) reused here", + "pull_request": 48 + }, + "files": 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"acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + }, + "integration_note": "Against main d55bcd62, binary_io.hpp adds only six standard-library includes. Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + } + }, + "gzip_sha256": "4629d45d5074f87706db46be3aa3cd369071cd215bc6560d641115aadcce54a0", + "word_sha256": "bd0cbf73756f2e4f8d3879ec6c7a194990eb9ec40aaf3580bdded6994798d920" + }, + "25": { + "compiled": { + "h": 25, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 36586, + "baseline_pr48_roles": 48329, + "histogram": { + "1": 55478, + "0": 416276, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + }, + "rank_mass": 915250, + "elementary_xors": 205650, + "stats": { + "augmentations": 286, + "regions": 73695, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json b/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json new file mode 100644 index 0000000000..346cf87ea3 --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json @@ -0,0 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b/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json 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a/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json b/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json new file mode 100644 index 0000000000..2883a5f7c9 --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "frames": 52475, + "distinct_transitions": 138016, + "singles": 15939, + "rank_mass": 642620, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 53320, + "2": 77409, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "21": 165, + "22": 23 + }, + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json b/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json new file mode 100644 index 0000000000..3b4bc33ff6 --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json @@ -0,0 +1,35 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "frames": 73697, + "distinct_transitions": 190838, + "singles": 20700, + "rank_mass": 915250, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69278, + "2": 108881, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25 + }, + "word_sha256": "a54443429f47c486016771ce0436effda098e142afc52861c20957e9ff8e086b", + "copied_centers": 25, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz b/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz new file mode 100644 index 0000000000..3a7c7c41c1 Binary files /dev/null and b/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz differ diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz b/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz new file mode 100644 index 0000000000..6a239a3e9f Binary files /dev/null and b/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz differ diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + "exponent": 5333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5715743812, + "rhs": 1792000000313576, + "rhs_bits": 51 + }, + "rows": { + "exponent": 5715743812, + "rhs": 896000000156824000, + "rhs_bits": 60 + } + } + }, + { + "log2_input": 224000000000000, + "powers": { + "alpha": { + "exponent": 11431487624, + "rhs": 1792000000156824, + "rhs_bits": 51 + }, + "compact": { + "exponent": 11431487624, + "rhs": 7168000000627232, + "rhs_bits": 53 + }, + "leaf": { + "exponent": 10666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11431487624, + "rhs": 3584000000313576, + "rhs_bits": 52 + }, + "rows": { + "exponent": 11431487624, + "rhs": 1792000000156824000, + "rhs_bits": 61 + } + } + }, + { + "log2_input": 448000000000000, + "powers": { + "alpha": { + "exponent": 22862975248, + "rhs": 3584000000156824, + "rhs_bits": 52 + }, + "compact": { + "exponent": 22862975248, + "rhs": 14336000000627232, + "rhs_bits": 54 + }, + "leaf": { + 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b/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 at the new bit saving, +and the new complete profile has exact upper moment <1. All47 strict assembly +conditions and seven margins pass. **53 Lean endpoints** pass:34 new universal, +15 concrete,4 reused rational-helper lemmas. No omitted proof, project axiom or +native decision shortcut. The math scope includes dirty-word/complement safety, +coordinate conjugacy, fresh-kernel clearing, actual finite rounding and old-profile +rejection. It does not formalize the Python/C++ compiler or the all-size theorem. + +## Reproduce the accepted words + +Use an external checkout of frozen PR62 commit +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No newer sources are consumed. +See `verification/README.md` to compile its exact C++17 profiler, then run: + +``` +python verification/verify_words.py --upstream UPSTREAM --profiler PROFILER --word23 words/word-23.json.gz --word25 words/word-25.json.gz --output work/recheck +python verification/check_guards.py words/word-23.json.gz +python verification/check_guards.py words/word-25.json.gz +cd math +lake build Frozen62Research +``` + +The verifier checks immutable sources and its own adapter hashes, full input/dirty +bases in both orientations, exact source/scatter inventory, every literal frame +transition and all fixed-I+J profiles with bounded-minor and CRT checks. It rejects +optimized Python assertion mode. Use the supplied words for authoritative replay; +floating discovery prices propose candidates and have no trusted-proof role. +Discovery source snapshots, exact oracle fixtures (gzip-compressed) and matching +seeds retain original byte hashes. `discovery/SEARCH.md` explains the algorithms, +heuristic boundary and experimental commands. Historical workspace paths in the +source-generation receipts identify the original run; the accepted-word replay +uses the explicit upstream argument and needs no private directory layout. +Portable discovery regeneration: + +``` +python discovery/regenerate_portable.py --upstream UPSTREAM --work work/regenerate +``` + +This rewrites workspace paths only and checks both raw words and deterministic +gzip against the accepted words. Floating discovery is outside the trusted +certificate; the independent word/profile verifier establishes acceptance. + +The one-hour session froze information through #62. The unchanged data geometry +and its rational recovery are inherited; selected physical words/profile checks +are fresh. All-size analytic, compiler/frame transfer, finite-alphabet tape, +routing, prime selection/recovery and eventual-threshold contracts remain +conditional. No practical runtime or global-optimality claim is made. + +Alejandro Zarzuelo Urdiales is the human author/developer, following earlier +Archivara and personal July/October matrix/parity work developed with multiple +AI tools. This synthesis involved substantial OpenAI Codex assistance. Known +linear algebra, matroid exchange, dirty uncomputation and concavity principles +retain prior-work status. The finite construction credits Avi Eisenberg/ikeboy +(#62 interval/core-aware graph), eumemic (#57 frame compiler), Chafik Boukhalfa +(#60 ranking and earlier exact profiling), Rohan Arun and other retained notices. +The prior matrix/parity source is in `../matrix-exponent-synthesis/` and prior +Gaussian work in PR45. Its product counts retain their separate arithmetic scope. +The paper is supplied as LaTeX source; no newly compiled PDF is claimed. diff --git a/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md b/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md new file mode 100644 index 0000000000..b8dd669634 --- /dev/null +++ b/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md @@ -0,0 +1,136 @@ +# Local frame-compiler search, frozen through PR62 + +All experiments in this directory use the pinned PR62 pair graph at +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No later community source is consumed. +The original checkout is unchanged. Each emitted word and compiler copy has +a SHA256 recorded in its `compiled.json`; changed words are sent separately +to the independent literal replay and profile verifier. + +## New dependency-circuit choices + +The inherited compiler reduces retired fresh-signal rows against the current +live anchors and an echelon basis of compatible retired rows. Instead of +accepting the first dependent retired row, the new selectors collect the +available fundamental dependency circuits and choose a circuit by one of: + +- total charged target/provider rank growth (`all_growth`); +- number and rank growth of other retired providers (`all_collateral`); +- anchor-only dependence before general retired dependence (`anchor_first`); +- actual physical transition child-profile moment cost (`profile_cost*`). + +Every clearing XOR and every target/provider frame promotion is still emitted +and charged. A zero fresh-signal row can contain arbitrary physical dirty state; +its reuse is justified by the complete reversible word, not by claiming that +the physical register is initialized to zero. The compiler runs both complete +dirty-basis orientations, and the independent verifier repeats them. + +For the last selector let `C(A,B) = sum_t n_t(A,B) F_t`, where the `n_t` are +the exact inherited fixed-I+J pivot-run profile of the physical frame transition +and `F_t = t exp(a log(m/t))`. A candidate target `s` at old frame `A_s`, cleared +into frame `G` with providers `z`, is priced by + +``` +C(A_s,G) - C(A_s,I) + + sum_z [C(A_z,G) + C(G,I) - C(A_z,I)]. +``` + +This accounts for immediate promotions and the change in deferred cleanup, +assuming each other retired provider remains retired until cleanup. Future +reuse couples decisions, so this is a discovery heuristic, not an additive +global optimality certificate. Linear rank mass cancels between candidates; +`t*expm1(a*log(m/t))` avoids cancellation in floating discovery prices. +Missing transition profiles are recorded and collected for the next iteration. +Once a run has zero missing pairs, every local price uses an actual transition +profile. The final saving is accepted only through exact rational whole-profile +moment bounds and all assembly gates. + +`build_pair_oracle.py` is a local adaptation of the frozen C++ profiler that +additionally exports each transition histogram. It preserves the projector, +pivot, bounded-minor and three-prime CRT routines. Its synthetic transition-list +input is an oracle request, not a physical executable word. Each immutable +profile dump and the source/header hashes are recorded. + +## Moment-ordered carry selection + +The `--weighted` experiment orders the inherited linear/partition-matroid +candidate edges by their physical transition moment change before the original +greedy initialization and augmenting paths. For a value produced at `P`, +preserved through donor frame `G`, and carried to future target `T`, its +no-reclamation child-cost change is + +``` +C(G,T) - C(G,I) - C(0,P) - C(P,T). +``` + +At fixed cardinality, role and external-volume corrections are common to all +edge choices in the same axis. The inherited augmenting algorithm still seeks +maximum cardinality; it does not optimize the weights globally. Reclamation +adds coupling, so only the changed whole-word profile can establish an actual +improvement. This experiment makes no minimum-cost matroid claim. + +The `--exchange` variant starts from the frozen original maximum-cardinality +matching and tries bounded improving one-edge exchanges. A new edge may replace +the old donor of the same use when its donor block stays linearly independent; +or it may replace a selected edge in the same donor block and serve an unused +use. Both preserve cardinality and distinct-use constraints. The `--cycle` +variant additionally tests two-edge donor/use cycles, checking the independence +of both changed blocks. No improving two-edge cycle was found in the tested +native-price instance; this is not a proof that longer cycles cannot improve it. + +## Joint basis and schedule search + +`--basis shift1` profiles all candidate physical transitions after the point +permutation `i -> (i+1) mod h`, while preserving their original frame IDs. +Matching and reclamation are then priced in that basis. The emitted word is +renamed by `relabel_word.py`: all frame masks, canonical source/output triples, +common points and scatter port indices change together. Scratch slots and +literal XOR instructions are retained. The complete triple family and the +permutation-invariant `I+J` basis are inherited; every final renamed word still +gets fresh full-basis and actual physical-profile verification. + +This joint search differs from merely relabeling an already selected schedule: +the selected carries and clearing circuits are optimized under the new ordered +pivot-run prices. It remains a bounded discovery heuristic. + +## Regeneration + +The frozen graph/matching setup and a moment-cost exchange run are generated by: + +``` +python -S collect_matching_pairs.py --h 23 +python -S build_pair_oracle.py --h 23 --strategy matching_collect +python -S run_strategy.py --h 23 --strategy profile_cost --exchange +``` + +Repeat at `h=25`. For joint search, add `--basis shift1` to the oracle and +strategy commands. Reclamation may encounter transitions absent from the +initial carry-edge inventory. Run the oracle again on the emitted strategy +directory with `--incremental`, then run a new strategy label. The new label +must start with `profile_cost`; output directories are never overwritten. +`compiled.json` records the exact oracle dump hash, missing-pair count, word +hashes and source pin. Immutable earlier oracle dumps are retained by SHA256. +Use `--oracle path/to/the-immutable-dump.jsonl` to reproduce the prices of a +specific recorded run instead of consuming the subsequently enlarged cache. +The initial compiler matching cache is accepted only if its complete candidate +edge list matches the current frozen graph and every restored selected block +passes the same linear-independence check. + +The runner saves an immutable source copy and its hash for later runs. Floating +`expm1` prices at discovery saving `a=0.00005103` select proposals only. Neither +those prices nor their reported local gains are used as an arithmetic witness. + +## Acceptance boundary + +The independent verifier checks all input and dirty basis vectors in both +orientations, exact literal-scatter incidences, causal nested physical frames, +event equality reconstructed from the actual XOR word, rank mass, actual child +profiles and CRT agreement. It then computes the whole mixed-axis recurrence +and exact rational moment/assembly witnesses. Existing all-size geometry, +analytic envelopes, compiler/tape arguments and the surrounding reduction are +inherited from frozen PR62. A finite profile improvement does not by itself +formally prove those inherited hypotheses. + +Reduced XOR count alone is not accepted as an exponent improvement. In this +search `all_collateral` and `anchor_first` reduced clearing XORs but worsened +the certified characteristic. Actual child-size distributions decide the +saving, even when both physical-role counts and total rank mass are unchanged. diff --git a/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py b/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py new file mode 100644 index 0000000000..7c154b1a29 --- /dev/null +++ b/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py @@ -0,0 +1,275 @@ +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +import sys;sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'matrix-synthesis/bridge/pr62/references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s,add=True): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>s&1;e^=1<=prices[f]-1e-14:continue + if not can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:-prices[z])if prices[e] /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify diff --git a/references/frame-compiler/pr71/NOTICE b/references/frame-compiler/pr71/NOTICE new file mode 100644 index 0000000000..8adab44ba3 --- /dev/null +++ b/references/frame-compiler/pr71/NOTICE @@ -0,0 +1,324 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. diff --git a/references/frame-compiler/pr71/README.md b/references/frame-compiler/pr71/README.md new file mode 100644 index 0000000000..4a9b481aa3 --- /dev/null +++ b/references/frame-compiler/pr71/README.md @@ -0,0 +1,172 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. diff --git a/references/frame-compiler/pr71/SOURCE.json b/references/frame-compiler/pr71/SOURCE.json new file mode 100644 index 0000000000..c8cc31f3d0 --- /dev/null +++ b/references/frame-compiler/pr71/SOURCE.json @@ -0,0 +1,120 @@ +{ + "commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "Makefile": "6e9e48a677b2f66643226840f574a6535e3564ffb0c72284b60302684a5dfbe4", + "NOTICE": "1e0702aa665673508fa91169163c5785d680637fff636fda01f36e3b127c3ee0", + "README.md": "24817241fcad7f0a294ec6ad9666ee552ed9057e8d89e3c1d27e8fa2c7fe4229", + "certificates/split-pair-compiler.json": "6561fab8609e8aa3a291a8197cd8b834b0881ee0b9a5b991926c2c93c4d5f884", + "certificates/split-pair-kappa.json": 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Actual imported source closure is PR65 plus shared PR48." + } + }, + "status": "Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed" +} diff --git a/references/frame-compiler/pr71/certificates/split-pair-profiles-23.json b/references/frame-compiler/pr71/certificates/split-pair-profiles-23.json new file mode 100644 index 0000000000..bf40dc76b4 --- /dev/null +++ b/references/frame-compiler/pr71/certificates/split-pair-profiles-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27455,"loss":506,"rank_sum":631971,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38745,"crt_matrices":5750,"crt_disagreements":0,"blocks":[0,357148,21253,8022,5466,4156,3835,3250,2612,2109,1750,1529,1008,863,555,461,234,149,40,9,0,23,0,0]} diff --git a/references/frame-compiler/pr71/certificates/split-pair-profiles-25.json b/references/frame-compiler/pr71/certificates/split-pair-profiles-25.json new file mode 100644 index 0000000000..2f4bb6b9e9 --- /dev/null +++ b/references/frame-compiler/pr71/certificates/split-pair-profiles-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":36015,"loss":600,"rank_sum":900975,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52075,"crt_matrices":7444,"crt_disagreements":0,"blocks":[0,492698,27869,10467,7897,5674,5027,4110,3809,3047,2490,2047,1814,1443,1151,898,567,470,271,163,47,13,0,25,0,0]} diff --git a/references/frame-compiler/pr71/certificates/split-pair-transitions-23.json b/references/frame-compiler/pr71/certificates/split-pair-transitions-23.json new file mode 100644 index 0000000000..1a389c32fd --- /dev/null +++ b/references/frame-compiler/pr71/certificates/split-pair-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27455, + "frames": 59803, + "distinct_transitions": 152272, + "singles": 15939, + "rank_mass": 631971, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69190, + "2": 73632, + "3": 10224, + "4": 15382, + "5": 6461, + "6": 1593, + "7": 694, + "8": 1229, + "9": 411, + "10": 539, + "11": 98, + "12": 671, + "13": 254, + "14": 1927, + "15": 439, + "16": 440, + "17": 487, + "18": 3417, + "19": 6882, + "21": 171, + "22": 23 + }, + "word_sha256": "b0379d99fd6c10307da0d0fc526ed6171f19105a47bae61730fc3745ef60bd9e", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr71/certificates/split-pair-transitions-25.json b/references/frame-compiler/pr71/certificates/split-pair-transitions-25.json new file mode 100644 index 0000000000..e5864300a1 --- /dev/null +++ b/references/frame-compiler/pr71/certificates/split-pair-transitions-25.json @@ -0,0 +1,37 @@ +{ + "h": 25, + "v": 2300, + "R": 36015, + "frames": 84845, + "distinct_transitions": 212584, + "singles": 20700, + "rank_mass": 900975, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 91026, + "2": 108047, + "3": 13560, + "4": 19874, + "5": 8387, + "6": 2967, + "7": 1127, + "8": 1443, + "9": 664, + "10": 791, + "11": 38, + "12": 758, + "13": 149, + "14": 681, + "15": 167, + "16": 2265, + "17": 680, + "18": 566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "word_sha256": "4c956749f0ec72c61875c51099afdf23e69ccea268a9b43b8d46da2ffdb24903", + "copied_centers": 25, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr71/certificates/split-pair-validation.json b/references/frame-compiler/pr71/certificates/split-pair-validation.json new file mode 100644 index 0000000000..471a5bed88 --- /dev/null +++ b/references/frame-compiler/pr71/certificates/split-pair-validation.json @@ -0,0 +1,237 @@ +{ + "axes": { + "23": { + "profile": { + "R": 27455, + "blocks": [ + 0, + 357148, + 21253, + 8022, + 5466, + 4156, + 3835, + 3250, + 2612, + 2109, + 1750, + 1529, + 1008, + 863, + 555, + 461, + 234, + 149, + 40, + 9, + 0, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 5750, + "distinct_matrices": 38745, + "field_prime": 2305843009213693951, + "frames": 59803, + "h": 23, + "loss": 506, + "rank_sum": 631971, + "v": 1771 + }, + "replay": { + "elementary_xors": 162103, + "full_basis_vectors": 30997, + "h": 23, + "histogram": { + "0": 175253, + "1": 58564, + "2": 78945, + "3": 10224, + "4": 15382, + "5": 6461, + "6": 1593, + "7": 694, + "8": 1229, + "9": 411, + "10": 539, + "11": 98, + "12": 671, + "13": 254, + "14": 1927, + "15": 439, + "16": 440, + "17": 487, + "18": 3417, + "19": 6882, + "21": 171, + "22": 23 + }, + "output_roles": 5336, + "rank_mass": 631971, + "roles": 27455, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 673206 + }, + "transitions": { + "R": 27455, + "copied_centers": 23, + "distinct_transitions": 152272, + "frames": 59803, + "h": 23, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69190, + "2": 73632, + "3": 10224, + "4": 15382, + "5": 6461, + "6": 1593, + "7": 694, + "8": 1229, + "9": 411, + "10": 539, + "11": 98, + "12": 671, + "13": 254, + "14": 1927, + "15": 439, + "16": 440, + "17": 487, + "18": 3417, + "19": 6882, + "21": 171, + "22": 23 + }, + "rank_mass": 631971, + "singles": 15939, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 1771, + "word_sha256": "b0379d99fd6c10307da0d0fc526ed6171f19105a47bae61730fc3745ef60bd9e" + } + }, + "25": { + "profile": { + "R": 36015, + "blocks": [ + 0, + 492698, + 27869, + 10467, + 7897, + 5674, + 5027, + 4110, + 3809, + 3047, + 2490, + 2047, + 1814, + 1443, + 1151, + 898, + 567, + 470, + 271, + 163, + 47, + 13, + 0, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 7444, + "distinct_matrices": 52075, + "field_prime": 2305843009213693951, + "frames": 84845, + "h": 25, + "loss": 600, + "rank_sum": 900975, + "v": 2300 + }, + "replay": { + "elementary_xors": 225757, + "full_basis_vectors": 40615, + "h": 25, + "histogram": { + "0": 242882, + "1": 77226, + "2": 114947, + "3": 13560, + "4": 19874, + "5": 8387, + "6": 2967, + "7": 1127, + "8": 1443, + "9": 664, + "10": 791, + "11": 38, + "12": 758, + "13": 149, + "14": 681, + "15": 167, + "16": 2265, + "17": 680, + "18": 566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "output_roles": 6925, + "rank_mass": 900975, + "roles": 36015, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 935228 + }, + "transitions": { + "R": 36015, + "copied_centers": 25, + "distinct_transitions": 212584, + "frames": 84845, + "h": 25, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 91026, + "2": 108047, + "3": 13560, + "4": 19874, + "5": 8387, + "6": 2967, + "7": 1127, + "8": 1443, + "9": 664, + "10": 791, + "11": 38, + "12": 758, + "13": 149, + "14": 681, + "15": 167, + "16": 2265, + "17": 680, + "18": 566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "rank_mass": 900975, + "singles": 20700, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 2300, + "word_sha256": "4c956749f0ec72c61875c51099afdf23e69ccea268a9b43b8d46da2ffdb24903" + } + } + }, + "bit_saving": "12854322426487/250000000000000000", + "certificate_sha256": "0fcb53fa374273efab6370953c966e8fa065dbfdba43691843a4788cb2cda42e", + "kappa": "51414646104039/1000000000000000000", + "margins": 7, + "producer_words_regenerated_and_matched": true, + "scope": "Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.", + "source_binding": "Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.", + "status": "PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly", + "strict_constraints": 47 +} diff --git a/references/frame-compiler/pr71/certificates/split-pair-word-23.json.gz b/references/frame-compiler/pr71/certificates/split-pair-word-23.json.gz new file mode 100644 index 0000000000..38b82cbb3d Binary files /dev/null and b/references/frame-compiler/pr71/certificates/split-pair-word-23.json.gz differ diff --git a/references/frame-compiler/pr71/certificates/split-pair-word-25.json.gz b/references/frame-compiler/pr71/certificates/split-pair-word-25.json.gz new file mode 100644 index 0000000000..da9935d15a Binary files /dev/null and b/references/frame-compiler/pr71/certificates/split-pair-word-25.json.gz differ diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr48/SOURCE.json b/references/frame-compiler/pr71/references/frame-compiler/pr48/SOURCE.json new file mode 100644 index 0000000000..4e38e34dc8 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/SOURCE.json @@ -0,0 +1,16 @@ +{ + "files": { + 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"b7194b8586844956904b33e9fe18f0c75606c11b", + "scope": "Unmodified producer inputs for experimental frame compiler; attribution retained in each file", + "source_pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/48" +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py b/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py new file mode 100644 index 0000000000..c7fd42867d --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py @@ -0,0 +1,196 @@ +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit', 'complex'): + data = finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": 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OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": 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0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": "41187950749917624099/1000000000000000000000000", + "cell_above_band": "666666666665666652937349833360791967/1333388250600666556832132000000000000", + "compact_leaf": "26927049500082375901/1000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "13729317166639208033/333347062650166639208033", + "epsilon_positive": "333333333333000000000000/333347062650166639208033", + "g1_above_kappa": "3408408254232349301008147/3333470626501666392080330000000000000", + "g2_above_kappa": "4241/2500000000000", + "g3_above_kappa": "74937627730682908927817/3333470626501666392080330000000000000", + "g4_above_kappa": "4241/2500000000000", + "g5_above_kappa": "5299956450675231223831763/13333882506006665568321320000000000000", + "g6_above_kappa": "11966897703678564007992423/13333882506006665568321320000000000000", + "g7_above_kappa": "3333196040161742016173902349301008147/3333470626501666392080330000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "13729317166639208033/333347062650166639208033", + "lambda_above_internal": "82375901/2000000000000000000000000", + "lambda_above_sigma": "61024099000082375901/2000000000000000000000000", + "lambda_above_tau": "82375901/2000000000000000000000000", + "lambda_prime_above_lambda": "82375901/2000000000000000000000000", + "lambda_prime_below_one": "41187950499917624099/1000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "21966907133275670202633360791967/533355300240266622732852800000000000", + "phase_leaf_above_bit": "53854099/2000000000000", + "phase_local": "109834536999766601613833360791967/2666776501201333113664264000000000000", + "prime_interval_packing": "13729317166639208033/333347062650166639208033", + "q_below_internal": "82375901/1000000000000000000000000", + "q_below_leaf": "26927049500082375901/1000000000000000000000000", + "q_below_reservations": "1/4000000000000", + "q_positive": "41187950499917624099/1000000000000000000000000", + "record_suffix": "13729317166639208033/333347062650166639208033", + "row_product_gap": "6548/25", + "short_record_fallback": "666639206901368489075295096355187267/666694125300333278416066000000000000", + "small_field_exposure": "1/1000000000000" + }, + "finite_bridge": { + "bit": { + "W": 177530859, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis 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Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + } + }, + "gzip_sha256": "4629d45d5074f87706db46be3aa3cd369071cd215bc6560d641115aadcce54a0", + "word_sha256": "bd0cbf73756f2e4f8d3879ec6c7a194990eb9ec40aaf3580bdded6994798d920" + }, + "25": { + "compiled": { + "h": 25, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 36586, + "baseline_pr48_roles": 48329, + "histogram": { + "1": 55478, + "0": 416276, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + }, + "rank_mass": 915250, + "elementary_xors": 205650, + "stats": { + "augmentations": 286, + "regions": 73695, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json new file mode 100644 index 0000000000..346cf87ea3 --- /dev/null +++ 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mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json new file mode 100644 index 0000000000..42958fc74b --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json @@ -0,0 +1,195 @@ +{ + "artifact_sha256": { + "frame-profiles-23.json": "fec377bcf1512a427674983256b900229d4133026445b6e680c6e1e6dde5af7d", + "frame-profiles-25.json": "28b4b911e26fbc02dde0d2e1458ed16227f756126ab8144d6d45e164d1165262", + "frame-transitions-23.json": "86646f1110595294cccc15603c552f0a153574a690b69c3b144d84a449891103", + "frame-transitions-25.json": "c333c348665d12b95e168ca4fac48bfdca335104edd0f29c81fe94bec292e774", + "frame-word-23.json.gz": "a44e038e1c548ea8ac31dd04acc2bba7951b22e17df7b7ad3464ea2b504a8da4", + "frame-word-25.json.gz": "ad8b299697f90b185b6b791313b505586be97965519052100d097df6199e00c5", + "paired-candidate.json": "34a500d739537235dfc5d24325c22856ca4567b9eac998a3bce9b13db5501940" + }, + "axes": { + "23": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 36432, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 31460, + "elementary_xors": 149137, + "h": 23, + "histogram": { + "0": 302057, + "1": 42694, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "2": 82722, + "21": 165, + "22": 23, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 642620, + "roles": 27918, + "stats": { + "augmentations": 220, + "clearing_xors": 1577, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "regions": 52473 + } + }, + "gzip_sha256": "a44e038e1c548ea8ac31dd04acc2bba7951b22e17df7b7ad3464ea2b504a8da4", + "replay": { + "elementary_xors": 149137, + "full_basis_vectors": 31460, + "h": 23, + "histogram": { + "0": 162914, + "1": 42694, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "2": 82722, + "21": 165, + "22": 23, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525 + }, + "output_roles": 5336, + "rank_mass": 642620, + "roles": 27918, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 621342 + }, + "schedule": "cover-core", + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4" + }, + "25": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 48329, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 41186, + "elementary_xors": 205977, + "h": 25, + "histogram": { + "0": 416741, + "1": 55478, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "2": 115781, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 915250, + "roles": 36586, + "stats": { + "augmentations": 286, + "clearing_xors": 2154, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "regions": 73695 + } + }, + "gzip_sha256": "ad8b299697f90b185b6b791313b505586be97965519052100d097df6199e00c5", + "replay": { + "elementary_xors": 205977, + "full_basis_vectors": 41186, + "h": 25, + "histogram": { + "0": 224465, + "1": 55478, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "2": 115781, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569 + }, + "output_roles": 6925, + "rank_mass": 915250, + "roles": 36586, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 856108 + }, + "schedule": "reverse-node", + "word_sha256": "a54443429f47c486016771ce0436effda098e142afc52861c20957e9ff8e086b" + } + }, + "source_sha256": { + "research/pair-assembly/frame/frame_verify.py": "fafe25d57166a747eeb847444a2e02dd7eed19038b93a2c495014d147d04a8fb", + "research/pair-assembly/pair_graph.py": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "research/reordered-rank-pair/test_negative.py": "88832242e6f74e3fe08d109d4f21ff188a9ca0ae50c3e8f31da0243fe9501510", + "research/reordered-rank-pair/verify.py": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352", + "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3", + "scripts/experiments/binary_frame_profiles.cpp": "8e2e391d3ee57cbb1372c68e4aa031e1b861321536eabd642ada54e12e678669", + "scripts/experiments/binary_frame_replay.py": "392e78e62d7685c99a5888a7da743ea6c3dcad631af4a743c91e0c09348442bc", + "scripts/experiments/rank_pair_compiler.py": "9984aaccf880e4840402322d76678bfddb33ce7e494af78430a43429f51b85fd" + }, + "status": "Exact topological scheduling of unchanged PR63 graph/compiler; both physical orientations and fixed profiles checked" +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json new file mode 100644 index 0000000000..3b648dbe21 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "loss": 506, + "rank_sum": 642620, + "field_prime": 2305843009213693951, + "frames": 52475, + "distinct_matrices": 36399, + "crt_matrices": 6049, + "crt_disagreements": 0, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json new file mode 100644 index 0000000000..19cc34b4ca --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json @@ -0,0 +1,40 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "loss": 600, + "rank_sum": 915250, + "field_prime": 2305843009213693951, + "frames": 73697, + "distinct_matrices": 50394, + "crt_matrices": 8127, + "crt_disagreements": 0, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json new file mode 100644 index 0000000000..2883a5f7c9 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "frames": 52475, + "distinct_transitions": 138016, + "singles": 15939, + "rank_mass": 642620, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 53320, + "2": 77409, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "21": 165, + "22": 23 + }, + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json new file mode 100644 index 0000000000..3b4bc33ff6 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json @@ -0,0 +1,35 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "frames": 73697, + "distinct_transitions": 190838, + "singles": 20700, + "rank_mass": 915250, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69278, + "2": 108881, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25 + }, + "word_sha256": "a54443429f47c486016771ce0436effda098e142afc52861c20957e9ff8e086b", + "copied_centers": 25, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz new file mode 100644 index 0000000000..3a7c7c41c1 Binary files /dev/null and b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz differ diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz new file mode 100644 index 0000000000..6a239a3e9f Binary files /dev/null and b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz differ diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 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}, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + 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a/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) ++ slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();pending={};stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): +@@ -149,7 +151,8 @@ + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 +- return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) ++ endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 ++ return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} +@@ -161,6 +164,9 @@ + old,e=bb[p];row^=old;expr^=e + return expr + for s in anchors:ins(s) ++ for s,target in pending.items(): ++ if contains(blocks[frames[s]]['frame'],blocks[g]['frame']) and contains(blocks[g]['frame'],blocks[target]['frame']): ++ ins(s);stats['live_anchor_candidates']+=1 + best=None + # Inspect every eligible dependent candidate across all retired ranks. + # Rank the actual fixed-basis growth/cleanup profiles by an integer entropy score. +@@ -176,7 +182,9 @@ + if best is None or key= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and kappa > previous_kappa + bridge = json.loads((OLD/'certificate.json').read_text())['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/split-pair/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr67_commit='b3745601e947a94316bf25c2c6263d93c06e3364', + pr67_kappa=previous_kappa, ratio_pr67=kappa/previous_kappa, + absolute_gain_pr67=kappa-previous_kappa, + pr67_complete_profile_exclusion_lower=prior65_lower, + full_pr67_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected split-pair partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'split-pair-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py b/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py new file mode 100644 index 0000000000..1290ef2eb8 --- /dev/null +++ b/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py @@ -0,0 +1,275 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py b/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py new file mode 100644 index 0000000000..7908c963a4 --- /dev/null +++ b/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py @@ -0,0 +1,78 @@ +#!/usr/bin/env python3 +"""Replay the aligned split-pair/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from split_pair_compose import compose, check_sources +from split_pair_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'split-pair-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='split-pair-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + 'c++', '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'split-pair-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'split-pair-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'split-pair-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'split-pair-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'split-pair-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/references/frame-compiler/pr71/tests/test_split_pair.py b/references/frame-compiler/pr71/tests/test_split_pair.py new file mode 100644 index 0000000000..5088cff133 --- /dev/null +++ b/references/frame-compiler/pr71/tests/test_split_pair.py @@ -0,0 +1,238 @@ +"""Physical and exact-arithmetic controls for the aligned split/pair witness.""" +from copy import deepcopy +from fractions import Fraction +from itertools import combinations +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile +import unittest +from unittest.mock import patch + +ROOT = Path(__file__).resolve().parents[1] +EXPERIMENTS = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXPERIMENTS)) +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from binary_frame_math import moment + + +class SplitPairControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.words = {h: json.loads(gzip.decompress((ROOT/f'certificates/split-pair-word-{h}.json.gz').read_bytes())) + for h in (23,25)} + + def reject_mutation(self, mutate, checker='both'): + for h, original in self.words.items(): + with self.subTest(h=h), tempfile.TemporaryDirectory() as directory: + changed = deepcopy(original) + mutate(changed) + path = Path(directory)/'word.json' + path.write_text(json.dumps(changed, separators=(',', ':'))+'\n') + with self.assertRaises((AssertionError, ValueError, IndexError, KeyError)): + if checker != 'transitions': + replay(path) + if checker != 'replay': + prepare(path, Path(directory)/'transitions.bin') + + def test_selected_words_pass_independent_replay(self): + recorded = json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + actual = replay(ROOT/f'certificates/split-pair-word-{h}.json.gz') + self.assertEqual(json.loads(json.dumps(actual)), recorded['axes'][str(h)]['replay']) + + def test_omitted_literal_xor_is_rejected(self): + self.reject_mutation(lambda word: word['ops'].pop(0)) + + def test_self_xor_is_rejected(self): + def mutate(word): + word['ops'][0][1] = word['ops'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_non_nested_operation_frame_is_rejected(self): + def mutate(word): + narrow = next(i for i,(core,cover) in enumerate(word['frames']) if core == cover) + operation = next(op for op in word['ops'] if word['frames'][op[2]][0] != word['frames'][op[2]][1]) + operation[2] = narrow + self.reject_mutation(mutate) + + def test_aliased_terminal_role_is_rejected(self): + def mutate(word): + word['outputs'][1][0] = word['outputs'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_missing_copied_center_is_rejected(self): + def mutate(word): + index = next(i for i,(_,_,_,target) in enumerate(word['outputs']) if len(target) == 1) + word['outputs'].pop(index) + self.reject_mutation(mutate) + + def test_omitted_transition_cannot_reduce_paid_profile(self): + self.reject_mutation(lambda word: word['events'].pop(0), 'transitions') + + def test_understated_physical_width_is_rejected(self): + def mutate(word): + word['R'] -= 1 + self.reject_mutation(mutate) + + def test_complete_pr67_profile_fails_new_bit_saving(self): + from split_pair_arithmetic import refine + previous = json.loads((ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/paired-candidate.json').read_text())['bit'] + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + result = refine.exact_moment(previous['m'], previous['W'], {int(t): n for t,n in previous['child_multiplicities'].items()}, Fraction(current['bit_saving'])) + self.assertGreater(result['lower'], 1) + self.assertGreater(Fraction(current['kappa']), Fraction(current['comparison']['pr67_kappa'])) + + def test_private_import_preserves_path_and_arithmetic_module(self): + import split_pair_graph as provider + import split_pair_arithmetic as arithmetic + sentinel = object() + existing = sys.modules.get('refine', sentinel) + previous_path = sys.path[:] + graph, schedule = provider._private_modules() + refine, audit = arithmetic.private_arithmetic() + self.assertIs(audit.refine, refine) + self.assertIs(sys.modules.get('refine', sentinel), existing) + self.assertEqual(sys.path, previous_path) + + def test_failed_graph_build_restores_original_providers(self): + import split_pair_graph as provider + previous_class, previous_points = provider._graph.circuit_class, provider._graph.alternating_points + with patch.object(provider._graph, 'graph', side_effect=RuntimeError('deliberate graph failure')): + with self.assertRaises(RuntimeError): + provider.graph(23) + self.assertIs(provider._graph.circuit_class, previous_class) + self.assertIs(provider._graph.alternating_points, previous_points) + + def test_failed_compilation_restores_engine_graph_and_schedule(self): + import split_pair_compiler as producer + previous_graph, previous_build = producer.compiler.graph, producer.compiler.build + missing = object() + runtime = {name:getattr(producer.compiler,name,missing) for name in ('PENDING_COST','ORACLE_EXE','ORACLE_INPUT','oracles')} + with patch.object(producer.compiler, 'compile_', side_effect=RuntimeError('deliberate compiler failure')): + with self.assertRaises(RuntimeError): + producer.compile_axis(23) + self.assertIs(producer.compiler.graph, previous_graph) + self.assertIs(producer.compiler.build, previous_build) + for name,value in runtime.items(): + self.assertIs(getattr(producer.compiler,name,missing),value) + + def test_uncertified_configurations_are_rejected(self): + import split_pair_graph as provider + wrong_anchor = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_anchor['anchor'] = False + boolean_group = deepcopy(provider.EXPECTED_CONFIGS[23]); boolean_group['groups'][0] = True + changed_schedule = deepcopy(provider.EXPECTED_CONFIGS[23]); changed_schedule['schedule'] = 'reverse-node' + for changed in (wrong_anchor, boolean_group, changed_schedule): + with self.subTest(configuration=changed), patch.object(provider.json, 'loads', return_value=changed): + with self.assertRaises(ValueError): + provider.configuration(23) + for dimension in (True, 22, 24, '23'): + with self.subTest(dimension=dimension), self.assertRaises(ValueError): + provider.configuration(dimension) + + def test_recursive_weighted_exclusions_and_contraction(self): + import split_pair_graph as provider + for h in (23,25): + block_sizes = [] + parent = provider._graph.circuit_class(h) + selected = provider.split_class(parent, provider.configuration(h)['groups']) + case = self + class Audited(selected): + def grouping(self, points): + groups = super().grouping(points) + case.assertEqual([x for group in groups for x in group], list(points)) + case.assertLess(len(groups), len(points)) + return groups + + def _block(self, points, edges, weights, level): + def expected(omitted): + values = [value for pair,value in edges.items() if not set(pair) & omitted] + values += [value for point,value in weights.items() if point not in omitted] + support = 0 + for value in values: + case.assertEqual(support & self.support[value], 0) + support |= self.support[value] + return support + total, single, pairs = super()._block(points, edges, weights, level) + case.assertEqual(self.support[total], expected(set())) + case.assertEqual(set(single), set(points)) + for a in points: + case.assertEqual(self.support[single[a]], expected({a})) + case.assertEqual(set(pairs), set(combinations(points,2))) + for a,b in combinations(points,2): + case.assertEqual(self.support[pairs[a,b]], expected({a,b})) + block_sizes.append(len(points)) + return total, single, pairs + local = Audited(h-1) + block_sizes.clear() + local.pair(list(range(h-1))) + self.assertEqual(sorted(block_sizes, reverse=True), [h-1, 12 if h==23 else 13, 7 if h==23 else 8, 5, 3, 2]) + + def test_next_fine_grid_points_and_old_assembly_controls_reject(self): + from split_pair_arithmetic import refine + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + bit = current['bit']; saving = Fraction(current['bit_saving']); kappa = Fraction(current['kappa']) + grid = Fraction(1,10**18) + rows = {int(t): n for t,n in bit['child_multiplicities'].items()} + self.assertLess(refine.exact_moment(bit['m'],bit['W'],rows,saving)['upper'], 1) + self.assertGreater(refine.exact_moment(bit['m'],bit['W'],rows,saving+grid)['lower'], 1) + for label, variant in ( + ('next_kappa', dict(kappa=kappa+grid)), + ('zero_backoff', dict(h=Fraction())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))): + call = dict(a_bit=saving, kappa=kappa, h=Fraction(1,10**12));call.update(variant) + with self.subTest(control=label), self.assertRaises(refine.balanced.InvalidAssembly): + refine.balanced.assembly(current['finite_bridge'], **call) + + def test_mass_preserving_profile_mutation_is_rejected(self): + from split_pair_compose import check_sources + profile_path = ROOT/'certificates/split-pair-profiles-23.json' + changed = json.loads(profile_path.read_text()) + before = sum(t*n for t,n in enumerate(changed['blocks'])) + changed['blocks'][2] += 3; changed['blocks'][3] -= 2 + self.assertTrue(all(n >= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'split-pair-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from split_pair_compose import check_sources + manifest_path = ROOT/'research/split-pair/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/split-pair-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import split_pair_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('split_pair_graph.py', 'split_pair_engine.py', 'split_pair_compiler.py', 'split_pair_arithmetic.py', 'split_pair_compose.py', 'verify_split_pair.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr71/tests/test_split_pair_pending.py b/references/frame-compiler/pr71/tests/test_split_pair_pending.py new file mode 100644 index 0000000000..e6d63f72a4 --- /dev/null +++ b/references/frame-compiler/pr71/tests/test_split_pair_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/split_pair_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main() diff --git a/references/frame-compiler/pr74-aligned/FETCH.json b/references/frame-compiler/pr74-aligned/FETCH.json new file mode 100644 index 0000000000..31e4fc60d2 --- /dev/null +++ b/references/frame-compiler/pr74-aligned/FETCH.json @@ -0,0 +1,108 @@ +{ + "repo": "tomdif/integer-mult-bounds", + "commit": "428b5c167686b42a83f1abf7003c6d17aec561ea", + "files": [ + { + "path": "research/aligned-exchange-frames/partition_graph.py", + "git_blob_sha1": "e1c5c076a525df526e8490590033f406ef2a3f5e", + "sha256": "63e23b1d33094f99e96821f1859fee2612907d0cab928f983cce3d279a331900", + "size": 6224 + }, + { + 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Rank-first reclamation on interval-strip pair assembly, 8 October 2026 +Composition and exact profile witness: Dominik Scholz, with substantial OpenAI +GPT-6 Astra / Codex assistance. The PR #60 descending-frame-rank compiler by +Chafik Boukhalfa is reused unchanged on Avi Eisenberg's PR #62 scalar graph. +The joint frame compiler and paid reclamation are eumemic's PR #57, developed +with OpenAI Codex assistance. PR #62 records Anthropic Claude assistance. +This composition improves actual fixed-basis block profiles with unchanged +role counts; no new slot-priority rule or scalar graph is claimed. All prior +contributors, licenses, compiler arguments and conditional analytic/tape +interfaces remain credited. See research/rank-pair/PROOF.md. + +Ordered scalar frames, minimum-raise reclamation and coordinate relabeling +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. +The new finite construction and exact arithmetic certificates are in +research/ordered-frames, with an earlier parameter refinement in +research/rank-pair-refinement. These build on Dominik Scholz's PR #63 +composition, Chafik Boukhalfa's PR #60 reclamation compiler, Avi Eisenberg's +PR #62 scalar graph and eumemic's PR #57 reversible frame compiler. +Concurrent PR #65/#67 work is acknowledged in the proof. All inherited +licenses, author notices and conditional proof boundaries remain in force. + +Balanced split frames with core node ordering and coordinate relabeling +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. +This composition combines eumemic's PR69 coarse column sums, Chafik Boukhalfa's +PR71 anchored split/next-use-live compiler, and the earlier PR74 node ordering +and coordinate relabeling. Rohan Garg's PR59 split operation, Avi Eisenberg's +PR62 scalar graph, Rohan Arun's PR65/67 schedules and profile-cost selection, +Dominik Scholz's PR63/68 composition and pending controls, and eumemic's PR57 +compiler remain credited. Original source closures and notices are preserved +under references/frame-compiler/pr69 and pr71; all preceding licenses apply. +See research/balanced-split-frames/PROOF.md for the finite conditional scope. + +Aligned multi-pair recursion and coordinated carrier exchanges +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. +This finite construction splits and aligns six or nine top-level pairs, +adds cardinality-preserving two-edge carrier cycles, and composes future-unit +basis completion and coordinate-aware pricing with the inherited compiler. +Chafik Boukhalfa's PR79 future completion, Rohan Arun's PR82 composition and +geometric pricing, Alejandro Zarzuelo Urdiales's PR70 carrier exchanges, +Dominik Scholz's PR76 profile pricing, eumemic's PR69 balanced sums, Rohan +Garg's PR59 split operation, and the PR71/PR74 sources remain credited. +All earlier source-specific licenses and notices apply. Selected exact PR82 +Git blobs supplement the preserved PR69/PR71 archives. See +research/aligned-exchange-frames/PROOF.md for the finite conditional scope. + +The selected aligned-recursion update also preserves Chafik Boukhalfa's PR84 +indexed engine and its outgoing-use routing. Explicit coordinate pricing +and the new deeper aligned/half-plane scalar graphs compose with that source; +PR84's original source, license, notices and strategy audits are archived +unchanged under references/frame-compiler/pr84. diff --git a/references/frame-compiler/pr74-aligned/SOURCE.json b/references/frame-compiler/pr74-aligned/SOURCE.json new file mode 100644 index 0000000000..64233dfcf7 --- /dev/null +++ b/references/frame-compiler/pr74-aligned/SOURCE.json @@ -0,0 +1,25 @@ +{ + "commit": "428b5c167686b42a83f1abf7003c6d17aec561ea", + "files": { + "FETCH.json": "92e596b5868b86428523c16675cc25fe4563148012535b167aa48ff7b420cc58", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "a8224aed09f2ccccf88a943cb14a8db6ba4b6ada545a9b457f1c3649e257bb00", + "research/aligned-exchange-frames/PROOF.md": "1a931b3d2a757f9a55911394da5fa9617775a7fee4da0739189a7a169f62efef", + "research/aligned-exchange-frames/README.md": "584c64da8ea46b46dfcc6a8b86f4543bba641f10d36f95bf407b2a459591da50", + "research/aligned-exchange-frames/SOURCE.json": "e76eeb5bbc3fabc4e63135d611f7f48b891ce0b85e9c765b51b4c963feb38c4f", + "research/aligned-exchange-frames/certificate.json": "6f3a4a0e15ef5527e92b865722a9fd8f15658231e6ebbbc55e96c3a433e12846", + "research/aligned-exchange-frames/check.py": "86d4ab1b52c490a350ae84e2805d8a95557dfcf709597ecc365aaef4a0178f31", + "research/aligned-exchange-frames/exchange-proof.md": "0a6df5c08fcfda77349e1f543128502951cee2bea8fb08904360d8bfe0d10b12", + "research/aligned-exchange-frames/exchange_policy.py": "671704f8a5a8276c68aeef0432658e20e8c7dfff6b5fcf5b342f40644d920d30", + "research/aligned-exchange-frames/future_completion.py": "bfe7dd61b01abb445c363503bca61b217bf2e82d977de2336de3a48e1b8effd7", + "research/aligned-exchange-frames/graph_audit.py": "a5fdeec4789469052c0a60ee894851c412c7b9de4844942c09ccaa048b9da94c", + "research/aligned-exchange-frames/partition-proof.md": "aeeb9fec06d38eb829b9be4de934d63cf65fb0064440306520de12d41f21921d", + "research/aligned-exchange-frames/partition_graph.py": "63e23b1d33094f99e96821f1859fee2612907d0cab928f983cce3d279a331900", + "research/aligned-exchange-frames/producer.py": "533819362dbf7a211647182c32d9bd6c89a9e71c1d0987baf555dc333a05e9c8", + "research/aligned-exchange-frames/profile-23.json": "9ceb5e50591c52ed8c225f248b9f1f99f9a66dac4cecb00b8942aab84417d0da", + "research/aligned-exchange-frames/profile-25.json": "76fb46fe77da64e867c86adff6a8fa65a488065d6413c62e9e946d51e75c8f7e", + "research/aligned-exchange-frames/selection.json": "eebd008b4c93622200659c6b001a440ce3857b5e34d93e50a5219a4c74fb21b5" + }, + "pr": 74, + "scope": "Original aligned partition source and notices; reported foreign witness accepted without producer replay." +} diff --git a/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/PROOF.md b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/PROOF.md new file mode 100644 index 0000000000..54cdb61d93 --- /dev/null +++ b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/PROOF.md @@ -0,0 +1,228 @@ +# A paid finite witness from aligned partitions and carried-signal exchanges + +## Statement and conditional scope + +The authoritative exact values of `kappa` and `bit_saving` are the rational +fields with those names in [certificate.json](certificate.json). Together +with its complete paid profile and assembly checks, they certify the inherited +conditional bound + +`T(n) = O(n (log n)^(1-kappa))`. + +The all-size compiler and analytic transfer remain assumptions, as do the +inherited fixed-alphabet tape simulation, precision, routing, prime selection, +and exact recovery hypotheses. The finite graph, word, profile, and rational +checks below do not establish those general hypotheses. This document makes +no claim that the selected finite witness is optimal. + +## 1. Pinned scalar construction + +The original PR #71 source closure is archived at commit +`1bef94fd40a746452548c84a4a8f8834670a3113`, and the balanced coarse-sum source +from PR #69 at `91aa1f17e6e3fc063241686a41a34ddd0dc24c50`. The original sources, +licenses, notices, and predecessor manifests are preserved. The selected +source manifest also pins the local producer, policies, configurations, and +independent checkers; construction rejects changed inputs. + +The scalar graph uses dimensions 23 and 25 with the complete bases of 1,771 +and 2,300 triples. It splits six aligned top-level pairs for dimension 23 and +nine for dimension 25. The deeper choices are `[1,1]` and `[1,1,2]`, +respectively. The first three levels use half-plane row/column factoring; +later levels use columns. The matching intact global pairs are placed first in each +common-point ordering. The precise choices, contraction cap, weighted +exclusion identity, anchor permutation, and source hashes are proved in +[partition-proof.md](partition-proof.md). + +The contraction cap retains at least one pair and strictly decreases the +number of points in every recursive call. Splitting several pairs preserves +the partition into groups of size one or two, so the inherited weighted +singleton/pair identities apply. Balanced row/column sums retain each original +summand exactly once. No cancellation or uncharged linear identity is used. + +The active nodes are grouped by their original `(core,cover)` frames, then +ordered by increasing frame rank, decreasing core, increasing cover, and +first original node. Source IDs and the original order inside each frame +remain fixed. Every edge between different frames has strictly increasing +rank; the preserved internal order handles edges within a frame. The graph +audit checks this literal remapping, exact operand chronology, all dense +global triple supports, disjoint additions, every core/cover recurrence, and +the entire prescribed output set. The resulting scalar graphs have 84,930 +and 117,256 additions and 5,336 and 6,925 prescribed outputs. + +## 2. Matching and future unit-row completion + +The inherited compiler first computes a matching of eligible carried signals. +The selected PR #84 engine makes up to three single-edge passes and three +two-edge cycle passes. Its archived code is unchanged except for private +location bindings, explicit coordinate pricing, and the frozen pass count. Every selected +edge remains in the inherited eligible list. Use uniqueness, matching +cardinality, and independence of each region's desired-output-plus-carried +rows are preserved. [exchange-proof.md](exchange-proof.md) gives the local +exchange argument and the final explicit independence checks. + +At a region with `d` input coordinates, let the independent desired output +rows and selected carried unit rows form the initial row list. The PR #79 +future-compatible completion orders the remaining candidate unit rows by +the number of later compatible uses, then by current signal support size +and input index. It appends a row only after an exact binary independence +test. Since all `d` standard unit rows are considered and span the input +space, this extends the independent list to a full basis regardless of the +priority rule. The priority changes the chosen completion; it is not a +correctness assumption about later reclamation. + +The inherited elimination synthesizes the complete invertible basis change +as literal XORs. All copies, swaps as synthesized XORs, carried signals, +clearing operations, and required frame raises are serialized. Pending live +controls can enter a clearing basis only when their current frame is +contained in the present frame and the present frame is contained in their +next-use frame. Each such control retains its value. These eligibility checks +are separate from the score that chooses among eligible operations. + +The exact PR #84 retired and pending indexes select the same eligible roles +in the inherited iteration order, updating them at every raise, retirement, +assignment and removal. They accelerate candidate queries; the independent +literal replay validates the resulting physical construction. For h25, +outgoing uses are sorted by descending future deadline, with terminal uses +last in execution time and use ID breaking ties. This changes which physical +role is retained for each use; all other occurrences still receive paid copies. +h23 retains baseline outgoing-use order. + +## 3. Discovery coordinates and final physical coordinates + +`selection.json` records two explicit permutations for each axis. +`pricing_permutation` specifies the coordinate flag used by both matching +and clearing discovery oracles. Core and cover masks are permuted before +the oracle evaluates its fixed-basis transition profiles. Its reproducible +integer profile-entropy score only chooses a finite construction. It does +not replace any charged operation or serve as a moment certificate. + +`coordinate_permutation` specifies the final relabeling of the physical word; +it may differ from the pricing permutation. The producer applies it to all +frame masks, source-triple labels, scatter targets, output common points, +and output triples. Scratch IDs, literal XORs, and frame IDs are unchanged. +Each relabeled word is replayed and its actual ordered profiles are rebuilt. +Thus a subsequent coordinate improvement requires its own actual profile +even when the construction was priced using an earlier coordinate flag. + +For a permutation matrix `P`, the fixed basis `I+J` and the inherited +permutation-invariant projector metric commute with `P`. The envelope +projectors consequently transform by conjugation. Incidence, containment, +and invertibility remain valid, while ordered contiguous child profiles may +change. This is why the final word's exact profiles are regenerated. + +Each permutation also gives a bijection on the complete triple family. +The full two-axis data-block family and its rational recovery cases are +therefore reindexed. Their aggregate inherited geometry and paid profile +remain valid; the final axis profiles retain all copied centers, endpoints, +and growth costs. + +## 4. Complete dirty-basis word and exact profiles + +The full two-copy word is checked on every ordinary-input coordinate and +every arbitrary scratch coordinate, in both the forward and dual +orientations. The checks establish the prescribed input/output shear and +exact restoration of the scratch registers for arbitrary dirty contents. +An independent checker repeats the calculation from the serialized word, +validates every physical frame inclusion, and checks its expected hash. + +The selected role counts are `R_23=26409` and `R_25=34772`. The full basis +checks therefore use `2*1771+26409=29951` and `2*2300+34772=39372` coordinates. +These role counts describe the literal physical construction, including +reclamation and all selected basis changes. + +The transition preparer derives the fixed-`I+J` matrix inventory from the +serialized events and endpoints. The retained exact bounded-minor/CRT +profiler computes the final child blocks, and all CRT profile disagreements +must be zero. The same nested-frame formulas and exactness bounds apply: +the partition and matching changes alter which legal transitions occur, +without changing their matrix family. The per-axis rank identities are + +`sum_t t*b_(23,t) = 23*26409 + 23*22 = 607913`, + +`sum_t t*b_(25,t) = 25*34772 + 25*24 = 869900`. + +Rebuilding profiles from the selected final word prevents a discovery +histogram or an earlier coordinate profile from being substituted for the +actual paid costs. + +## 5. Complete recurrence + +Let `N=4073300=1771*2300` and `m=575=23*25`. The complete width is + +`W = 2N + (N/1771)*R_23 + (N/2300)*R_25 = 130468512`. + +The child multiplicity multiset contains all of the following terms: + +| Contribution | Paid children | +| --- | --- | +| Data blocks | `18N` of size 1; `2N` each of sizes 21, 17, and 481 | +| Endpoint copies | `N` additional children of size 1 | +| Internal axis `h` | `(N/binom(h,3))*b_(h,t)` children of each size `t` | +| Exterior axis `h` | `(N/binom(h,3))*R_h` each of sizes `h` and `m-2h` | +| Data growth, each axis `h` | `2N` each of sizes 1 and `h-2` | + +The checker reconstructs these contributions separately and compares their +sum with the supplied multiplicities. Their total rank is + +`sum_t t*n_t = mW - 1846900 = 75017547500`. + +The maximum child size is 529, strictly below `m`. The deficit `1846900` +is unchanged because the full input/output geometry is unchanged. The +inherited complex recurrence and its charges are retained in the finite +bridge and assembly; they are not omitted from the final saving. + +## 6. Strict moment and finite assembly + +For the exact rational `a=certificate.json.bit_saving`, define + +`M(a) = sum_t [t*n_t/(mW)] * exp(a*log(m/t))`. + +The certificate supplies a rigorous upper bound below 1 at `a` and a +rigorous lower bound above 1 at `a+10^-18`. Every logarithm is positive, +so the characteristic is strictly increasing. Production arithmetic uses +the retained exact rational logarithm/exponential bounds. The independent +arithmetic checker reconstructs the complete paid multiset and uses its own +40-term atanh logarithm sums and degree-ten exponential expansion with a +geometric tail bound. It does not import the production arithmetic or +assembly routines. + +The assembly retains positive backoff `10^-18`. Since +`2^26 < W < 2^27`, the bit width is 27. The product-row coefficient is +`9*27+20*30=843`. With degree 2000 and suffix slope 8000, its degree gap is +`2000-(51/25)*843=7007/25`. The checker derives these quantities from the +actual width, avoiding stale predecessor constants. + +The exact value `kappa=certificate.json.kappa` must satisfy all 47 assembly +inequalities and all seven strict margins. The independent checker derives +and checks those slacks separately; the next `10^-18` kappa grid value is +rejected. The source, replay, profile, moment, and assembly gates together +certify this finite conditional witness. Arithmetic cutoff bounds are not +complete operational runtime thresholds. + +## Credits and notices + +The aligned multi-pair choices, continued core ordering, selected coordinate +flags, two-edge extension, composition, packaging, and independent audits +were prepared for Thomas DiFiore with substantial OpenAI Codex assistance. +The construction builds on: + +- Rohan Garg's split operation (PR #59); +- Avi Eisenberg's interval strips and core-aware pair assembly (PR #62); +- Dominik Scholz's ranked composition and pending live controls (PR #63/#68); +- Rohan Arun's region schedules, profile-cost selection and geometric + pricing composition (PR #65/#67/#82); +- eumemic's reversible compiler and physical/profile interfaces (PR #57), + and balanced coarse-sum reassociation (PR #69); +- Chafik Boukhalfa's anchored splits and next-use-aware live selection + (PR #71), future unit completion (PR #79), and exact candidate indexes, + bounded two-cycles and outgoing-use routing (PR #84); +- Alejandro Zarzuelo Urdiales's carried-signal exchange method (PR #70); +- Dominik Scholz's integer profile-entropy pricing and one-edge exchanges + (PR #76); +- our earlier PR #74 core-order and coordinate-relabeling continuation. + +The preserved archives retain all earlier credits, including RaD/hipotures, +icekylinx, James Chang, Zhihao Chen, Aurel Prosz, Swapnil Jain, Douglas Colkitt, +OpenAI, Harvey–van der Hoeven, and predecessor AI-assistance disclosures. +Original Apache-2.0 licenses and notices remain in force. No predecessor +authorship, endorsement, or priority claim is implied by this composition. diff --git a/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/README.md b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/README.md new file mode 100644 index 0000000000..1755a94c40 --- /dev/null +++ b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/README.md @@ -0,0 +1,58 @@ +# Aligned recursion and indexed carrier exchanges + +**Conditional κ = 5.2782144231390e-05 = 5278214423139/100000000000000000.** +The bit saving is `52784930333197/1000000000000000000`. This verified finite construction uses +**130,468,512 wires**, with axis role counts **26,409 / 34,772**. + +It improves the previous PR74 saving by **1.8350912%** and the pinned PR84 +claim by **0.9773150%**. These are historical comparisons, not a global +optimality claim. Both complete prior child lists are strictly excluded at +the new accepted bit saving, along with the pinned PR71 and PR82 profiles. + +## What changed + +- Align and split six top-level pairs for h23 and nine for h25. +- Choose deeper split vectors `[first6,1,1]` and `[first9,1,1,2]`. +- Use half-plane row/column coarse sums for three levels, then columns. +- Compose core node ordering with PR84's future basis completion, exact + candidate indexes, three single-exchange and three two-cycle passes. +- Route h25 outgoing uses by descending future deadline; retain h23's + baseline routing. Price transitions in the explicitly selected coordinates. + +Every resulting graph, dirty physical word and ordered fixed-basis profile +is checked. [PROOF.md](PROOF.md), [partition-proof.md](partition-proof.md), +and [exchange-proof.md](exchange-proof.md) give the identities and scope. +The independent checker reconstructs all paid parts and all 47 inequalities +and seven margins using separate rational logarithm/exponential formulas. + +## Reproduce + +```sh +make aligned-exchange-frames-verify +``` + +Requires Python 3.11+ and a C++17 compiler. This regenerates both words, +checks dense scalar supports, replays every ordinary and arbitrary dirty +basis vector in both orientations, rebuilds literal frame transitions and +CRT profiles, then checks exact moments and next-grid exclusions. +Verification never refreshes source pins. `pin_sources.py` is an explicit +maintainer freeze operation; `SOURCE.json` binds the selected construction. + +The exact values, profiles, strict margins and arithmetic cutoffs are in +[certificate.json](certificate.json). Configuration and word hashes are in +[selection.json](selection.json). Fresh-run and CI evidence are recorded +separately; earlier package verification does not stand in for this gate. + +## Credits and limitations + +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. +The construction composes work by Chafik Boukhalfa (PR71/79/84), Rohan Arun +(PR65/67/78/82), Dominik Scholz (PR63/68/76), Alejandro Zarzuelo Urdiales +(PR70), eumemic (PR57/69), Rohan Garg (PR59), Avi Eisenberg (PR62), and the +other retained contributors. Exact original Git sources, licenses and +notices remain under `references/frame-compiler/pr69`, `pr71`, `pr82`, `pr84`. + +The inherited all-size compiler, analytic transfer, routing, precision, +prime selection, exact recovery and fixed-alphabet tape hypotheses remain +assumptions. This is a finite conditional witness, not an unconditional +multiplication theorem or measured runtime speedup. diff --git a/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/SOURCE.json b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/SOURCE.json new file mode 100644 index 0000000000..7b7a434a5d --- /dev/null +++ b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/SOURCE.json @@ -0,0 +1,30 @@ +{ + "files": { + "references/frame-compiler/pr69/SOURCE.json": "928fa8cce0964a6894af3f40cbde6d983aac395336e5277f751c9cbf1b07957f", + "references/frame-compiler/pr71/SOURCE.json": "1c79309362044dd386f72946ccb2e258e98d07d7239ea89d8a8646338d24228a", + "references/frame-compiler/pr82/SOURCE.json": "45c50e529dc75e4d9524dd566fcaa9ff584f67fa7ad7ee5983ff11248b030690", + "references/frame-compiler/pr84/SOURCE.json": "f504112f43c57bb2f32423d9935efabb3ac95a3a31141770286fc0c39b1941e1", + "research/aligned-exchange-frames/PROOF.md": "1a931b3d2a757f9a55911394da5fa9617775a7fee4da0739189a7a169f62efef", + "research/aligned-exchange-frames/README.md": "584c64da8ea46b46dfcc6a8b86f4543bba641f10d36f95bf407b2a459591da50", + "research/aligned-exchange-frames/check.py": "86d4ab1b52c490a350ae84e2805d8a95557dfcf709597ecc365aaef4a0178f31", + "research/aligned-exchange-frames/exchange-proof.md": "0a6df5c08fcfda77349e1f543128502951cee2bea8fb08904360d8bfe0d10b12", + "research/aligned-exchange-frames/exchange_policy.py": "671704f8a5a8276c68aeef0432658e20e8c7dfff6b5fcf5b342f40644d920d30", + "research/aligned-exchange-frames/future_completion.py": "bfe7dd61b01abb445c363503bca61b217bf2e82d977de2336de3a48e1b8effd7", + "research/aligned-exchange-frames/graph_audit.py": "a5fdeec4789469052c0a60ee894851c412c7b9de4844942c09ccaa048b9da94c", + "research/aligned-exchange-frames/independent_check.py": "be1aa3f498067683aa80235690f74dd1dff615913e14f3ba07ce003822913d7d", + "research/aligned-exchange-frames/partition-proof.md": "aeeb9fec06d38eb829b9be4de934d63cf65fb0064440306520de12d41f21921d", + "research/aligned-exchange-frames/partition_graph.py": "63e23b1d33094f99e96821f1859fee2612907d0cab928f983cce3d279a331900", + "research/aligned-exchange-frames/pin_sources.py": "8a6731b2ced88ef32bd74db1c0c7541210de9f3ff63272f9ffc4c112f79d80c1", + "research/aligned-exchange-frames/producer.py": "533819362dbf7a211647182c32d9bd6c89a9e71c1d0987baf555dc333a05e9c8", + "research/aligned-exchange-frames/profile-23.json": "9ceb5e50591c52ed8c225f248b9f1f99f9a66dac4cecb00b8942aab84417d0da", + "research/aligned-exchange-frames/profile-25.json": "76fb46fe77da64e867c86adff6a8fa65a488065d6413c62e9e946d51e75c8f7e", + "research/aligned-exchange-frames/selection.json": "eebd008b4c93622200659c6b001a440ce3857b5e34d93e50a5219a4c74fb21b5", + "research/aligned-exchange-frames/transitions-23.json": "70714f6f4773299742d30d1ba9bc0618ddca19df9b77fa28978350291e95176d", + "research/aligned-exchange-frames/transitions-25.json": "7838fe1cff8f13204f068868eb66c4abb1ef8a35e622b9e99107b92eecbb33dd", + "research/aligned-exchange-frames/word-23.json.gz": "833b1e3467d48273a237b74ca624c3e42a0584d7bfb2e91cb2ac78d10da864d1", + "research/aligned-exchange-frames/word-25.json.gz": "9aa6d5eaf638568d34a0de5417dbe19418ff50b11c7ad729c62d68174a937036", + "research/balanced-split-frames/certificate.json": "cec62c4ca612e458b638982056c80be8741ed634904077a5c220427e23cc3edd", + "research/rank-pair-refinement/refine.py": "a19a79ea064fe66cb5f4e2971d6ab277cdfd452975c539e23066174533430691" + }, + "scope": "Root-relative selected code, proof, exact words and profiles; archived manifests bind original Git sources. Axis, graph and arithmetic receipts are checked outputs." +} diff --git a/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/certificate.json b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/certificate.json new file mode 100644 index 0000000000..6ec5b38501 --- /dev/null +++ b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/certificate.json @@ -0,0 +1,761 @@ +{ + "W": 130468512, + "accepted": { + "lower": "19999999999999999997513661269543528014377862883619/20000000000000000000000000000000000000000000000000", + "strict_gap": "12431693652282354649230759363981/100000000000000000000000000000000000000000000000000", + "terms": { + "1": { + "lower": "1226643454455034979739212400763637216956422815043/50000000000000000000000000000000000000000000000000", + "upper": "1226643454455034979739212400763637281886291387703/50000000000000000000000000000000000000000000000000" + }, + "10": { + "lower": 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"25": { + "crt_disagreements": 0, + "full_basis_vectors": 39372, + "roles": 34772 + } + }, + "bit_saving": "52784930333197/1000000000000000000", + "child_multiplicities": { + "1": 1839823774, + "10": 6707076, + "11": 4742508, + "12": 4569203, + "13": 2757010, + "14": 2545939, + "15": 1509099, + "16": 1643051, + "17": 8782573, + "18": 1117110, + "19": 104489, + "2": 59587066, + "20": 1078677, + "21": 16524971, + "22": 299299, + "23": 68931575, + "25": 61581212, + "3": 70343959, + "4": 25030095, + "481": 8146600, + "5": 17043529, + "525": 61581212, + "529": 60740700, + "6": 15341690, + "7": 11184256, + "8": 10057785, + "9": 7209097 + }, + "comparison": { + "pr71_commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "pr71_complete_profile_exclusion_lower": "4000002530263010439662639528657941408729786822041/4000000000000000000000000000000000000000000000000", + "pr71_kappa": "51414646104039/1000000000000000000", + "relative_gain_pr71": "455832709117/17138215368013" + }, + "eventual_bounds": { + "additional_eventual_conditions": [ + "BHP prime threshold and distinct-prime packing", + "Fixed rational basis, eligible common prime and native table setup", + "Catalogue/descriptor domination, logarithm absorption, exact recovery" + ], + "all_interval_argument": "For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). Successive intervals double LHS; the positive affine RHS grows at most linearly, so 2^j >= j+1 proves persistence.", + "common_cutoff": 14000000000000000000, + "cutoff_log2_input": { + "alpha": 5743214657, + "compact": 22972858625, + "geometry": 3999929625045871804, + "guard": 4205968, + "log_p": 25, + "normalization": 14000000000000000000, + "period": 45945717249, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000000000, + "powers": { + "alpha": { + "exponent": 738942256940779, + "rhs": 112000000000000151632, + "rhs_bits": 67 + }, + "compact": { + "exponent": 738942256940779, + "rhs": 448000000000000606464, + "rhs_bits": 69 + }, + "leaf": { + "exponent": 666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 738942256940779, + "rhs": 224000000000000303192, + "rhs_bits": 68 + }, + "rows": { + "exponent": 738942256940779, + "rhs": 112000000000000151632000, + "rhs_bits": 77 + } + } + 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replayed axis constructions.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions required') +from pathlib import Path +from collections import Counter +from fractions import Fraction as Q +import importlib.util,argparse,json,subprocess,tempfile,hashlib,os,shlex +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +from producer import check_sources +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m +exact=load('candidate_exact',ROOT/'research/rank-pair-refinement/refine.py') +balanced=load('candidate_assembly',DEP/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') + +def profile(path): + v=json.loads(Path(path).read_text()) + return v['profile'] if 'profile' in v else v + +def calculate(first,second): + profiles=[profile(first),profile(second)] + N=4073300;m=575 + assert [p['h'] for p in profiles]==[23,25] + W=2*N+sum(N//p['v']*p['R'] for p in profiles) + parts={'data':Counter({1:18*N,21:2*N,17:2*N,481:2*N}),'endpoint_copy':Counter({1:N})} + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 + assert p['rank_sum']==h*p['R']+p['loss']==sum(t*n for t,n in enumerate(p['blocks'])) + assert p['loss']==h*(h-1) + parts[f'internal_{h}']=Counter({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + parts[f'exterior_{h}']=Counter({h:bank,m-2*h:bank}) + parts[f'growth_{h}']=Counter({1:2*N,h-2:2*N}) + rows=sum(parts.values(),Counter());assert sum(t*n for t,n in rows.items())==m*W-1846900 + lo,hi,grid=1,71700000000000,10**18 + while lo+11 + result.update(status='Verified finite conditional witness; inherited all-size transfer remains assumed', + source_manifest_sha256=hashlib.sha256((HERE/'SOURCE.json').read_bytes()).hexdigest(), + axes=axes,eventual_bounds=balanced.cutoffs(result['finite_bridge'],result['assembly']), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113',pr71_kappa=Q(previous['kappa']), + relative_gain_pr71=result['kappa']/Q(previous['kappa'])-1, + pr71_complete_profile_exclusion_lower=old_lower)) + comparisons={} + for name,relative in ( + ('previous_pr74','research/balanced-split-frames/certificate.json'), + ('pr82','references/frame-compiler/pr82/research/envelope-balanced/certificate.json'), + ('pr84','references/frame-compiler/pr84/certificates/indexed-cycle-kappa.json')): + prior=json.loads((ROOT/relative).read_text());physical=prior.get('bit',prior) + counts={int(t):n for t,n in physical['child_multiplicities'].items()} + assert sum(t*n for t,n in counts.items())==575*physical['W']-1846900 + lower=exact.moment(arithmetic,575,physical['W'],counts,result['bit_saving'])['lower'] + assert lower>1 and result['kappa']>Q(prior['kappa']) + comparisons[name]=dict(source_certificate=relative,kappa=Q(prior['kappa']),relative_gain=result['kappa']/Q(prior['kappa'])-1,complete_profile_exclusion_lower=lower) + result['additional_comparisons']=comparisons + result=arithmetic.js(result) + path=HERE/'certificate.json' + if record:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:assert result==json.loads(path.read_text()) + print('PASS exact moment, next-grid exclusions, 47 inequalities and seven margins',flush=True) + return result + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--record',action='store_true');args=parser.parse_args();generate(args.record) diff --git a/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/exchange-proof.md b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/exchange-proof.md new file mode 100644 index 0000000000..09ccd4ed5e --- /dev/null +++ b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/exchange-proof.md @@ -0,0 +1,137 @@ +# Paid carried-signal exchanges + +## Scope and provenance + +The selected producer uses Chafik Boukhalfa's pinned PR #84 indexed engine, +with up to three single-edge and three two-edge exchange passes. The local +invariant proof below applies at every accepted exchange and hence through +all passes. Our independently developed one-pass reference implementation +is retained as `exchange_policy.py`; it is not the selected runtime engine. +PR #70, by Alejandro Zarzuelo Urdiales, supplied the carried-signal exchange +method, and Dominik Scholz's PR #76 supplied integer profile-entropy pricing. +This composition and its independent reference work were prepared for +Thomas DiFiore with substantial OpenAI Codex assistance. All inherited +contributors, source notices and licenses remain credited. + +This is a finite construction argument. The inherited all-size compiler, +analytic, fixed-tape, precision, routing, prime-selection and recovery +hypotheses remain assumptions. The search is bounded and makes no claim of +minimum cost or global optimality. + +## Matching invariant + +Each eligible edge has the form `(g,u,i)`: region `g` carries its input +coordinate `i` to use `u`. The inherited graph builder supplies the entire +eligible edge list. Each edge already satisfies the required signal identity, +chronology and frame containment. The exchange policy selects edges from +that list and does not add an eligibility rule. + +For region `g`, let `O_g` be the span over F2 of its independent desired +output rows. Let `C_g` contain the selected input unit rows carried out of +that region. The matching invariants are: + +1. The rows consisting of a basis of `O_g` followed by `C_g` are independent. +2. Every use `u` is assigned to at most one selected edge. +3. The total number of selected edges equals the initial matching cardinality. + +The function `can(e,drop)` recomputes the local binary basis after excluding +`drop`, when present, and checks independence of the new edge's unit row. +Removing a selected row from another region also preserves independence. + +## One-edge exchanges + +Consider an unselected edge `e=(g,u,i)`. + +If `u` is assigned to edge `f`, the policy checks that adding `e` is locally +independent after removing `f` when both edges belong to `g`. When `f` belongs +to another region, it checks independence against the unchanged selected +rows at `g`. Replacing `f` by `e` preserves the assigned use and cardinality. +The donor region either has a checked replacement or loses a row. + +If `u` is unassigned, the policy finds a selected edge `f` in the same region +such that the replacement passes the same independence check. Removing `f` +frees its use, and adding `e` assigns the previously free use `u`. Cardinality +and use uniqueness are again preserved. + +Each accepted replacement strictly lowers the fixed integer discovery cost. +The selected implementation makes three deterministic passes. + +## Two-edge cycles + +Suppose the matching contains + +- `z=(g,u_z,i_z)`, and +- `f=(g',u_f,i_f)`, with `g != g'`. + +The policy considers eligible unselected edges + +- `e=(g,u_f,i_e)`, and +- `w=(g',u_z,i_w)`. + +It checks `can(e,z)` and `can(w,f)`, and requires +`price(e)+price(w) < price(z)+price(f)`. +The two local checks concern different regions. Replacing `{z,f}` with +`{e,w}` therefore preserves local independence in both regions. Every other +region is unchanged. The set of assigned uses is exactly the same, and two +selected edges replace two selected edges. Thus all three invariants hold. + +The implementation removes both old edges before inserting either new edge. +It asserts use uniqueness during insertion, then checks total cardinality +and every region's complete output-plus-carried-row independence at the end. +Each pass is deterministic, with explicit integer and edge-ID tie breaking. +The selected engine stops after at most three passes, or an unchanged pass. +Three-edge cycles are outside the selected policy. + +## Discovery pricing and final coordinates + +The discovery oracle receives each region's core and cover after applying +the selected pricing permutation in `selection.json`. A separately recorded +final permutation can subsequently relabel the compiled word; its complete +profiles are recomputed. The oracle's integer weights are retained +from PR #76: bounded rational logarithms define reproducible approximations +to `t log(t)`. The fixed oracle profile of each eligible transition supplies +its score. Prices remain fixed during the bounded matching passes. + +These prices choose among eligible matchings. Acceptance of the construction +uses the complete physical word and its independently reconstructed paid +profile. An improvement of a discovery score alone is insufficient evidence +for an exponent improvement. + +## Literal implementation and paid cost + +After matching, the inherited compiler constructs independent output rows, +selected carried unit rows, and an independent completion to a full basis. +Its binary elimination synthesizes that invertible basis change as literal +XORs at the common frame. All selected carrying, frame growth, copied +outputs, clearing controls and cleanup are represented in the resulting +word. Changing the matching does not remove any of these charges. + +The complete word is checked on all ordinary-input and arbitrary-dirty +basis vectors in both orientations. Its literal frame transitions determine +the exact fixed-basis recursive child multiset. Copied centers, endpoint +copies, data growth, data blocks and the inherited complex costs are included +by the complete recurrence checker. The exponent is accepted only after +exact moment bounds and the full assembly checks pass. + +## A strict profile-dominance criterion + +A useful sufficient condition can be stated without a discovery score. +At fixed physical width, replace `q` size-1 children by `n_t` size-`t` +children, where every `t>1`, `n_t>=0`, and `sum(t*n_t)=q`. The rank is +unchanged. For any positive saving `a`, the replaced contribution to the +characteristic changes from a factor proportional to `q` to +`sum(t*n_t/t^a)`, which is strictly smaller when at least one child is added. +All unchanged paid terms cancel in this comparison. + +As a checked example on the fixed PR #82 graphs at commit +`3410b940aa26e5876202152dfa7c4f66451ee22c`, the additional two-edge pass produced: + +| Axis | Size-1 children removed | Larger children added | +| --- | ---: | --- | +| h23 | 147 | 63 of size 2; 7 of size 3 | +| h25 | 216 | 56 of size 2; 12 of size 3; 2 of size 7; 6 of size 9 | + +Both ranks and role counts were unchanged, and both complete words passed +independent dirty replay and exact profiles. This establishes strict moment +improvement for every positive saving for that experiment. The selected +aligned graphs have their own separately checked complete costs. diff --git a/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/exchange_policy.py b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/exchange_policy.py new file mode 100644 index 0000000000..674f81f54e --- /dev/null +++ b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/exchange_policy.py @@ -0,0 +1,132 @@ +"""Composable carried-signal exchanges for an inherited frame compiler. + +PR70 exchange methodology: Alejandro Zarzuelo Urdiales. +PR76 integer profile-entropy pricing and one-edge passes: Dominik Scholz, +commit 2333abcea79793fe301b479a7c971cc2be45596c, with OpenAI assistance. +The selected two-edge cycles and factory packaging are prepared for +Thomas DiFiore with substantial OpenAI Codex assistance. Apache-2.0. +Every candidate still needs complete dirty replay and actual paid profiles. +""" +from pathlib import Path +from types import SimpleNamespace +import json,struct,subprocess,importlib.util,sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +MATH_PATH=ROOT/'references/frame-compiler/pr71/scripts/experiments/binary_frame_math.py' +_math_spec=importlib.util.spec_from_file_location('aligned_exchange_pinned_math',MATH_PATH) +_math=importlib.util.module_from_spec(_math_spec) +_math_spec.loader.exec_module(_math) +logs=_math.logs + + +def install(compiler, oracle_executable, h, work_dir, passes=3, + two_passes=1, permutation=None, record_matching=False): + """Mutate this private compiler's matching callback; leave synthesis intact.""" + a=SimpleNamespace(h=h,work_dir=Path(work_dir),passes=passes, + two_passes=two_passes,price_coordinates=permutation is not None) + assert h in (23,25) and passes==3 and two_passes==1, 'Changed selected exchange configuration' + assert permutation is not None, 'Selected policy requires explicit coordinate pricing' + a.work_dir.mkdir(parents=True,exist_ok=True) + executable=Path(oracle_executable) + if permutation is not None:assert sorted(permutation)==list(range(h)) + def permute_mask(bits):return sum(1<>i&1) + original_match=compiler.match + def exchange_match(blocks,uses,enabled): + result=original_match(blocks,uses,enabled) + edges,chosen,right,stats=result + initial_cardinality=len(chosen) + if not a.passes:return result + owner={x:g for g,b in enumerate(blocks) for x in b['nodes']} + path=a.work_dir/'matching-oracle.bin' + with path.open('wb')as stream: + h=a.h;v=h*(h-1)*(h-2)//6 + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks: + frame=tuple(permute_mask(v) for v in b['frame']) if a.price_coordinates else b['frame'] + stream.write(struct.pack('<2QI',*frame,b['rank'])) + oracle=subprocess.Popen([str(executable),str(path)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + weights=[0]+[int(t*sum(logs(t))*10**30//2)for t in range(1,h+1)];cache={} + def entropy(x,y): + if (x,y)not in cache: + oracle.stdin.write(f'{x} {y}\n');oracle.stdin.flush();line=oracle.stdout.readline();assert line + values=list(map(int,line.split()));assert len(values)==h+1 + cache[x,y]=sum(n*w for n,w in zip(values,weights)) + return cache[x,y] + def cost(edge): + g,u,i=edge;p=owner[blocks[g]['inputs'][i]];t=uses[u][1] + return -entropy(g+2,t+2)+entropy(g+2,1)+entropy(0,p+2)+entropy(p+2,t+2) + try: + prices=[] + for j,e in enumerate(edges): + prices.append(cost(e)) + if j%20000==0:print('edge prices',j,len(edges),'pairs',len(cache),flush=True) + finally: + oracle.stdin.close();assert oracle.wait(timeout=10)==0 + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e]));initial=sum(prices[e]for e in chosen) + def can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]=0:continue + if not can(e,z) or not can(w,f):continue + key=(delta,z,w) + if best is None or keystep and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1< 3: + if choice in (1,2,3): + indices=[{1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice]] + elif isinstance(choice,str): + indices=list(range(min(int(choice[5:]),len(groups)))) + selected = [i for i in sorted(set(indices)) if len(groups[i]) == 2] + # Each split adds one group. This cap leaves at least one pair. + selected = selected[:max(0, n-len(groups)-1)] + result = [] + for i, group in enumerate(groups): + result.extend([[point] for point in group] if i in selected else [group]) + assert all(len(group) in (1, 2) for group in result) + assert len(result) < n + assert [point for group in result for point in group] == list(points) + return result + return Partition + + module.circuit_class = selected_class + original_points = module.alternating_points + def anchored_points(dimension, common): + order = original_points(dimension, common) + pairs = [(a,a+1) for a in range(0, dimension-1, 2) if common not in (a,a+1)] + head = [point for pair in pairs[:count] for point in pair] + result = head + [point for point in order if point not in head] + assert sorted(result) == [point for point in range(dimension) if point != common] + return result + module.alternating_points = anchored_points + circuit = module.graph(h) + if ordered: + circuit = reorder(circuit) + assert circuit.verify()['circuit_sha256'] == config['expected_scalar_sha256'] + else: + circuit.verify() + return circuit diff --git a/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/producer.py b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/producer.py new file mode 100644 index 0000000000..3f43c4a6ad --- /dev/null +++ b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/producer.py @@ -0,0 +1,105 @@ +#!/usr/bin/env python3 +"""Aligned recursive partitions, future bases, and coordinated carry exchanges. + +Composition for Thomas DiFiore with OpenAI Codex assistance. Apache-2.0. +The pinned PR71 engine and PR69 graph are retained unchanged. Future-unit +completion follows PR79; weighted carry exchanges follow PR70/76. PR84 contributes exact candidate indexes, additional exchange passes and +future-use output routing. Our multi-pair aligned partitions and pricing +composition are checked as literal +finite words, including all physical frames and arbitrary dirty inputs. +""" +import sys +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +from hashlib import sha256 +import argparse,gzip,importlib.util,json,os,shlex,subprocess,tempfile,types +from concurrent.futures import ProcessPoolExecutor +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +from binary_frame_replay import replay +from partition_graph import graph + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module);return module +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + + +def check_sources(): + for folder in (DEP,ROOT/'references/frame-compiler/pr69',ROOT/'references/frame-compiler/pr82',ROOT/'references/frame-compiler/pr84'): + manifest=json.loads((folder/'SOURCE.json').read_text()) + for name,digest in manifest['files'].items():assert sha256((folder/name).read_bytes()).hexdigest()==digest,name + manifest=json.loads((HERE/'SOURCE.json').read_text()) + required={str((HERE/name).relative_to(ROOT)) for name in ('producer.py','partition_graph.py','exchange_policy.py','future_completion.py','check.py','graph_audit.py','independent_check.py','selection.json')} + assert required<=set(manifest['files']), 'Incomplete selected source closure' + for name,digest in manifest['files'].items():assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + + +def compile_axis(h): + check_sources() + config=json.loads((HERE/'selection.json').read_text())['axes'][str(h)] + assert config['engine']=='indexed-pr84' and config['single_exchange_passes']==3 + assert config['two_exchange_passes']==3 + assert config['output_mode'] in ('baseline','route-late') + price=config['pricing_permutation'];assert sorted(price)==list(range(h)) + source_path=ROOT/'references/frame-compiler/pr84/scripts/experiments/indexed_cycle_engine.py' + source=source_path.read_text() + old="for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank']))" + new="for b in blocks:stream.write(struct.pack('<2QI',*(permute_mask(mask) for mask in b['frame']),b['rank']))" + assert source.count(old)==1;source=source.replace(old,new) + marker=' # Bounded two-donor exchanges after single-edge local optimization.' + assert source.count(marker)==1 + prefix,suffix=source.split(marker);assert suffix.count('for phase in range(3):')==1 + source=prefix+marker+suffix.replace('for phase in range(3):','for phase in range(TWO_PASSES):') + engine=types.ModuleType('aligned_private_engine') + engine.__file__=str(DEP/'scripts/experiments/split_pair_engine.py') + exec(compile(source,str(source_path)+':aligned-indexed','exec'),engine.__dict__) + engine.permute_mask=lambda bits:sum(1<>i&1) + engine.graph=graph;engine.PENDING_COST=True;engine.oracles=[] + engine.OUTPUT_MODE=config['output_mode'];engine.TWO_PASSES=config['two_exchange_passes'] + with tempfile.TemporaryDirectory(prefix='aligned-exchange-compile-') as directory: + work=Path(directory);oracle=work/'oracle' + subprocess.run([*shlex.split(os.environ.get('CXX','c++')),'-O3','-std=c++17','-I',str(DEP/'references/frame-compiler/pr48/scripts/partial_swap'),str(DEP/'references/frame-compiler/pr67/research/slot-cost-rank-pair/profile_oracle.cpp'),'-o',str(oracle)],check=True) + engine.ORACLE_EXE=str(oracle);engine.ORACLE_INPUT=str(work/'oracle.bin') + try:compiled,word=engine.compile_(h,matching=True,reclaim=True,dirty=True) + finally: + for process in engine.oracles:process.stdin.close();assert process.wait(timeout=10)==0 + compiled.pop('seconds',None) + compiled['scalar']=graph(h).verify() + compiled['graph_configuration']=config + compiled['private_engine_sha256']=sha256(source.encode()).hexdigest() + word=relabel(word,config['coordinate_permutation']) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + assert sha256(raw).hexdigest()==config['expected_word_sha256'],'Selected word differs' + path=HERE/f'word-{h}.json.gz' + with path.open('wb') as stream: + with gzip.GzipFile(filename='',fileobj=stream,mode='wb',mtime=0) as archive:archive.write(raw) + receipt=replay(path) + axis=dict(configuration=config,compiled=compiled,replay=receipt,word_sha256=sha256(raw).hexdigest(),gzip_sha256=sha256(path.read_bytes()).hexdigest()) + (HERE/f'axis-{h}.json').write_text(json.dumps(axis,indent=2)+'\n') + print(f'PASS fresh aligned/exchange word h={h}, roles={receipt["roles"]}',flush=True) + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--h',type=int,choices=(23,25));args=parser.parse_args() + if args.h:compile_axis(args.h) + else: + with ProcessPoolExecutor(max_workers=2) as pool:list(pool.map(compile_axis,(23,25))) diff --git a/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/profile-23.json b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/profile-23.json new file mode 100644 index 0000000000..a217fee46b --- /dev/null +++ b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/profile-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 26409, + "loss": 506, + "rank_sum": 607913, + "field_prime": 2305843009213693951, + "frames": 78515, + "distinct_matrices": 40708, + "crt_matrices": 5083, + "crt_disagreements": 0, + "blocks": [ + 0, + 370499, + 11858, + 15932, + 4919, + 4023, + 3213, + 2140, + 1959, + 1435, + 1179, + 870, + 837, + 498, + 407, + 295, + 267, + 74, + 324, + 0, + 171, + 23, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/profile-25.json b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/profile-25.json new file mode 100644 index 0000000000..f33aaaa4ef --- /dev/null +++ b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/profile-25.json @@ -0,0 +1,40 @@ +{ + "h": 25, + "v": 2300, + "R": 34772, + "loss": 600, + "rank_sum": 869900, + "field_prime": 2305843009213693951, + "frames": 108758, + "distinct_matrices": 54701, + "crt_matrices": 5955, + "crt_disagreements": 0, + "blocks": [ + 0, + 504794, + 18246, + 19029, + 7745, + 4399, + 4490, + 3536, + 3135, + 2207, + 2256, + 1548, + 1493, + 910, + 909, + 469, + 581, + 263, + 210, + 59, + 387, + 101, + 169, + 25, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/selection.json b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/selection.json new file mode 100644 index 0000000000..ef0b559d02 --- /dev/null +++ b/references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/selection.json @@ -0,0 +1,159 @@ +{ + "axes": { + "23": { + "groups": [ + "first6", + 1, + 1 + ], + "anchor_pairs": 6, + "coarse_word": "hhh", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "engine": "indexed-pr84", + "future_unit_completion": true, + "single_exchange_passes": 3, + "two_exchange_passes": 3, + "output_mode": "baseline", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "pricing_permutation": [ + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 18, + 17, + 19, + 20, + 21, + 22, + 0, + 1, + 3, + 2, + 4 + ], + "coordinate_permutation": [ + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 18, + 17, + 19, + 20, + 21, + 22, + 0, + 1, + 3, + 2, + 4 + ], + "expected_scalar_sha256": "dd88562359e47b54fee18e58c9f5a6007f2f6f46ef8e73d64b4a9213d854e2ad", + "expected_word_sha256": "5e387869128c22e49b98113d276c229764bcc7554ba88d69c74efa84cdb248e2" + }, + "25": { + "groups": [ + "first9", + 1, + 1, + 2 + ], + "anchor_pairs": 9, + "coarse_word": "hhh", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "engine": "indexed-pr84", + "future_unit_completion": true, + "single_exchange_passes": 3, + "two_exchange_passes": 3, + "output_mode": "route-late", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "pricing_permutation": [ + 6, + 5, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 23, + 22, + 24, + 1, + 0, + 2, + 3, + 4 + ], + "coordinate_permutation": [ + 6, + 5, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 23, + 22, + 24, + 1, + 0, + 2, + 3, + 4 + ], + "expected_scalar_sha256": "4720efefb683d3a8458968c2240c50337694940bf3cc0383e4aa71fcfeec1a48", + "expected_word_sha256": "3844b5a2cc48842cbd0c5bc1ae7c336fd760dabcf163093f92f0042bc5dd2757" + } + }, + "expected": { + "kappa": "5278214423139/100000000000000000", + "bit_saving": 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Rank-first reclamation on interval-strip pair assembly, 8 October 2026 +Composition and exact profile witness: Dominik Scholz, with substantial OpenAI +GPT-6 Astra / Codex assistance. The PR #60 descending-frame-rank compiler by +Chafik Boukhalfa is reused unchanged on Avi Eisenberg's PR #62 scalar graph. +The joint frame compiler and paid reclamation are eumemic's PR #57, developed +with OpenAI Codex assistance. PR #62 records Anthropic Claude assistance. +This composition improves actual fixed-basis block profiles with unchanged +role counts; no new slot-priority rule or scalar graph is claimed. All prior +contributors, licenses, compiler arguments and conditional analytic/tape +interfaces remain credited. See research/rank-pair/PROOF.md. + +Ordered scalar frames, minimum-raise reclamation and coordinate relabeling +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. +The new finite construction and exact arithmetic certificates are in +research/ordered-frames, with an earlier parameter refinement in +research/rank-pair-refinement. These build on Dominik Scholz's PR #63 +composition, Chafik Boukhalfa's PR #60 reclamation compiler, Avi Eisenberg's +PR #62 scalar graph and eumemic's PR #57 reversible frame compiler. +Concurrent PR #65/#67 work is acknowledged in the proof. All inherited +licenses, author notices and conditional proof boundaries remain in force. + +Balanced split frames with core node ordering and coordinate relabeling +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. +This composition combines eumemic's PR69 coarse column sums, Chafik Boukhalfa's +PR71 anchored split/next-use-live compiler, and the earlier PR74 node ordering +and coordinate relabeling. Rohan Garg's PR59 split operation, Avi Eisenberg's +PR62 scalar graph, Rohan Arun's PR65/67 schedules and profile-cost selection, +Dominik Scholz's PR63/68 composition and pending controls, and eumemic's PR57 +compiler remain credited. Original source closures and notices are preserved +under references/frame-compiler/pr69 and pr71; all preceding licenses apply. +See research/balanced-split-frames/PROOF.md for the finite conditional scope. diff --git a/references/frame-compiler/pr74/SOURCE.json b/references/frame-compiler/pr74/SOURCE.json new file mode 100644 index 0000000000..87bd75428a --- /dev/null +++ b/references/frame-compiler/pr74/SOURCE.json @@ -0,0 +1,19 @@ +{ + "commit": "3f78d8967c009153f2df5c6a6577b6ab1d37e2ca", + "files": { + "FETCH.json": "4aee950c461d4b46ca42d323d7a7041118ba2b1002d7a867616f3c7ea4d66c1c", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "c087c747998243c96db63203920affd28cec880b702c36017c40a3eb29947fa9", + "research/balanced-split-frames/PROOF.md": "f7a908eea56fdab2f2e8f4ce694a0132c37844ae1cb657962b6549f585bfcdfb", + "research/balanced-split-frames/README.md": "f620b1a18df2b6c0f5d179ebf50f90e630270bba90e14c0d4bff189e3056ee49", + "research/balanced-split-frames/SOURCE.json": "c933a96c636f1e22e02be6fb775a9da2cd14c11fa2d07ba75af17c7e99f00049", + "research/balanced-split-frames/certificate.json": "cec62c4ca612e458b638982056c80be8741ed634904077a5c220427e23cc3edd", + "research/balanced-split-frames/check.py": "45fb95cb2a6b0573efbe37938c149936f4aa4fff1a88425380af7bc59239b4ae", + "research/balanced-split-frames/producer.py": "ec94e4b7af370f7e921fffa3679e80d081a672dbd3ff198043edfb0dc7a9cc9d", + "research/balanced-split-frames/profile-23.json": "7f61525499f56ccc3a183a2741ef823cce30423475fa586ba7d36610b5b66844", + "research/balanced-split-frames/profile-25.json": "9b4d0647e3667af963c164c048c6ea750d90397b046336ede5a5b6902a9f6473", + "research/balanced-split-frames/selection.json": "cbc616540af0ff5b63a90a920c70acd660fbb67052e4dc19889fe0443f2129f4" + }, + "pr": 74, + "scope": "Exact attributed contributor inputs and reported comparison certificate, not a new audit of the entire foreign claim." +} diff --git a/references/frame-compiler/pr74/research/balanced-split-frames/PROOF.md b/references/frame-compiler/pr74/research/balanced-split-frames/PROOF.md new file mode 100644 index 0000000000..7244811413 --- /dev/null +++ b/references/frame-compiler/pr74/research/balanced-split-frames/PROOF.md @@ -0,0 +1,145 @@ +# A paid composition of balanced coarse sums, split recursion and frame order + +## Statement and boundary + +The complete finite profile below certifies + +`kappa = 10366199626713/200000000000000000` + +for the inherited conditional bound `T(n)=O(n(log n)^(1-kappa))`. +The all-size compiler, analytic transfer, fixed-alphabet tape simulation, +precision, routing, prime selection and exact recovery hypotheses are inherited. +Finite source checks and arithmetic do not establish those general hypotheses. + +## 1. Pinned ingredients + +PR #71 is frozen at `1bef94fd40a746452548c84a4a8f8834670a3113` in +`references/frame-compiler/pr71/`, including its complete consumed source +closure, selected words, data interfaces, licenses, notices and root documents. +Its own source manifest is preserved without re-pinning. PR #69's original +coarse-sum compiler and notices are frozen at +`91aa1f17e6e3fc063241686a41a34ddd0dc24c50` in the adjacent `pr69/` archive. + +The new producer reads PR #69's literal BEFORE/AFTER replacement, applies it +exactly once to the archived PR #62 scalar graph consumed by PR #71, and keeps +PR #71's `[1,1,2]` split choices and lowest-intact-pair anchoring. The original +source files are unchanged. After reordering, it uses the archived PR #71 +compiler and its next-use profile-cost selection unchanged. + +## 2. Shared intermediate sums preserve the scalar map + +For two disjoint groups A and B, replace the chain forming +`sum_{a in A,b in B} e(a,b)` by +`sum_{b in B} (sum_{a in A} e(a,b))`. +Each operand support occurs exactly once. The nested sums are disjoint, +so this is an equality over the inherited scalar field. Existing node +interning shares the column intermediates with later strip computations. +The singleton cases and strictly decreasing recursive partitions retain the +same identity. No negative coefficient or cancellation is introduced. + +`graph_audit.py` reconstructs dense global triple-coordinate supports using +its own recurrence. For each dimension it checks every input, addition, +core, cover and prescribed output, and compares the complete output support +inventory with original PR #71. This checks 67,460 / 94,993 additions and +5,336 / 6,925 outputs. Original PR #71 has 68,771 / 96,718 additions. + +## 3. Legal node order and fully charged live reclamation + +Keep source IDs fixed. Group remaining active nodes by their original +(core, cover), retaining their original order within each group. Sort groups +lexicographically by + +`(popcount(cover)-popcount(core), -core, cover, first_original_node)`. + +Remap every operand and output ID, clear support caches indexed by old IDs, +and verify again. The independent audit proves that each literal edge and +output is preserved, every operand precedes its consumer, every envelope is +unchanged, and this is exactly the selected renumbering. Matching is recomputed +on the resulting graph and the compiler uses its natural region order. + +PR #71's unchanged pending live controls enter a clearing basis only when +their current frame is contained in the present frame and that frame is +contained in their next-use frame. Controls retain their values. The complete +word contains every chosen clearing XOR and every required frame raise. +The discovery score is never substituted for the actual charged profile. + +Both complete words are regenerated with dirty-basis checks enabled. A +separate serialized-word checker replays every input and arbitrary dirty +basis column in both orientations. The final roles are 27,136 / 35,744. + +## 4. Coordinate relabeling and the data family + +Apply each selected permutation to the frame core/cover masks, source-triple +indices, scatter target-triple indices, output common points and output +triples. Literal XORs, scratch IDs and frame IDs remain unchanged. The complete +permutations are frozen in `selection.json`; both relabeled words are replayed. + +For permutation matrix P, both fixed bases `I+J` and the inverse metric +`I-J/9` commute with P. Envelope projectors therefore transform by conjugation. +Containment and every legal incidence remain valid. Ordered contiguous child +profiles can change, and every one is regenerated from the literal word +using the inherited exact bounded-minor/CRT profiler, with zero disagreements. + +Each coordinate permutation induces a bijection on the complete triple set. +Consequently the complete two-axis data-block family is only reindexed: its +aggregate inherited profile and rational recovery cases remain valid. Copied +centers, endpoints and data growth remain explicitly charged. + +## 5. Complete recurrence and assembly + +Let `N=4073300`, `m=575`, and let `R_h` and `b_{h,t}` be the verified role count +and exact internal profile. The physical width is + +`W = 2N + (N/1771)R_23 + (N/2300)R_25 = 133862024`. + +The complete child multiset includes: + +- data: `18N` children of size 1 and `2N` each of sizes 21, 17 and 481; +- paid endpoint copies: `N` additional size-1 children; +- internal axis h: `(N/binom(h,3))*b_{h,t}` children of size t; +- exterior axis h: `(N/binom(h,3))*R_h` each of sizes h and `m-2h`; +- data growth per axis: `2N` each of sizes 1 and `h-2`. + +The total rank is `76968816900 = mW-1846900`; maximum child size is 529. +The exact characteristic is +`M(a)=sum_t (t*n_t/(mW))*exp(a*log(m/t))`. +At `a=25916842362591/500000000000000000`, a rigorous upper bound is below 1. +At `a+10^-18`, a rigorous lower bound is above 1. Positive logarithms make +the characteristic increasing. The complete original PR #71 profile is +separately excluded at the new accepted saving. + +Production arithmetic uses the retained rational logarithm/exponential +helper. The independent checker derives the complete paid multiset and uses +40 exact atanh terms for logarithms and Taylor degree 10 with a geometric +exponential tail. It imports no production arithmetic and checks each of the +47 assembly slacks and seven margins independently. The next kappa grid value +is rejected. Negative controls reject omitted paid children, fabricated slacks +and incorrect source hashes. + +Use positive backoff `10^-18`. Since W is below `2^27`, its `bit_length()` is +27. The product-row coefficient becomes `9*27+20*30=843`. Keeping degree 2000 +and suffix slope 8000 gives degree gap `2000-(51/25)*843=7007/25`. +These values are derived and checked; no stale predecessor constants remain. +Arithmetic cutoff bounds are not complete operational runtime thresholds. + +## Credits + +The composition, core-order continuation, coordinate choices, packaging and +independent audits were prepared for Thomas DiFiore with substantial OpenAI +Codex assistance. Coarse-sum reassociation is eumemic's PR #69. Anchored split +frames and next-use-aware live selection are Chafik Boukhalfa's PR #71. +Rohan Garg supplied the split operation (#59); Avi Eisenberg supplied interval +strips and core-aware pair assembly (#62); Rohan Arun supplied region schedules +and profile-cost selection (#65/#67); Dominik Scholz supplied ranked composition +and pending live controls (#63/#68); eumemic supplied the reversible compiler +and physical/profile checking interfaces (#57). Our earlier PR #74 supplied the +core node ordering and coordinate-relabeling continuation used here. + +The preserved archives retain all earlier credits, including RaD/hipotures, +icekylinx, James Chang, Zhihao Chen, Aurel Prosz, Swapnil Jain, Alejandro Zarzuelo +Urdiales, Douglas Colkitt, OpenAI and Harvey–van der Hoeven, and predecessor +AI-assistance disclosures. No predecessor authorship or endorsement of this +composition is implied. Existing licenses and notices remain in force. + +Concurrent PR #75–#79 contributions, including carry exchanges, balanced split +constructions and coordinate flags, are acknowledged. No priority claim is made. diff --git a/references/frame-compiler/pr74/research/balanced-split-frames/README.md b/references/frame-compiler/pr74/research/balanced-split-frames/README.md new file mode 100644 index 0000000000..5784b8b928 --- /dev/null +++ b/references/frame-compiler/pr74/research/balanced-split-frames/README.md @@ -0,0 +1,70 @@ +# Balanced split frames with shared sums and reusable live controls + +**κ = 10366199626713 / 200000000000000000 = 0.000051830998133565** + +The conditional bound is `T(n) = O(n (log n)^(1-kappa))`. +This is **0.9788258% above our original PR #74 result**, **0.8097927% above +pinned PR #71**, and **0.8082664% above PR #75's claim observed on 8 October +2026**. The later PR #79 claim `5.1745625472866e-5`, observed at 19:55 UTC on the same +date, is also below this result by **0.1649853%**. These compare asymptotic exponent savings; they are not measured +multiplication speedups. + +| Quantity | Original PR #74 | Pinned PR #71 | This composition | +| --- | ---: | ---: | ---: | +| h23 auxiliary roles | 27,698 | 27,455 | 27,136 | +| h25 auxiliary roles | 36,310 | 36,015 | 35,744 | +| Physical width | 136,157,010 | 135,075,665 | 133,862,024 | +| Conditional κ | 5.132858076595e-5 | 5.1414646104039e-5 | 5.1830998133565e-5 | + +## Construction + +Compose eumemic's PR #69 column-balanced coarse sums with Chafik Boukhalfa's +PR #71 anchored split recursion and next-use-aware live reclamation. Apply +our original-envelope node order before carrier matching, then relabel the +geometric coordinates and recompute the actual fixed-basis profiles. + +The balanced graph has 67,460 / 94,993 active additions, compared with +PR #71's 68,771 / 96,718. Every prescribed output is unchanged. The complete +physical words pay for all XORs, frame raises, copied centers and data blocks. +The width now lies below `2^27`; its role-logarithm and product-row constants +are recomputed in the exact certificate. + +## Evidence and reproduction + +- [Proof, scope and contributor credits](PROOF.md) +- [Exact certificate](certificate.json) +- [Selected graph and coordinate choices](selection.json) +- [Immutable source manifest](SOURCE.json) +- [Independent dense scalar audit](graph-audit.json) +- [Independent exact arithmetic audit](independent-audit.json) +- [Verification receipt](validation.json) and [raw log](verification.log) + +Use Python 3.11 or newer and a C++17 compiler with unsigned 128-bit support: + +```sh +make balanced-split-frames-verify +``` + +This regenerates both words from pinned sources, checks their selected raw +hashes, audits the complete scalar graph, independently replays every input +and dirty basis vector in both orientations, reconstructs every literal frame +transition and exact profile, and checks the full paid recurrence and assembly. +The two replay dimensions contain 30,678 / 40,344 basis coordinates. +Both profiles have zero CRT disagreements. Independent arithmetic verifies +all 47 strict inequalities, seven margins, adjacent-grid rejection, and +exclusion of the complete pinned PR #71 profile at the new bit saving. + +The earlier full-suite receipt in `../ordered-frames/validation.json` covers +that historical source state. Current upstream checks and formal packages +remain separate CI jobs. The new source archives retain original notices +and original root documentation so predecessor pins remain unchanged. + +All inherited analytic, all-size compiler, fixed-tape, precision, routing, +prime-selection and recovery hypotheses remain assumed. This is a verified +finite conditional witness, with no global-optimality or practical-speed claim. + +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. Original +PR #74 remains available in `../ordered-frames/`; all predecessor credits and +licenses remain applicable. + +Concurrent PR #75–#79 work is acknowledged; no priority claim is made. diff --git a/references/frame-compiler/pr74/research/balanced-split-frames/SOURCE.json b/references/frame-compiler/pr74/research/balanced-split-frames/SOURCE.json new file mode 100644 index 0000000000..06404d9283 --- /dev/null +++ b/references/frame-compiler/pr74/research/balanced-split-frames/SOURCE.json @@ -0,0 +1,21 @@ +{ + "files": { + "references/frame-compiler/pr69/SOURCE.json": "928fa8cce0964a6894af3f40cbde6d983aac395336e5277f751c9cbf1b07957f", + "references/frame-compiler/pr71/SOURCE.json": "1c79309362044dd386f72946ccb2e258e98d07d7239ea89d8a8646338d24228a", + "research/balanced-split-frames/check.py": "45fb95cb2a6b0573efbe37938c149936f4aa4fff1a88425380af7bc59239b4ae", + "research/balanced-split-frames/graph_audit.py": "b95cf9269fbcaf7f7b9732b28d7a8b790feefc262e86a36de33a92ab7906a8b3", + "research/balanced-split-frames/independent_check.py": "02dd998ebe68f111a42657e1591416b28b618a8d58bbd4fb0686d3afd929db1a", + "research/balanced-split-frames/producer.py": "ec94e4b7af370f7e921fffa3679e80d081a672dbd3ff198043edfb0dc7a9cc9d", + "research/balanced-split-frames/profile-23.json": "7f61525499f56ccc3a183a2741ef823cce30423475fa586ba7d36610b5b66844", + "research/balanced-split-frames/profile-25.json": "9b4d0647e3667af963c164c048c6ea750d90397b046336ede5a5b6902a9f6473", + "research/balanced-split-frames/selection.json": "cbc616540af0ff5b63a90a920c70acd660fbb67052e4dc19889fe0443f2129f4", + "research/balanced-split-frames/transitions-23.json": "0e9b6bbb1f9f08b34077bb93a60b39c2d61cf8f1329c884fd47326bf32bfac60", + "research/balanced-split-frames/transitions-25.json": "3bffd56836edefb309825f4ba303dc27ae88455aa7c8fc918af3ef24d82caee3", + "research/balanced-split-frames/word-23.json.gz": "956b886339ccbd3d599c5e0ec403b870958d052f3442067e8f12a56318e9525d", + "research/balanced-split-frames/word-25.json.gz": "ea090af1c4b56b7dae31d1f0d3fece4417677160f07c372e0455d7f8ac31c7b0", + "research/rank-pair-refinement/refine.py": "a19a79ea064fe66cb5f4e2971d6ab277cdfd452975c539e23066174533430691" + }, + "pr69_commit": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "pr71_commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "scope": "Selected sources and finite inputs. The archived PR69 and PR71 manifests bind the complete inherited source closure; generated axis receipts and arithmetic/audit certificates are checked outputs." +} diff --git a/references/frame-compiler/pr74/research/balanced-split-frames/certificate.json b/references/frame-compiler/pr74/research/balanced-split-frames/certificate.json new file mode 100644 index 0000000000..6a3cfa48df --- /dev/null +++ b/references/frame-compiler/pr74/research/balanced-split-frames/certificate.json @@ -0,0 +1,740 @@ +{ + "W": 133862024, + "accepted": { + "lower": "99999999999999999979924873504956311258242134978917/100000000000000000000000000000000000000000000000000", + "strict_gap": "20075126495043683558076755370663/100000000000000000000000000000000000000000000000000", + "terms": { + "1": { + "lower": "578243869104998674370968149468068831065643870861/25000000000000000000000000000000000000000000000000", + "upper": 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+import sys +if sys.flags.optimize:raise ValueError('Assertions required') +from pathlib import Path +from collections import Counter +from fractions import Fraction as Q +import importlib.util,argparse,json,subprocess,tempfile,hashlib,os,shlex +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +from producer import check_sources +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m +exact=load('candidate_exact',ROOT/'research/rank-pair-refinement/refine.py') +balanced=load('candidate_assembly',DEP/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') + +def profile(path): + v=json.loads(Path(path).read_text()) + return v['profile'] if 'profile' in v else v + +def calculate(first,second): + profiles=[profile(first),profile(second)] + N=4073300;m=575 + assert [p['h'] for p in profiles]==[23,25] + W=2*N+sum(N//p['v']*p['R'] for p in profiles) + parts={'data':Counter({1:18*N,21:2*N,17:2*N,481:2*N}),'endpoint_copy':Counter({1:N})} + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 + assert p['rank_sum']==h*p['R']+p['loss']==sum(t*n for t,n in enumerate(p['blocks'])) + assert p['loss']==h*(h-1) + parts[f'internal_{h}']=Counter({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + parts[f'exterior_{h}']=Counter({h:bank,m-2*h:bank}) + parts[f'growth_{h}']=Counter({1:2*N,h-2:2*N}) + rows=sum(parts.values(),Counter());assert sum(t*n for t,n in rows.items())==m*W-1846900 + lo,hi,grid=1,71700000000000,10**18 + while lo+11 + result.update(status='Verified finite conditional witness; inherited all-size transfer remains assumed', + source_manifest_sha256=hashlib.sha256((HERE/'SOURCE.json').read_bytes()).hexdigest(), + axes=axes,eventual_bounds=balanced.cutoffs(result['finite_bridge'],result['assembly']), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113',pr71_kappa=Q(previous['kappa']), + relative_gain_pr71=result['kappa']/Q(previous['kappa'])-1, + pr71_complete_profile_exclusion_lower=old_lower)) + result=arithmetic.js(result) + path=HERE/'certificate.json' + if record:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:assert result==json.loads(path.read_text()) + print('PASS exact moment, next-grid exclusions, 47 inequalities and seven margins',flush=True) + return result + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--record',action='store_true');args=parser.parse_args();generate(args.record) diff --git a/references/frame-compiler/pr74/research/balanced-split-frames/producer.py b/references/frame-compiler/pr74/research/balanced-split-frames/producer.py new file mode 100644 index 0000000000..8d68303a3b --- /dev/null +++ b/references/frame-compiler/pr74/research/balanced-split-frames/producer.py @@ -0,0 +1,132 @@ +#!/usr/bin/env python3 +"""Balanced coarse sums + anchored split/live frames + core ordering and coordinates. + +Composition for Thomas DiFiore with OpenAI Codex assistance. Apache-2.0. +PR69 coarse sums: eumemic. PR71 split/live composition: Chafik Boukhalfa. +Graph: Avi Eisenberg PR62; split operation: Rohan Garg PR59; reclamation: +Rohan Arun PR65/67, Dominik Scholz PR63/68, eumemic PR57. Original notices +and exact sources are retained under references/frame-compiler/pr69 and pr71. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +from hashlib import sha256 +import argparse,ast,gzip,importlib.util,json,types +from concurrent.futures import ProcessPoolExecutor +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +import split_pair_graph as provider +import split_pair_compiler as ancestor +from binary_frame_replay import replay + + +def check_sources(): + for folder in (DEP,ROOT/'references/frame-compiler/pr69'): + manifest=json.loads((folder/'SOURCE.json').read_text()) + for name,digest in manifest['files'].items(): + assert sha256((folder/name).read_bytes()).hexdigest()==digest,name + manifest=json.loads((HERE/'SOURCE.json').read_text()) + required={str((HERE/name).relative_to(ROOT)) for name in ('producer.py','check.py','graph_audit.py','independent_check.py','selection.json')} + assert required <= set(manifest['files']), 'Incomplete selected source closure' + for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + + +def reorder(c): + groups={} + for x in sorted(c.active): + if c.args[x]: groups.setdefault((c.core[x],c.union[x]),[]).append(x) + def key(item): + (core,cover),nodes=item + return cover.bit_count()-core.bit_count(),-core,cover,min(nodes) + ids=list(range(len(c.inputs)+1))+[x for _,nodes in sorted(groups.items(),key=key) for x in nodes] + mapping={x:i for i,x in enumerate(ids)} + args,core,cover,provenance=c.args,c.core,c.union,c.provenance + c.args=[tuple(mapping[y] for y in args[x]) if args[x] else None for x in ids] + c.core=[core[x] for x in ids];c.union=[cover[x] for x in ids] + c.provenance=[provenance[x] for x in ids] + c.active={mapping[x] for x in c.active};c.outputs={k:mapping[v] for k,v in c.outputs.items()} + c.support_in.cache_clear() + c.verify() + return c + + +def graph(h,ordered=True): + source=Path(provider._graph.__file__).read_text() + original=ROOT/'references/frame-compiler/pr69/scripts/experiments/balanced_coarse_compiler.py' + replacements={} + for node in ast.parse(original.read_text()).body: + if isinstance(node,ast.Assign): + for target in node.targets: + if isinstance(target,ast.Name) and target.id in ('BEFORE','AFTER'): + replacements[target.id]=ast.literal_eval(node.value) + assert source.count(replacements['BEFORE'])==1 + module=types.ModuleType('balanced_split_private_graph');module.__file__=provider._graph.__file__ + exec(compile(source.replace(replacements['BEFORE'],replacements['AFTER']),module.__file__+':balanced-coarse','exec'),module.__dict__) + previous=provider._graph + try: + provider._graph=module + c=provider.graph(h) + finally: + provider._graph=previous + return reorder(c) if ordered else c + + +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + +def compile_axis(h): + check_sources() + config=json.loads((HERE/'selection.json').read_text())['axes'][str(h)] + previous_graph,previous_order=provider.graph,provider.ordered_build + # graph() calls the original provider; keep that callable private while + # the inherited driver resolves the selected composed graph dynamically. + original_graph=previous_graph + def selected_graph(dimension): + provider.graph=original_graph + try:return graph(dimension) + finally:provider.graph=selected_graph + try: + provider.graph=selected_graph + provider.ordered_build=lambda original,dimension:original + compiled,word=ancestor.compile_axis(h) + finally: + provider.graph,provider.ordered_build=previous_graph,previous_order + compiled['graph_configuration']=config + word=relabel(word,config['coordinate_permutation']) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + path=HERE/f'word-{h}.json.gz' + with path.open('wb') as stream: + with gzip.GzipFile(filename='',fileobj=stream,mode='wb',mtime=0) as archive:archive.write(raw) + receipt=replay(path) + assert sha256(raw).hexdigest()==config['expected_word_sha256'] + axis=dict(configuration=config,compiled=compiled,replay=receipt, + word_sha256=sha256(raw).hexdigest(),gzip_sha256=sha256(path.read_bytes()).hexdigest()) + (HERE/f'axis-{h}.json').write_text(json.dumps(axis,indent=2)+'\n') + print(f'PASS fresh balanced/split/core word h={h}, roles={receipt["roles"]}',flush=True) + + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--h',type=int,choices=(23,25));args=parser.parse_args() + if args.h:compile_axis(args.h) + else: + with ProcessPoolExecutor(max_workers=2) as pool:list(pool.map(compile_axis,(23,25))) diff --git a/references/frame-compiler/pr74/research/balanced-split-frames/profile-23.json b/references/frame-compiler/pr74/research/balanced-split-frames/profile-23.json new file mode 100644 index 0000000000..013f4e59c7 --- /dev/null +++ b/references/frame-compiler/pr74/research/balanced-split-frames/profile-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27136,"loss":506,"rank_sum":624634,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38292,"crt_matrices":5488,"crt_disagreements":0,"blocks":[0,355721,21666,6948,6524,3093,4314,2400,3266,1501,2094,1008,1374,586,732,353,307,139,62,16,0,23,0,0]} diff --git a/references/frame-compiler/pr74/research/balanced-split-frames/profile-25.json b/references/frame-compiler/pr74/research/balanced-split-frames/profile-25.json new file mode 100644 index 0000000000..1e3b6b89aa --- /dev/null +++ b/references/frame-compiler/pr74/research/balanced-split-frames/profile-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35744,"loss":600,"rank_sum":894200,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52202,"crt_matrices":7623,"crt_disagreements":0,"blocks":[0,490052,26188,13531,7191,4637,5355,4229,3705,2610,2620,2080,1814,1357,1070,868,612,463,233,56,141,0,71,25,0,0]} diff --git a/references/frame-compiler/pr74/research/balanced-split-frames/selection.json b/references/frame-compiler/pr74/research/balanced-split-frames/selection.json new file mode 100644 index 0000000000..57cf3b6b65 --- /dev/null +++ b/references/frame-compiler/pr74/research/balanced-split-frames/selection.json @@ -0,0 +1,86 @@ +{ + "source_pr71": "1bef94fd40a746452548c84a4a8f8834670a3113", + "source_pr69": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "axes": { + "23": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 22, + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 20, + 19, + 21 + ], + "expected_word_sha256": "8dc6696a274e70ca0af3fc49c4bdede362adaedc8dc322f335e3dab499f1ed48" + }, + "25": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 2, + 1, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "expected_word_sha256": "2c923afe366219ee3fffc9db063c91e44cdf7cbbdb62246b8e6a297dc440b577" + } + } +} diff --git a/references/frame-compiler/pr78/FETCH.json b/references/frame-compiler/pr78/FETCH.json new file mode 100644 index 0000000000..4db82db4a1 --- /dev/null +++ b/references/frame-compiler/pr78/FETCH.json @@ -0,0 +1,48 @@ +{ + "pr": 78, + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf", + "files": [ + { + "path": "research/coordinate-flags/verify.py", + "blob_sha": "216ccd3d58c1331fffdb008df7547982cb43d2ae", + "sha256": "b59a5345c8684bb67a5ea666d5de11422c45cdf19f2c13de1520623a71bae7e1", + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf" + }, + { + "path": "research/coordinate-flags/order-23.json", + "blob_sha": "035f01df59be3312e30ec692754d3a331a766799", + "sha256": "def92cd69f3fba2986c7a230ece45f9eb63fd38fef512d055bf0adffe9edfa82", + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf" + }, + { + "path": "research/coordinate-flags/order-25.json", + "blob_sha": "7c06a68e6e4a4ff0ad8a43cd240ec7a51892f328", + "sha256": "209dee5fac04fa91a5bf63ed0307a56e849cc6800fa543254590045e0c95d6a5", + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf" + }, + { + "path": "research/coordinate-flags/README.md", + "blob_sha": "950f4eaa2d83c75ec5b9fa4046dd5e663c804d79", + "sha256": "cbc4f20613e1dfafcce7c5f82c274fdd48898cc968d14fbea7bf9b1a47607e85", + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf" + }, + 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Coordinate-flag relabeling and finite verification: Rohan Arun with OpenAI Codex assistance. Based on Chafik Boukhalfa PR71 and the inherited contributions credited in research/coordinate-flags/README.md. Existing contributor originals are preserved. diff --git a/references/frame-compiler/pr78/SOURCE.json b/references/frame-compiler/pr78/SOURCE.json new file mode 100644 index 0000000000..15f08e2813 --- /dev/null +++ b/references/frame-compiler/pr78/SOURCE.json @@ -0,0 +1,15 @@ +{ + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf", + "files": { + "FETCH.json": "79d6b40af23f03d6737be9a072ebca4f96aa6a663895cffdee4052432b5d13b8", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "0a0e0314b9d1e23a193e92aa633fc50c432b6e3ea326f40d5cbb1ea538823149", + "research/coordinate-flags/README.md": "cbc4f20613e1dfafcce7c5f82c274fdd48898cc968d14fbea7bf9b1a47607e85", + "research/coordinate-flags/SOURCE.json": "c0ec88783c06431d95e1e8efabbb2928857f1d4ca8d0ada10206e99322ae78e2", + "research/coordinate-flags/order-23.json": "def92cd69f3fba2986c7a230ece45f9eb63fd38fef512d055bf0adffe9edfa82", + "research/coordinate-flags/order-25.json": "209dee5fac04fa91a5bf63ed0307a56e849cc6800fa543254590045e0c95d6a5", + "research/coordinate-flags/verify.py": "b59a5345c8684bb67a5ea666d5de11422c45cdf19f2c13de1520623a71bae7e1" + }, + "pr": 78, + "scope": "Exact attributed contributor inputs and reported comparison certificate, not a new audit of the entire foreign claim." +} diff --git a/references/frame-compiler/pr78/research/coordinate-flags/README.md b/references/frame-compiler/pr78/research/coordinate-flags/README.md new file mode 100644 index 0000000000..950f4eaa2d --- /dev/null +++ b/references/frame-compiler/pr78/research/coordinate-flags/README.md @@ -0,0 +1,68 @@ +# Coordinate flags for the split-pair witness + +This finite conditional witness gives kappa = 12857195906507 / 250000000000000000 += 5.1428783626028e-5, about 0.02750% above PR71's 5.1414646104039e-5. +The bit saving is 25715714341 / 500000000000000. Roles, physical width, +recursive rank mass, scalar operations, paid clearing and copied endpoints +remain those of PR71. The changed object is the coordinate flag used to +decompose internal frame transitions into consecutive pivot blocks. + +## General relabeling argument + +Let P be a permutation matrix on the h coordinates. It commutes with J, +so P commutes with the fixed basis L = I+J and preserves the form I-J/9. +For a core/cover frame F(C,U), the relabeled projector is +P F(C,U) P^-1 = F(P C,P U). Consequently, every frame inclusion, rank, +nondegeneracy condition, projector denominator bound and elementary role +operation is preserved. The existing exact CRT bounds apply unchanged. + +Relabel each input triple T to P T, each output (c,T) to (P c,P T), +each frame mask by P, and each scatter row by the induced triple permutation. +The role slots and literal XOR operations do not change. This conjugates +the complete linear word by the input/output permutation and therefore +preserves its identity on every ordinary input and arbitrary dirty role. +The verifier independently replays that identity in both orientations. + +The data component sums over every pair of source triples. Independent +coordinate permutations on the two axes induce a bijection on that complete +Cartesian product. Hence its existing complete histogram, copied-center +costs and endpoint corrections are unchanged. This argument uses the full +case set; it would not justify retaining a selected subset's histogram. + +North-east corner rank profiles depend on the fixed coordinate order. +Conjugating by P can change which adjacent pivots form a recursive block, +even though total rank is unchanged. We regenerate these profiles from the +actual relabeled words rather than assuming their costs are invariant. +Both dimensions use the selected orders in order-23.json and order-25.json. + +## Verification and scope + +Run `make coordinate-flags-verify`. It checks source closure, regenerates +both words byte for byte, replays every ordinary and dirty basis vector in +both orientations, reconstructs physical transitions, and recomputes all +fixed-I+J profiles with the inherited exact CRT bounds. Six negative controls +reject inconsistent coordinates, missing source/output relabeling, missing +operations and aliased terminal roles. + +The complete paid child list is rebuilt independently. Directed rational +moment bounds, an independent logarithm/exponential computation, 47 strict +constraints, seven margins, both next-grid rejections and exclusion of +PR71's complete profile at the new saving are checked. + +The search used structured coordinate orders and bounded adjacent swaps. +No global optimum or practical speedup is claimed. This remains conditional +on the inherited all-size residual compiler, routing, recovery, prime +selection, fixed finite-alphabet multitape simulation and analytic transfer. +The full expanded repository rerun is pending; this package is a draft. + +## Credit + +Chafik Boukhalfa's PR71 supplies the split-pair graph and next-use scoring. +Rohan Garg introduced the split operation (PR59); Avi Eisenberg supplied +interval/pair assembly (PR62); Dominik Scholz supplied ranked frames and +pending controls (PR63/68); Rohan Arun supplied schedule and profile-cost +search (PR65/67); eumemic supplied the reversible compiler and physical +checkers (PR57). Credit also icekylinx, James Chang, Zhihao Chen, Aurel +Prosz/Paureel, Swapnil Jain, Alejandro Zarzuelo Urdiales, RaD/hipotures, +Douglas Colkitt, OpenAI and all inherited contributors. Existing sources, +licenses and notices are retained. 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"58f13f82ce1bb7f2b5549e17628bc6034e5e05cb24db2acb9a91c24820872f70", + "scripts/experiments/split_pair_graph.py": "9d4ee7179f880f9576e81c7ad3a5290fe61380a7531d559ef3cf0939bb30089c", + "scripts/experiments/verify_split_pair.py": "5cc7031569b17b560f68d4238191a32e5d7f66e7fdcbaabd0ca87020c89f89c8", + "tests/test_split_pair.py": "07c8c24306a6ca8ffe55934cbeb40069cbc198b01921232aff66cc50fd50aee5", + "tests/test_split_pair_pending.py": "b111a8d09e978944b3468a96f7fd486c7a1283d133a7a6ffe625c6d5cad550a1" + }, + "scope": "Selected word, source, proof and complete paid arithmetic closure; baseline root provenance refreshed only for integration documents." +} diff --git a/references/frame-compiler/pr78/research/coordinate-flags/order-23.json b/references/frame-compiler/pr78/research/coordinate-flags/order-23.json new file mode 100644 index 0000000000..035f01df59 --- /dev/null +++ b/references/frame-compiler/pr78/research/coordinate-flags/order-23.json @@ -0,0 +1,53 @@ +{ + "h": 23, + "order": [ + 1, + 3, + 2, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 21, + 20, + 22, + 0 + ], + "mapping": { + "1": 0, + "3": 1, + "2": 2, + "4": 3, + "5": 4, + "6": 5, + "7": 6, + "8": 7, + "9": 8, + "10": 9, + "11": 10, + "12": 11, + "13": 12, + "14": 13, + "15": 14, + "16": 15, + "17": 16, + "18": 17, + "19": 18, + "21": 19, + "20": 20, + "22": 21, + "0": 22 + } +} diff --git a/references/frame-compiler/pr78/research/coordinate-flags/order-25.json b/references/frame-compiler/pr78/research/coordinate-flags/order-25.json new file mode 100644 index 0000000000..7c06a68e6e --- /dev/null +++ b/references/frame-compiler/pr78/research/coordinate-flags/order-25.json @@ -0,0 +1,57 @@ +{ + "h": 25, + "order": [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 23, + 22, + 24, + 0 + ], + "mapping": { + "1": 0, + "2": 1, + "3": 2, + "4": 3, + "5": 4, + "6": 5, + "7": 6, + "8": 7, + "9": 8, + "10": 9, + "11": 10, + "12": 11, + "13": 12, + "14": 13, + "15": 14, + "16": 15, + "17": 16, + "18": 17, + "19": 18, + "20": 19, + "21": 20, + "23": 21, + "22": 22, + "24": 23, + "0": 24 + } +} diff --git a/references/frame-compiler/pr78/research/coordinate-flags/verify.py b/references/frame-compiler/pr78/research/coordinate-flags/verify.py new file mode 100644 index 0000000000..216ccd3d58 --- /dev/null +++ b/references/frame-compiler/pr78/research/coordinate-flags/verify.py @@ -0,0 +1,89 @@ +"""Rebuild the coordinate-permuted PR71 words and their exact paid bound.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2];HERE=Path(__file__).resolve().parent +sys.path.insert(0,str(ROOT/'scripts/experiments')) +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +from split_pair_arithmetic import refine,audit +import binary_frame_math as arithmetic +from pin_split_pair_sources import required_paths +from fractions import Fraction as Q +from collections import Counter +from itertools import combinations +from math import comb +from hashlib import sha256 +import gzip,json,subprocess,tempfile + +def required(): + names=required_paths()|{'research/split-pair/SOURCE.json','certificates/split-pair-kappa.json', + '.github/workflows/verify.yml'} + names.update(str(p.relative_to(ROOT)) for p in HERE.iterdir() if p.is_file() and p.name not in ('SOURCE.json','validation.json')) + return names + +def sources(): + manifest=json.loads((HERE/'SOURCE.json').read_text()) + assert required()<=set(manifest['files']),'Source closure incomplete' + for name,digest in manifest['files'].items():assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + +def relabel(word,config): + h=word['h'];order=config['order'];assert sorted(order)==list(range(h)) + perm={old:new for new,old in enumerate(order)} + assert perm=={int(k):v for k,v in config['mapping'].items()} + triples=list(combinations(range(h),3));lookup={t:i for i,t in enumerate(triples)} + index={i:lookup[tuple(sorted(perm[x] for x in triple))] for i,triple in enumerate(triples)} + def mask(m):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(index[int(i)]):s for i,s in word['sources'].items()} + v=word['v'];word['scatter']=[[v+index[a-v],b] for a,b in word['scatter']] + word['outputs']=[[s,g,perm[c],sorted(perm[x] for x in triple)] for s,g,c,triple in word['outputs']] + return word + +def exact(profiles): + cert=json.loads((HERE/'certificate.json').read_text());baseline=json.loads((HERE/'baseline-pr71.json').read_text()) + N=comb(23,3)*comb(25,3);m=575;W=2*N+sum(N//p['v']*p['R'] for p in profiles) + L=sum(N//p['v']*p['loss'] for p in profiles) + rows=Counter({1:19*N,21:2*N,17:2*N,481:2*N}) + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 and p['v']==comb(h,3) + assert sum(t*n for t,n in enumerate(p['blocks']))==h*p['R']+h*(h-1)==p['rank_sum'] + rows.update({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + rows[h]+=bank;rows[m-2*h]+=bank;rows[1]+=2*N;rows[h-2]+=2*N + bit=dict(m=m,N=N,W=W,L=L,total_rank=sum(t*n for t,n in rows.items()),child_multiplicities=dict(sorted(rows.items()))) + assert bit['total_rank']==m*W-N+L + assert arithmetic.js(bit)==cert['bit'] + saving=Q(cert['bit_saving']);moment=refine.exact_moment(m,W,rows,saving) + rejected=refine.exact_moment(m,W,rows,saving+Q(1,10**18)) + assert moment['upper']<11 + print('PASS exact conditional kappa',result['kappa'],'47 constraints, seven margins, independent bounds and next-grid controls') + +def verify(): + sources();profiles=[] + with tempfile.TemporaryDirectory(prefix='coordinate-flags-') as directory: + work=Path(directory);exe=work/'profiles' + subprocess.run(['c++','-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'scripts/experiments/binary_frame_profiles.cpp'),'-o',str(exe)],check=True) + for h in (23,25): + original=json.loads(gzip.decompress((ROOT/f'certificates/split-pair-word-{h}.json.gz').read_bytes())) + config=json.loads((HERE/f'order-{h}.json').read_text());word=relabel(original,config) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + assert raw==gzip.decompress((HERE/f'word-{h}.json.gz').read_bytes()) + path=work/f'word-{h}.json';path.write_bytes(raw);checked=replay(path) + stored=json.loads((HERE/f'replay-{h}.json').read_text());assert arithmetic.js(checked)==stored['replay'] + trans=work/f'transitions-{h}.bin';receipt=prepare(path,trans);assert arithmetic.js(receipt)==stored['transitions'] + subprocess.run([str(exe),str(trans)],check=True) + profile=json.loads(Path(str(trans)+'.profiles.json').read_text());assert profile==json.loads((HERE/f'profiles-{h}.json').read_text()) + profiles.append(profile);print('PASS complete relabelled physical word and profile',h,flush=True) + exact(profiles) +if __name__=='__main__':verify() diff --git a/references/frame-compiler/pr79/.gitattributes b/references/frame-compiler/pr79/.gitattributes new file mode 100644 index 0000000000..48ba61f217 --- /dev/null +++ b/references/frame-compiler/pr79/.gitattributes @@ -0,0 +1,15 @@ +* text=auto eol=lf +*.pdf binary +# Unified diffs require a leading space on blank context lines. +*.patch -whitespace +# Preserve the exact upstream bytes, including original whitespace. +upstream/** -whitespace +# Preserve the exact pinned third-party proof snapshots and notices. +references/copied-centers/pr29/** -whitespace +references/copied-centers/pr33/** -whitespace +references/semantic-bulk/** -whitespace + +# Immutable contributor archives retain original CRLF and whitespace bytes. +references/frame-compiler/pr69/** -text -whitespace +references/frame-compiler/pr70/** -text -whitespace +references/frame-compiler/pr71/** -text -whitespace diff --git a/references/frame-compiler/pr79/.github/workflows/verify.yml b/references/frame-compiler/pr79/.github/workflows/verify.yml new file mode 100644 index 0000000000..33886a2cdf --- /dev/null +++ b/references/frame-compiler/pr79/.github/workflows/verify.yml @@ -0,0 +1,63 @@ +name: Verify research artifacts + +on: + push: + pull_request: + workflow_dispatch: + +permissions: + contents: read + +jobs: + verify: + runs-on: ubuntu-24.04 + timeout-minutes: 20 + strategy: + fail-fast: false + matrix: + python-version: ['3.11', '3.13', '3.14'] + group: [community, producers, certificates, ternary, research, tests, strips, clones, positive, joint, pair, balanced] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: ${{ matrix.python-version }} + - name: Install headers for the exact enlarged-frame profiler + if: matrix.group == 'positive' + run: | + if ! test -f /usr/include/boost/multiprecision/cpp_int.hpp; then + sudo apt-get update + sudo apt-get install -y libboost-dev + fi + - name: Check arithmetic, source hashes, finite identities, and patches + run: make verify-${{ matrix.group }} + - name: Require reproducible certificates and patches + run: git diff --exit-code + + formal: + runs-on: ubuntu-24.04 + timeout-minutes: 30 + strategy: + fail-fast: false + matrix: + package: [historical, gaussian, matrix] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: '3.13' + - name: Install elan; each project pins its Lean toolchain + run: | + curl --proto '=https' --tlsv1.2 -sSf https://raw.githubusercontent.com/leanprover/elan/0e36a07b9bbcc5381fa6250df109f9a4f94d7bac/elan-init.sh -o /tmp/elan-init.sh + sh /tmp/elan-init.sh -y --default-toolchain none + echo "$HOME/.elan/bin" >> "$GITHUB_PATH" + - name: Fetch pinned Mathlib build cache + if: matrix.package == 'historical' + working-directory: formal/lean + run: lake exe cache get + - name: Check formal package and theorem axiom dependencies + run: make formal-${{ matrix.package }}-verify diff --git a/references/frame-compiler/pr79/LICENSE b/references/frame-compiler/pr79/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/pr79/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Keep local verification sequential: +# different groups regenerate certificates that another group may read. +verify: + $(MAKE) verify-community + $(MAKE) verify-producers + $(MAKE) verify-certificates + $(MAKE) verify-ternary + $(MAKE) verify-research + $(MAKE) verify-strips + $(MAKE) verify-clones + $(MAKE) verify-positive + $(MAKE) verify-joint + $(MAKE) verify-pair + $(MAKE) verify-balanced + $(MAKE) verify-tests + +verify-community: community-audit-check community-followup-check copied-reversed-producer copied-reversed-check copied-fixed-reversed-producer copied-fixed-reversed-check + $(MAKE) copied-fixed-verify + $(MAKE) climbed-48-verify + +verify-producers: + $(MAKE) copied-centers-verify + $(MAKE) structured-bulk-verify + $(MAKE) endpoint-gauge-producer endpoint-gauge-certificate + $(MAKE) partial-swap-producer partial-swap-certificate + +verify-certificates: + python3 scripts/prime_field_network.py + python3 scripts/complex_network.py + python3 scripts/fast_gaussian.py + $(MAKE) batched-certificate batched-patch + python3 scripts/certify.py + python3 scripts/search_network.py + python3 scripts/make_patch.py + python3 scripts/nonadjacent.py + python3 scripts/make_nonadjacent_patch.py + python3 scripts/tune_routing.py + python3 scripts/research_networks.py + python3 scripts/search_network_variants.py + python3 scripts/block_label_targets.py + python3 scripts/audit_block_labels.py + python3 scripts/audit_additive_labels.py + python3 scripts/small_block_witness.py + python3 scripts/incidence_network.py + python3 scripts/make_incidence_patch.py + python3 scripts/search_incidence_partitions.py + python3 scripts/dag_network.py + python3 scripts/make_dag_patch.py + python3 scripts/shared_point_network.py + python3 scripts/make_shared_point_patch.py + python3 scripts/paired_network.py + python3 scripts/make_paired_patch.py + python3 scripts/prepare_layers.py + python3 scripts/audit_sparse_fusion.py + python3 scripts/audit_fused_block.py + python3 scripts/audit_short_guards.py + python3 scripts/audit_gather_schedules.py + python3 scripts/audit_coded_carries.py + python3 scripts/audit_cancellation.py + python3 scripts/audit_joint_frames.py + python3 scripts/audit_compact_controls.py + python3 scripts/compact_control_layer.py + python3 scripts/make_compact_control_patch.py + python3 scripts/audit_scratch_pooling.py + python3 scripts/reuse_network.py + python3 scripts/make_reuse_patch.py + +verify-ternary: + python3 scripts/complex_compression.py + python3 scripts/make_complex_compression_patch.py + python3 scripts/audit_ternary_side.py + python3 scripts/make_ternary_patch.py + +verify-tests: + python3 scripts/run_isolated_tests.py + git apply --check --directory=upstream patches/frozen-154.patch + git apply --check --directory=upstream patches/balanced-153.patch + git apply --check --directory=upstream patches/same-network-129.patch + git apply --check --directory=upstream patches/h46-111.patch + git apply --check --directory=upstream patches/h46-109.patch + git apply --check --directory=upstream patches/h46-108.patch + git apply --check --directory=upstream patches/h46-rational.patch + git apply --check --directory=upstream patches/nonadjacent-layout.patch + git apply --check --directory=upstream patches/frozen-nonadjacent-107.patch + git apply --check --directory=upstream patches/h46-nonadjacent-78.patch + git apply --check --directory=upstream patches/h46-nonadjacent-76.patch + git apply --check --directory=upstream patches/h46-shared-side-75.patch + git apply --check --directory=upstream patches/h46-incidence-67.patch + git apply --check --directory=upstream patches/h46-dag-63.patch + git apply --check --directory=upstream patches/h46-shared-point.patch + git apply --check --directory=upstream patches/h50-paired-59.patch + git apply --check --directory=upstream patches/compact-control-34.patch + git apply --check --directory=upstream patches/complex-compression-31.patch + git apply --check --directory=upstream patches/ternary-30.patch + git apply --check --directory=upstream patches/batched-23.patch + +note: + mkdir -p artifacts + tectonic --outdir artifacts notes/parameter-note.tex + +audit-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/nonadjacent-axis-note.tex + +tuned-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/routing-tuned-note.tex + +reuse-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/stage-reuse-note.tex + +incidence-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/incidence-note.tex + +dag-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/dag-note.tex + +shared-point-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/shared-point-note.tex + +paired-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/paired-note.tex + +compact-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/compact-control-note.tex + +complex-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/complex-compression-note.tex + +ternary-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/ternary-note.tex + +fetch: + python3 scripts/fetch_upstream.py + +.PHONY: batched-certificate batched-patch batched-note +PDFLATEX ?= pdflatex +TEX_ENGINE ?= pdflatex +TECTONIC ?= tectonic + +batched-certificate: + python3 scripts/controlled_bit_rank_moment.py --output certificates/controlled-bit-rank-moment.json > /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify + +.PHONY: balanced-split-verify verify-balanced +balanced-split-verify: + python3 scripts/experiments/verify_balanced_split.py + python3 scripts/experiments/audit_balanced_split_completion.py + python3 scripts/experiments/audit_balanced_split_exchange.py + python3 -m unittest discover -s tests -p 'test_balanced_split*.py' -v + +verify-balanced: balanced-split-verify diff --git a/references/frame-compiler/pr79/NOTICE b/references/frame-compiler/pr79/NOTICE new file mode 100644 index 0000000000..8a6bef1613 --- /dev/null +++ b/references/frame-compiler/pr79/NOTICE @@ -0,0 +1,337 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Balanced coarse split composition (2026-10-08) +--------------------------------------------- +Eumemic / @eumemic supplied PR69's balanced coarse sums, with OpenAI Codex +assistance. Alejandro Zarzuelo Urdiales / @alejandrozu supplied PR70's bounded +carry-exchange strategy with the AI disclosures retained in the source archive. +Chafik Boukhalfa / @chafreaky, with OpenAI Codex assistance, selected the row/ +half-plane coarse rules, future-compatible unit completion, exact integer-price +carry adaptation, composition and this certificate package. The PR71 anchored +split vector, schedules, arithmetic, pending controls and their contributor +chain are retained as credited above. Original PR69/70 sources, licenses and +notices and the complete published PR71 baseline are preserved under +references/frame-compiler. All earlier notices remain applicable. diff --git a/references/frame-compiler/pr79/README.md b/references/frame-compiler/pr79/README.md new file mode 100644 index 0000000000..1bd7139657 --- /dev/null +++ b/references/frame-compiler/pr79/README.md @@ -0,0 +1,184 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: balanced coarse split frames + +The [balanced-split proof and reproduction guide](research/balanced-split/README.md) +gives **κ=25872812736433/500000000000000000=5.1745625472866e-5**, approximately +**0.6437453019850683%** above the complete published PR71 witness. It composes +PR69 balanced coarse sums and a bounded PR70 carry exchange with PR71's +anchored split graph, future unit completion and profile-cost pending controls. +All actual words, dirty inputs, paid profiles and 47 strict assembly constraints +are checked by `make balanced-split-verify`. This finite conditional construction +retains the inherited all-size hypotheses and contributor notices. Chafik +Boukhalfa prepared the selected composition with OpenAI Codex assistance. + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. diff --git a/references/frame-compiler/pr79/SOURCE.json b/references/frame-compiler/pr79/SOURCE.json new file mode 100644 index 0000000000..6ba76e935b --- /dev/null +++ b/references/frame-compiler/pr79/SOURCE.json @@ -0,0 +1,257 @@ +{ + "commit": "9a58e62cf9e8954a4dde3c9b1372d733c276a6d1", + "files": { + ".gitattributes": "5f257f4e9e574ad5767f902242f519dad19cc455d6858f49234d0ccc345cabf1", + ".github/workflows/verify.yml": "1a9cccd742ba2a5aa5a5ac38c1b7559bc0dec46b23d3ce3ff3e26c3137e6c3a2", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "Makefile": "1bf5b63d413280a68fc2b91a7e83a6172632e50c8177ca097d9622af669ee8d6", + "NOTICE": "ef6c74f5103d624f1a9910668d4124b213775e9b7e24edde089d9f4d1377abbb", + "README.md": 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"b7194b8586844956904b33e9fe18f0c75606c11b", + "scope": "Unmodified producer inputs for experimental frame compiler; attribution retained in each file", + "source_pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/48" +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py b/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py new file mode 100644 index 0000000000..c7fd42867d --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py @@ -0,0 +1,196 @@ +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit', 'complex'): + data = finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": "41187950749917624099/1000000000000000000000000", + "cell_above_band": "666666666665666652937349833360791967/1333388250600666556832132000000000000", + "compact_leaf": "26927049500082375901/1000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "13729317166639208033/333347062650166639208033", + "epsilon_positive": "333333333333000000000000/333347062650166639208033", + "g1_above_kappa": "3408408254232349301008147/3333470626501666392080330000000000000", + "g2_above_kappa": "4241/2500000000000", + "g3_above_kappa": "74937627730682908927817/3333470626501666392080330000000000000", + "g4_above_kappa": "4241/2500000000000", + "g5_above_kappa": "5299956450675231223831763/13333882506006665568321320000000000000", + "g6_above_kappa": "11966897703678564007992423/13333882506006665568321320000000000000", + "g7_above_kappa": "3333196040161742016173902349301008147/3333470626501666392080330000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "13729317166639208033/333347062650166639208033", + "lambda_above_internal": "82375901/2000000000000000000000000", + "lambda_above_sigma": "61024099000082375901/2000000000000000000000000", + "lambda_above_tau": "82375901/2000000000000000000000000", + "lambda_prime_above_lambda": "82375901/2000000000000000000000000", + "lambda_prime_below_one": "41187950499917624099/1000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "21966907133275670202633360791967/533355300240266622732852800000000000", + "phase_leaf_above_bit": "53854099/2000000000000", + "phase_local": "109834536999766601613833360791967/2666776501201333113664264000000000000", + "prime_interval_packing": "13729317166639208033/333347062650166639208033", + "q_below_internal": "82375901/1000000000000000000000000", + "q_below_leaf": "26927049500082375901/1000000000000000000000000", + "q_below_reservations": "1/4000000000000", + "q_positive": "41187950499917624099/1000000000000000000000000", + "record_suffix": 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": "41187950749917624099/1000000000000000000000000", + "cell_above_band": "666666666665666652937349833360791967/1333388250600666556832132000000000000", + "compact_leaf": "26927049500082375901/1000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "13729317166639208033/333347062650166639208033", + "epsilon_positive": "333333333333000000000000/333347062650166639208033", + "g1_above_kappa": "3408408254232349301008147/3333470626501666392080330000000000000", + "g2_above_kappa": "4241/2500000000000", + "g3_above_kappa": "74937627730682908927817/3333470626501666392080330000000000000", + "g4_above_kappa": "4241/2500000000000", + "g5_above_kappa": "5299956450675231223831763/13333882506006665568321320000000000000", + "g6_above_kappa": "11966897703678564007992423/13333882506006665568321320000000000000", + "g7_above_kappa": "3333196040161742016173902349301008147/3333470626501666392080330000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "13729317166639208033/333347062650166639208033", + "lambda_above_internal": "82375901/2000000000000000000000000", + "lambda_above_sigma": "61024099000082375901/2000000000000000000000000", + "lambda_above_tau": "82375901/2000000000000000000000000", + "lambda_prime_above_lambda": "82375901/2000000000000000000000000", + "lambda_prime_below_one": "41187950499917624099/1000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "21966907133275670202633360791967/533355300240266622732852800000000000", + "phase_leaf_above_bit": "53854099/2000000000000", + "phase_local": "109834536999766601613833360791967/2666776501201333113664264000000000000", + "prime_interval_packing": "13729317166639208033/333347062650166639208033", + "q_below_internal": "82375901/1000000000000000000000000", + "q_below_leaf": "26927049500082375901/1000000000000000000000000", + "q_below_reservations": "1/4000000000000", + "q_positive": "41187950499917624099/1000000000000000000000000", + "record_suffix": "13729317166639208033/333347062650166639208033", + "row_product_gap": "6548/25", + "short_record_fallback": "666639206901368489075295096355187267/666694125300333278416066000000000000", + "small_field_exposure": "1/1000000000000" + }, + "finite_bridge": { + "bit": { + "W": 177530859, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "margins": { + "g1": "13729317166639208033/333347062650166639208033", + "g2": "82375901/2000000000000", + "g3": "13729316833292145382833360791967/333347062650166639208033000000000000", + "g4": "82375901/2000000000000", + "g5": "21966907133275670202633360791967/533355300240266622732852800000000000", + "g6": "109834536999766601613833360791967/2666776501201333113664264000000000000", + "g7": "333333333333000000000000/333347062650166639208033" + }, + "minimum_margin": "13729316833292145382833360791967/333347062650166639208033000000000000", + "parameters": { + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": "1", + "a_bit": "82375901/2000000000000", + "a_complex": "717/10000000", + "alpha_squared_power": "27458633999931353415833360791967/666694125300333278416066000000000000", + "beta": "1/20", + "c": "41187950749917624099/1000000000000000000000000", + "delta": "1/8000000000000", + "epsilon": 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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"scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1", + "scripts/partial_swap/graph.py": "fd8c567759e26a10d2bad05508fd0355eb70fb116664d4e06e1858d0d8cb2ef9", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + } + }, + "status": "Conditional exact arithmetic witness; general transfer proofs are dependencies" +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py b/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis 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Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + } + }, + "gzip_sha256": "4629d45d5074f87706db46be3aa3cd369071cd215bc6560d641115aadcce54a0", + "word_sha256": "bd0cbf73756f2e4f8d3879ec6c7a194990eb9ec40aaf3580bdded6994798d920" + }, + "25": { + "compiled": { + "h": 25, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 36586, + "baseline_pr48_roles": 48329, + "histogram": { + "1": 55478, + "0": 416276, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + }, + "rank_mass": 915250, + "elementary_xors": 205650, + "stats": { + "augmentations": 286, + "regions": 73695, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json new file mode 100644 index 0000000000..346cf87ea3 --- /dev/null +++ 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mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json new file mode 100644 index 0000000000..42958fc74b --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json @@ -0,0 +1,195 @@ +{ + "artifact_sha256": { + "frame-profiles-23.json": "fec377bcf1512a427674983256b900229d4133026445b6e680c6e1e6dde5af7d", + "frame-profiles-25.json": "28b4b911e26fbc02dde0d2e1458ed16227f756126ab8144d6d45e164d1165262", + "frame-transitions-23.json": "86646f1110595294cccc15603c552f0a153574a690b69c3b144d84a449891103", + "frame-transitions-25.json": "c333c348665d12b95e168ca4fac48bfdca335104edd0f29c81fe94bec292e774", + "frame-word-23.json.gz": "a44e038e1c548ea8ac31dd04acc2bba7951b22e17df7b7ad3464ea2b504a8da4", + "frame-word-25.json.gz": "ad8b299697f90b185b6b791313b505586be97965519052100d097df6199e00c5", + "paired-candidate.json": "34a500d739537235dfc5d24325c22856ca4567b9eac998a3bce9b13db5501940" + }, + "axes": { + "23": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 36432, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 31460, + "elementary_xors": 149137, + "h": 23, + "histogram": { + "0": 302057, + "1": 42694, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "2": 82722, + "21": 165, + "22": 23, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 642620, + "roles": 27918, + "stats": { + "augmentations": 220, + "clearing_xors": 1577, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "regions": 52473 + } + }, + "gzip_sha256": "a44e038e1c548ea8ac31dd04acc2bba7951b22e17df7b7ad3464ea2b504a8da4", + "replay": { + "elementary_xors": 149137, + "full_basis_vectors": 31460, + "h": 23, + "histogram": { + "0": 162914, + "1": 42694, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "2": 82722, + "21": 165, + "22": 23, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525 + }, + "output_roles": 5336, + "rank_mass": 642620, + "roles": 27918, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 621342 + }, + "schedule": "cover-core", + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4" + }, + "25": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 48329, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 41186, + "elementary_xors": 205977, + "h": 25, + "histogram": { + "0": 416741, + "1": 55478, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "2": 115781, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 915250, + "roles": 36586, + "stats": { + "augmentations": 286, + "clearing_xors": 2154, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "regions": 73695 + } + }, + "gzip_sha256": "ad8b299697f90b185b6b791313b505586be97965519052100d097df6199e00c5", + "replay": { + "elementary_xors": 205977, + "full_basis_vectors": 41186, + "h": 25, + "histogram": { + "0": 224465, + "1": 55478, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "2": 115781, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569 + }, + "output_roles": 6925, + "rank_mass": 915250, + "roles": 36586, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 856108 + }, + "schedule": "reverse-node", + "word_sha256": "a54443429f47c486016771ce0436effda098e142afc52861c20957e9ff8e086b" + } + }, + "source_sha256": { + "research/pair-assembly/frame/frame_verify.py": "fafe25d57166a747eeb847444a2e02dd7eed19038b93a2c495014d147d04a8fb", + "research/pair-assembly/pair_graph.py": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "research/reordered-rank-pair/test_negative.py": "88832242e6f74e3fe08d109d4f21ff188a9ca0ae50c3e8f31da0243fe9501510", + "research/reordered-rank-pair/verify.py": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352", + "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3", + "scripts/experiments/binary_frame_profiles.cpp": "8e2e391d3ee57cbb1372c68e4aa031e1b861321536eabd642ada54e12e678669", + "scripts/experiments/binary_frame_replay.py": "392e78e62d7685c99a5888a7da743ea6c3dcad631af4a743c91e0c09348442bc", + "scripts/experiments/rank_pair_compiler.py": "9984aaccf880e4840402322d76678bfddb33ce7e494af78430a43429f51b85fd" + }, + "status": "Exact topological scheduling of unchanged PR63 graph/compiler; both physical orientations and fixed profiles checked" +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json new file mode 100644 index 0000000000..3b648dbe21 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "loss": 506, + "rank_sum": 642620, + "field_prime": 2305843009213693951, + "frames": 52475, + "distinct_matrices": 36399, + "crt_matrices": 6049, + "crt_disagreements": 0, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json new file mode 100644 index 0000000000..19cc34b4ca --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json @@ -0,0 +1,40 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "loss": 600, + "rank_sum": 915250, + "field_prime": 2305843009213693951, + "frames": 73697, + "distinct_matrices": 50394, + "crt_matrices": 8127, + "crt_disagreements": 0, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json new file mode 100644 index 0000000000..2883a5f7c9 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "frames": 52475, + "distinct_transitions": 138016, + "singles": 15939, + "rank_mass": 642620, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 53320, + "2": 77409, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "21": 165, + "22": 23 + }, + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json new file mode 100644 index 0000000000..3b4bc33ff6 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json @@ -0,0 +1,35 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "frames": 73697, + "distinct_transitions": 190838, + "singles": 20700, + "rank_mass": 915250, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69278, + "2": 108881, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25 + }, + "word_sha256": "a54443429f47c486016771ce0436effda098e142afc52861c20957e9ff8e086b", + "copied_centers": 25, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz new file mode 100644 index 0000000000..3a7c7c41c1 Binary files /dev/null and b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz differ diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz new file mode 100644 index 0000000000..6a239a3e9f Binary files /dev/null and b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz differ diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 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}, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + 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a/references/frame-compiler/pr79/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr79/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 at the new bit saving, +and the new complete profile has exact upper moment <1. All47 strict assembly +conditions and seven margins pass. **53 Lean endpoints** pass:34 new universal, +15 concrete,4 reused rational-helper lemmas. No omitted proof, project axiom or +native decision shortcut. The math scope includes dirty-word/complement safety, +coordinate conjugacy, fresh-kernel clearing, actual finite rounding and old-profile +rejection. It does not formalize the Python/C++ compiler or the all-size theorem. + +## Reproduce the accepted words + +Use an external checkout of frozen PR62 commit +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No newer sources are consumed. +See `verification/README.md` to compile its exact C++17 profiler, then run: + +``` +python verification/verify_words.py --upstream UPSTREAM --profiler PROFILER --word23 words/word-23.json.gz --word25 words/word-25.json.gz --output work/recheck +python verification/check_guards.py words/word-23.json.gz +python verification/check_guards.py words/word-25.json.gz +cd math +lake build Frozen62Research +``` + +The verifier checks immutable sources and its own adapter hashes, full input/dirty +bases in both orientations, exact source/scatter inventory, every literal frame +transition and all fixed-I+J profiles with bounded-minor and CRT checks. It rejects +optimized Python assertion mode. Use the supplied words for authoritative replay; +floating discovery prices propose candidates and have no trusted-proof role. +Discovery source snapshots, exact oracle fixtures (gzip-compressed) and matching +seeds retain original byte hashes. `discovery/SEARCH.md` explains the algorithms, +heuristic boundary and experimental commands. Historical workspace paths in the +source-generation receipts identify the original run; the accepted-word replay +uses the explicit upstream argument and needs no private directory layout. +Portable discovery regeneration: + +``` +python discovery/regenerate_portable.py --upstream UPSTREAM --work work/regenerate +``` + +This rewrites workspace paths only and checks both raw words and deterministic +gzip against the accepted words. Floating discovery is outside the trusted +certificate; the independent word/profile verifier establishes acceptance. + +The one-hour session froze information through #62. The unchanged data geometry +and its rational recovery are inherited; selected physical words/profile checks +are fresh. All-size analytic, compiler/frame transfer, finite-alphabet tape, +routing, prime selection/recovery and eventual-threshold contracts remain +conditional. No practical runtime or global-optimality claim is made. + +Alejandro Zarzuelo Urdiales is the human author/developer, following earlier +Archivara and personal July/October matrix/parity work developed with multiple +AI tools. This synthesis involved substantial OpenAI Codex assistance. Known +linear algebra, matroid exchange, dirty uncomputation and concavity principles +retain prior-work status. The finite construction credits Avi Eisenberg/ikeboy +(#62 interval/core-aware graph), eumemic (#57 frame compiler), Chafik Boukhalfa +(#60 ranking and earlier exact profiling), Rohan Arun and other retained notices. +The prior matrix/parity source is in `../matrix-exponent-synthesis/` and prior +Gaussian work in PR45. Its product counts retain their separate arithmetic scope. +The paper is supplied as LaTeX source; no newly compiled PDF is claimed. diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md b/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md new file mode 100644 index 0000000000..b8dd669634 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md @@ -0,0 +1,136 @@ +# Local frame-compiler search, frozen through PR62 + +All experiments in this directory use the pinned PR62 pair graph at +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No later community source is consumed. +The original checkout is unchanged. Each emitted word and compiler copy has +a SHA256 recorded in its `compiled.json`; changed words are sent separately +to the independent literal replay and profile verifier. + +## New dependency-circuit choices + +The inherited compiler reduces retired fresh-signal rows against the current +live anchors and an echelon basis of compatible retired rows. Instead of +accepting the first dependent retired row, the new selectors collect the +available fundamental dependency circuits and choose a circuit by one of: + +- total charged target/provider rank growth (`all_growth`); +- number and rank growth of other retired providers (`all_collateral`); +- anchor-only dependence before general retired dependence (`anchor_first`); +- actual physical transition child-profile moment cost (`profile_cost*`). + +Every clearing XOR and every target/provider frame promotion is still emitted +and charged. A zero fresh-signal row can contain arbitrary physical dirty state; +its reuse is justified by the complete reversible word, not by claiming that +the physical register is initialized to zero. The compiler runs both complete +dirty-basis orientations, and the independent verifier repeats them. + +For the last selector let `C(A,B) = sum_t n_t(A,B) F_t`, where the `n_t` are +the exact inherited fixed-I+J pivot-run profile of the physical frame transition +and `F_t = t exp(a log(m/t))`. A candidate target `s` at old frame `A_s`, cleared +into frame `G` with providers `z`, is priced by + +``` +C(A_s,G) - C(A_s,I) + + sum_z [C(A_z,G) + C(G,I) - C(A_z,I)]. +``` + +This accounts for immediate promotions and the change in deferred cleanup, +assuming each other retired provider remains retired until cleanup. Future +reuse couples decisions, so this is a discovery heuristic, not an additive +global optimality certificate. Linear rank mass cancels between candidates; +`t*expm1(a*log(m/t))` avoids cancellation in floating discovery prices. +Missing transition profiles are recorded and collected for the next iteration. +Once a run has zero missing pairs, every local price uses an actual transition +profile. The final saving is accepted only through exact rational whole-profile +moment bounds and all assembly gates. + +`build_pair_oracle.py` is a local adaptation of the frozen C++ profiler that +additionally exports each transition histogram. It preserves the projector, +pivot, bounded-minor and three-prime CRT routines. Its synthetic transition-list +input is an oracle request, not a physical executable word. Each immutable +profile dump and the source/header hashes are recorded. + +## Moment-ordered carry selection + +The `--weighted` experiment orders the inherited linear/partition-matroid +candidate edges by their physical transition moment change before the original +greedy initialization and augmenting paths. For a value produced at `P`, +preserved through donor frame `G`, and carried to future target `T`, its +no-reclamation child-cost change is + +``` +C(G,T) - C(G,I) - C(0,P) - C(P,T). +``` + +At fixed cardinality, role and external-volume corrections are common to all +edge choices in the same axis. The inherited augmenting algorithm still seeks +maximum cardinality; it does not optimize the weights globally. Reclamation +adds coupling, so only the changed whole-word profile can establish an actual +improvement. This experiment makes no minimum-cost matroid claim. + +The `--exchange` variant starts from the frozen original maximum-cardinality +matching and tries bounded improving one-edge exchanges. A new edge may replace +the old donor of the same use when its donor block stays linearly independent; +or it may replace a selected edge in the same donor block and serve an unused +use. Both preserve cardinality and distinct-use constraints. The `--cycle` +variant additionally tests two-edge donor/use cycles, checking the independence +of both changed blocks. No improving two-edge cycle was found in the tested +native-price instance; this is not a proof that longer cycles cannot improve it. + +## Joint basis and schedule search + +`--basis shift1` profiles all candidate physical transitions after the point +permutation `i -> (i+1) mod h`, while preserving their original frame IDs. +Matching and reclamation are then priced in that basis. The emitted word is +renamed by `relabel_word.py`: all frame masks, canonical source/output triples, +common points and scatter port indices change together. Scratch slots and +literal XOR instructions are retained. The complete triple family and the +permutation-invariant `I+J` basis are inherited; every final renamed word still +gets fresh full-basis and actual physical-profile verification. + +This joint search differs from merely relabeling an already selected schedule: +the selected carries and clearing circuits are optimized under the new ordered +pivot-run prices. It remains a bounded discovery heuristic. + +## Regeneration + +The frozen graph/matching setup and a moment-cost exchange run are generated by: + +``` +python -S collect_matching_pairs.py --h 23 +python -S build_pair_oracle.py --h 23 --strategy matching_collect +python -S run_strategy.py --h 23 --strategy profile_cost --exchange +``` + +Repeat at `h=25`. For joint search, add `--basis shift1` to the oracle and +strategy commands. Reclamation may encounter transitions absent from the +initial carry-edge inventory. Run the oracle again on the emitted strategy +directory with `--incremental`, then run a new strategy label. The new label +must start with `profile_cost`; output directories are never overwritten. +`compiled.json` records the exact oracle dump hash, missing-pair count, word +hashes and source pin. Immutable earlier oracle dumps are retained by SHA256. +Use `--oracle path/to/the-immutable-dump.jsonl` to reproduce the prices of a +specific recorded run instead of consuming the subsequently enlarged cache. +The initial compiler matching cache is accepted only if its complete candidate +edge list matches the current frozen graph and every restored selected block +passes the same linear-independence check. + +The runner saves an immutable source copy and its hash for later runs. Floating +`expm1` prices at discovery saving `a=0.00005103` select proposals only. Neither +those prices nor their reported local gains are used as an arithmetic witness. + +## Acceptance boundary + +The independent verifier checks all input and dirty basis vectors in both +orientations, exact literal-scatter incidences, causal nested physical frames, +event equality reconstructed from the actual XOR word, rank mass, actual child +profiles and CRT agreement. It then computes the whole mixed-axis recurrence +and exact rational moment/assembly witnesses. Existing all-size geometry, +analytic envelopes, compiler/tape arguments and the surrounding reduction are +inherited from frozen PR62. A finite profile improvement does not by itself +formally prove those inherited hypotheses. + +Reduced XOR count alone is not accepted as an exponent improvement. In this +search `all_collateral` and `anchor_first` reduced clearing XORs but worsened +the certified characteristic. Actual child-size distributions decide the +saving, even when both physical-role counts and total rank mass are unchanged. diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py b/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py new file mode 100644 index 0000000000..7c154b1a29 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py @@ -0,0 +1,275 @@ +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +import sys;sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'matrix-synthesis/bridge/pr62/references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s,add=True): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>s&1;e^=1<=prices[f]-1e-14:continue + if not can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:-prices[z])if prices[e] /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/NOTICE b/references/frame-compiler/pr79/references/frame-compiler/pr71/NOTICE new file mode 100644 index 0000000000..8adab44ba3 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/NOTICE @@ -0,0 +1,324 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/README.md b/references/frame-compiler/pr79/references/frame-compiler/pr71/README.md new file mode 100644 index 0000000000..4a9b481aa3 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/README.md @@ -0,0 +1,172 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/SOURCE.json b/references/frame-compiler/pr79/references/frame-compiler/pr71/SOURCE.json new file mode 100644 index 0000000000..c8cc31f3d0 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/SOURCE.json @@ -0,0 +1,120 @@ +{ + "commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "Makefile": "6e9e48a677b2f66643226840f574a6535e3564ffb0c72284b60302684a5dfbe4", + "NOTICE": "1e0702aa665673508fa91169163c5785d680637fff636fda01f36e3b127c3ee0", + "README.md": "24817241fcad7f0a294ec6ad9666ee552ed9057e8d89e3c1d27e8fa2c7fe4229", + "certificates/split-pair-compiler.json": 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"b7194b8586844956904b33e9fe18f0c75606c11b", + "scope": "Unmodified producer inputs for experimental frame compiler; attribution retained in each file", + "source_pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/48" +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py new file mode 100644 index 0000000000..c7fd42867d --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py @@ -0,0 +1,196 @@ +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit', 'complex'): + data = finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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"scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1", + "scripts/partial_swap/graph.py": "fd8c567759e26a10d2bad05508fd0355eb70fb116664d4e06e1858d0d8cb2ef9", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + } + }, + "status": "Conditional exact arithmetic witness; general transfer proofs are dependencies" +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "PR48": { + "author": "Chafik Boukhalfa", + "commit": "b7194b8586844956904b33e9fe18f0c75606c11b", + 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Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + } + }, + "gzip_sha256": "4629d45d5074f87706db46be3aa3cd369071cd215bc6560d641115aadcce54a0", + "word_sha256": "bd0cbf73756f2e4f8d3879ec6c7a194990eb9ec40aaf3580bdded6994798d920" + }, + "25": { + "compiled": { + "h": 25, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 36586, + "baseline_pr48_roles": 48329, + "histogram": { + "1": 55478, + "0": 416276, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + }, + "rank_mass": 915250, + "elementary_xors": 205650, + "stats": { + "augmentations": 286, + "regions": 73695, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json new file mode 100644 index 0000000000..346cf87ea3 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json @@ -0,0 +1,1087 @@ +{ + "accepted_moment": { + "degree": 8, + "lower": "34287951499999999998997315662315085394575263036671/34287951500000000000000000000000000000000000000000", + "rounding_denominator": 10000000000000000000000000000000000000000, + "saving": "5103158916233/100000000000000000", + "strict_gap": "2278828040192983762647964739/77927162500000000000000000000000000000000000000", + "terms": { + "1": { + "exp_lower": "5001621630918375893019301295747281962987/5000000000000000000000000000000000000000", + "exp_upper": "10003243261836751786038602591494564437549/10000000000000000000000000000000000000000", + "log_lower": "3177185020398675220004135749131/500000000000000000000000000000", + "log_upper": "6354370040797350440008271498263/1000000000000000000000000000000", + "weight": "61988/2833715" + 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rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.", + "All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.", + "Neither global optimality nor measured practical speedup is claimed." + ], + "rejected_moment": { + "degree": 8, + "lower": "8571987875000000003683551653063012975552828889113/8571987875000000000000000000000000000000000000000", + "rounding_denominator": 10000000000000000000000000000000000000000, + "saving": "51031589162331/1000000000000000000", + "strict_gap": "-920887913265753353254538048853/2142996968750000000000000000000000000000000000000", + "terms": { + "1": { + "exp_lower": "2000648652367350369920582377063597092877/2000000000000000000000000000000000000000", + "exp_upper": "250081081545918796240072797132949649399/250000000000000000000000000000000000000", + "log_lower": "3177185020398675220004135749131/500000000000000000000000000000", + "log_upper": 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b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json new file mode 100644 index 0000000000..42958fc74b --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json @@ -0,0 +1,195 @@ +{ + "artifact_sha256": { + "frame-profiles-23.json": "fec377bcf1512a427674983256b900229d4133026445b6e680c6e1e6dde5af7d", + "frame-profiles-25.json": 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orientations PASS", + "word_length": 621342 + }, + "schedule": "cover-core", + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4" + }, + "25": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 48329, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 41186, + "elementary_xors": 205977, + "h": 25, + "histogram": { + "0": 416741, + "1": 55478, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "2": 115781, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 915250, + "roles": 36586, + "stats": { + "augmentations": 286, + "clearing_xors": 2154, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "regions": 73695 + } + }, + "gzip_sha256": 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"3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "research/reordered-rank-pair/test_negative.py": "88832242e6f74e3fe08d109d4f21ff188a9ca0ae50c3e8f31da0243fe9501510", + "research/reordered-rank-pair/verify.py": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352", + "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3", + "scripts/experiments/binary_frame_profiles.cpp": "8e2e391d3ee57cbb1372c68e4aa031e1b861321536eabd642ada54e12e678669", + "scripts/experiments/binary_frame_replay.py": "392e78e62d7685c99a5888a7da743ea6c3dcad631af4a743c91e0c09348442bc", + "scripts/experiments/rank_pair_compiler.py": "9984aaccf880e4840402322d76678bfddb33ce7e494af78430a43429f51b85fd" + }, + "status": "Exact topological scheduling of unchanged PR63 graph/compiler; both physical orientations and fixed profiles checked" +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json new file mode 100644 index 0000000000..3b648dbe21 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "loss": 506, + "rank_sum": 642620, + "field_prime": 2305843009213693951, + "frames": 52475, + "distinct_matrices": 36399, + "crt_matrices": 6049, + "crt_disagreements": 0, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json new file mode 100644 index 0000000000..19cc34b4ca --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json @@ -0,0 +1,40 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "loss": 600, + "rank_sum": 915250, + "field_prime": 2305843009213693951, + "frames": 73697, + "distinct_matrices": 50394, + "crt_matrices": 8127, + "crt_disagreements": 0, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json new file mode 100644 index 0000000000..2883a5f7c9 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "frames": 52475, + "distinct_transitions": 138016, + "singles": 15939, + "rank_mass": 642620, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 53320, + "2": 77409, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "21": 165, + "22": 23 + }, + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json new file mode 100644 index 0000000000..3b4bc33ff6 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json @@ -0,0 +1,35 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "frames": 73697, + "distinct_transitions": 190838, + "singles": 20700, + "rank_mass": 915250, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69278, + "2": 108881, + "3": 14362, + "4": 16908, + 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a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz new file mode 100644 index 0000000000..6a239a3e9f Binary files /dev/null and b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz differ diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + 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a/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) ++ slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();pending={};stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): +@@ -149,7 +151,8 @@ + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 +- return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) ++ endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 ++ return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} +@@ -161,6 +164,9 @@ + old,e=bb[p];row^=old;expr^=e + return expr + for s in anchors:ins(s) ++ for s,target in pending.items(): ++ if contains(blocks[frames[s]]['frame'],blocks[g]['frame']) and contains(blocks[g]['frame'],blocks[target]['frame']): ++ ins(s);stats['live_anchor_candidates']+=1 + best=None + # Inspect every eligible dependent candidate across all retired ranks. + # Rank the actual fixed-basis growth/cleanup profiles by an integer entropy score. +@@ -176,7 +182,9 @@ + if best is None or key= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and kappa > previous_kappa + bridge = json.loads((OLD/'certificate.json').read_text())['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/split-pair/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr67_commit='b3745601e947a94316bf25c2c6263d93c06e3364', + pr67_kappa=previous_kappa, ratio_pr67=kappa/previous_kappa, + absolute_gain_pr67=kappa-previous_kappa, + pr67_complete_profile_exclusion_lower=prior65_lower, + full_pr67_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected split-pair partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'split-pair-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py new file mode 100644 index 0000000000..1290ef2eb8 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py @@ -0,0 +1,275 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py new file mode 100644 index 0000000000..7908c963a4 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py @@ -0,0 +1,78 @@ +#!/usr/bin/env python3 +"""Replay the aligned split-pair/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from split_pair_compose import compose, check_sources +from split_pair_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'split-pair-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='split-pair-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + 'c++', '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'split-pair-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'split-pair-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'split-pair-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'split-pair-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'split-pair-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair.py new file mode 100644 index 0000000000..5088cff133 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair.py @@ -0,0 +1,238 @@ +"""Physical and exact-arithmetic controls for the aligned split/pair witness.""" +from copy import deepcopy +from fractions import Fraction +from itertools import combinations +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile +import unittest +from unittest.mock import patch + +ROOT = Path(__file__).resolve().parents[1] +EXPERIMENTS = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXPERIMENTS)) +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from binary_frame_math import moment + + +class SplitPairControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.words = {h: json.loads(gzip.decompress((ROOT/f'certificates/split-pair-word-{h}.json.gz').read_bytes())) + for h in (23,25)} + + def reject_mutation(self, mutate, checker='both'): + for h, original in self.words.items(): + with self.subTest(h=h), tempfile.TemporaryDirectory() as directory: + changed = deepcopy(original) + mutate(changed) + path = Path(directory)/'word.json' + path.write_text(json.dumps(changed, separators=(',', ':'))+'\n') + with self.assertRaises((AssertionError, ValueError, IndexError, KeyError)): + if checker != 'transitions': + replay(path) + if checker != 'replay': + prepare(path, Path(directory)/'transitions.bin') + + def test_selected_words_pass_independent_replay(self): + recorded = json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + actual = replay(ROOT/f'certificates/split-pair-word-{h}.json.gz') + self.assertEqual(json.loads(json.dumps(actual)), recorded['axes'][str(h)]['replay']) + + def test_omitted_literal_xor_is_rejected(self): + self.reject_mutation(lambda word: word['ops'].pop(0)) + + def test_self_xor_is_rejected(self): + def mutate(word): + word['ops'][0][1] = word['ops'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_non_nested_operation_frame_is_rejected(self): + def mutate(word): + narrow = next(i for i,(core,cover) in enumerate(word['frames']) if core == cover) + operation = next(op for op in word['ops'] if word['frames'][op[2]][0] != word['frames'][op[2]][1]) + operation[2] = narrow + self.reject_mutation(mutate) + + def test_aliased_terminal_role_is_rejected(self): + def mutate(word): + word['outputs'][1][0] = word['outputs'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_missing_copied_center_is_rejected(self): + def mutate(word): + index = next(i for i,(_,_,_,target) in enumerate(word['outputs']) if len(target) == 1) + word['outputs'].pop(index) + self.reject_mutation(mutate) + + def test_omitted_transition_cannot_reduce_paid_profile(self): + self.reject_mutation(lambda word: word['events'].pop(0), 'transitions') + + def test_understated_physical_width_is_rejected(self): + def mutate(word): + word['R'] -= 1 + self.reject_mutation(mutate) + + def test_complete_pr67_profile_fails_new_bit_saving(self): + from split_pair_arithmetic import refine + previous = json.loads((ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/paired-candidate.json').read_text())['bit'] + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + result = refine.exact_moment(previous['m'], previous['W'], {int(t): n for t,n in previous['child_multiplicities'].items()}, Fraction(current['bit_saving'])) + self.assertGreater(result['lower'], 1) + self.assertGreater(Fraction(current['kappa']), Fraction(current['comparison']['pr67_kappa'])) + + def test_private_import_preserves_path_and_arithmetic_module(self): + import split_pair_graph as provider + import split_pair_arithmetic as arithmetic + sentinel = object() + existing = sys.modules.get('refine', sentinel) + previous_path = sys.path[:] + graph, schedule = provider._private_modules() + refine, audit = arithmetic.private_arithmetic() + self.assertIs(audit.refine, refine) + self.assertIs(sys.modules.get('refine', sentinel), existing) + self.assertEqual(sys.path, previous_path) + + def test_failed_graph_build_restores_original_providers(self): + import split_pair_graph as provider + previous_class, previous_points = provider._graph.circuit_class, provider._graph.alternating_points + with patch.object(provider._graph, 'graph', side_effect=RuntimeError('deliberate graph failure')): + with self.assertRaises(RuntimeError): + provider.graph(23) + self.assertIs(provider._graph.circuit_class, previous_class) + self.assertIs(provider._graph.alternating_points, previous_points) + + def test_failed_compilation_restores_engine_graph_and_schedule(self): + import split_pair_compiler as producer + previous_graph, previous_build = producer.compiler.graph, producer.compiler.build + missing = object() + runtime = {name:getattr(producer.compiler,name,missing) for name in ('PENDING_COST','ORACLE_EXE','ORACLE_INPUT','oracles')} + with patch.object(producer.compiler, 'compile_', side_effect=RuntimeError('deliberate compiler failure')): + with self.assertRaises(RuntimeError): + producer.compile_axis(23) + self.assertIs(producer.compiler.graph, previous_graph) + self.assertIs(producer.compiler.build, previous_build) + for name,value in runtime.items(): + self.assertIs(getattr(producer.compiler,name,missing),value) + + def test_uncertified_configurations_are_rejected(self): + import split_pair_graph as provider + wrong_anchor = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_anchor['anchor'] = False + boolean_group = deepcopy(provider.EXPECTED_CONFIGS[23]); boolean_group['groups'][0] = True + changed_schedule = deepcopy(provider.EXPECTED_CONFIGS[23]); changed_schedule['schedule'] = 'reverse-node' + for changed in (wrong_anchor, boolean_group, changed_schedule): + with self.subTest(configuration=changed), patch.object(provider.json, 'loads', return_value=changed): + with self.assertRaises(ValueError): + provider.configuration(23) + for dimension in (True, 22, 24, '23'): + with self.subTest(dimension=dimension), self.assertRaises(ValueError): + provider.configuration(dimension) + + def test_recursive_weighted_exclusions_and_contraction(self): + import split_pair_graph as provider + for h in (23,25): + block_sizes = [] + parent = provider._graph.circuit_class(h) + selected = provider.split_class(parent, provider.configuration(h)['groups']) + case = self + class Audited(selected): + def grouping(self, points): + groups = super().grouping(points) + case.assertEqual([x for group in groups for x in group], list(points)) + case.assertLess(len(groups), len(points)) + return groups + + def _block(self, points, edges, weights, level): + def expected(omitted): + values = [value for pair,value in edges.items() if not set(pair) & omitted] + values += [value for point,value in weights.items() if point not in omitted] + support = 0 + for value in values: + case.assertEqual(support & self.support[value], 0) + support |= self.support[value] + return support + total, single, pairs = super()._block(points, edges, weights, level) + case.assertEqual(self.support[total], expected(set())) + case.assertEqual(set(single), set(points)) + for a in points: + case.assertEqual(self.support[single[a]], expected({a})) + case.assertEqual(set(pairs), set(combinations(points,2))) + for a,b in combinations(points,2): + case.assertEqual(self.support[pairs[a,b]], expected({a,b})) + block_sizes.append(len(points)) + return total, single, pairs + local = Audited(h-1) + block_sizes.clear() + local.pair(list(range(h-1))) + self.assertEqual(sorted(block_sizes, reverse=True), [h-1, 12 if h==23 else 13, 7 if h==23 else 8, 5, 3, 2]) + + def test_next_fine_grid_points_and_old_assembly_controls_reject(self): + from split_pair_arithmetic import refine + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + bit = current['bit']; saving = Fraction(current['bit_saving']); kappa = Fraction(current['kappa']) + grid = Fraction(1,10**18) + rows = {int(t): n for t,n in bit['child_multiplicities'].items()} + self.assertLess(refine.exact_moment(bit['m'],bit['W'],rows,saving)['upper'], 1) + self.assertGreater(refine.exact_moment(bit['m'],bit['W'],rows,saving+grid)['lower'], 1) + for label, variant in ( + ('next_kappa', dict(kappa=kappa+grid)), + ('zero_backoff', dict(h=Fraction())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))): + call = dict(a_bit=saving, kappa=kappa, h=Fraction(1,10**12));call.update(variant) + with self.subTest(control=label), self.assertRaises(refine.balanced.InvalidAssembly): + refine.balanced.assembly(current['finite_bridge'], **call) + + def test_mass_preserving_profile_mutation_is_rejected(self): + from split_pair_compose import check_sources + profile_path = ROOT/'certificates/split-pair-profiles-23.json' + changed = json.loads(profile_path.read_text()) + before = sum(t*n for t,n in enumerate(changed['blocks'])) + changed['blocks'][2] += 3; changed['blocks'][3] -= 2 + self.assertTrue(all(n >= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'split-pair-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from split_pair_compose import check_sources + manifest_path = ROOT/'research/split-pair/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/split-pair-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import split_pair_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('split_pair_graph.py', 'split_pair_engine.py', 'split_pair_compiler.py', 'split_pair_arithmetic.py', 'split_pair_compose.py', 'verify_split_pair.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair_pending.py b/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair_pending.py new file mode 100644 index 0000000000..e6d63f72a4 --- /dev/null +++ b/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/split_pair_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main() diff --git a/references/frame-compiler/pr79/research/balanced-split/PROOF.md b/references/frame-compiler/pr79/research/balanced-split/PROOF.md new file mode 100644 index 0000000000..c34f8542cc --- /dev/null +++ b/references/frame-compiler/pr79/research/balanced-split/PROOF.md @@ -0,0 +1,251 @@ +# Finite certificate and inherited scope + +## 1. Exact change and provenance + +This construction preserves PR71's anchored `[1,1,2]` split recursion, +PR65 region schedules, PR67 profile-cost reclamation and PR68 pending live +controls with next-use scoring. It composes three finite choices: PR69's +balanced coarse parenthesization, future-compatible unit completion, and a +bounded adaptation of PR70 carry exchanges. The contributor originals, +licenses and notices are retained in hash-checked archives. The published +PR71 source, words and complete arithmetic certificate are preserved at +`1bef94fd40a746452548c84a4a8f8834670a3113` for the full-profile comparison. +The new namespace is `balanced-split`. Two portable engines differ from the +independently audited discovery engines only in the repository-relative ROOT +constant; their relocation patches and SHA256s are recorded. + +The h23 coarse cell uses columns when `i+jstep and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority):''' +check(s.count(completion)==1 and s.count(changed_start)==1,'Changed source not uniquely recognized') +check(s.replace(changed_start,old_start).replace(completion,' for i in range(len(ins)):')==old,'Compiler changed beyond the claimed unit-completion priority') +tree=ast.parse(s) +helpers=[n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name in ('basis','independent')] +namespace={};exec(compile(ast.Module(body=helpers,type_ignores=[]),str(SOURCE),'exec'),namespace) +basis=namespace['basis'];independent=namespace['independent'] +future=next(n for n in ast.walk(tree) if isinstance(n,ast.FunctionDef) and n.name=='future_priority') +contains=lambda a,b:not(b[0]&~a[0]) and not(a[1]&~b[1]) +# Actual-use fixtures distinguish future compatible uses from backward or nonnested uses. +ns=dict(position={0:0,1:1,2:2,3:3},step=1,b={'frame':(1,3),'inputs':[10,11,12,13]},blocks=[{'frame':(1,3)},{'frame':(1,3)},{'frame':(1,7)},{'frame':(1,5)}],uses=[(10,2,None),(10,2,('terminal',)),(11,2,None),(11,0,None),(12,3,None),(13,3,None)],value_uses={10:[0,1],11:[2,3],12:[4],13:[5]},contains=contains,slots=[7,1,3,3],ins=[0,1,2,3]) +exec(compile(ast.Module(body=[future],type_ignores=[]),str(SOURCE),'exec'),ns) +check([ns['future_priority'](i) for i in range(4)]==[(-2,3,0),(-1,1,1),(0,2,2),(0,2,3)],'Priority does not use compatible actual future uses, symbolic support, index') +check(sorted(range(4),key=ns['future_priority'])==[0,1,2,3],'Priority is not deterministic') +# General span argument is below; these adversarial numerical fixtures check the actual helpers and literal synthesis. +rng=Random(20261008);cases=0;operations=0 +for n in range(1,10): + for trial in range(250): + rows=[] + for _ in range(rng.randrange(n+1)*3): + candidate=rng.randrange(1,1<>i&1) + if j!=i: + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];ops.append((a,z)) + for j in range(n): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];ops.append((j,i)) + check(rr==[1< 1 and kappa > previous_kappa + bridge = finite_bridge(p['W']) + validate_bridge(bridge, p['W']) + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/balanced-split/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113', + pr71_kappa=previous_kappa, ratio_pr71=kappa/previous_kappa, + absolute_gain_pr71=kappa-previous_kappa, + pr71_complete_profile_exclusion_lower=prior71_lower, + full_pr71_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected balanced-split partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring, PR69 balanced coarse sums, future unit completion and bounded PR70 carry exchanges; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'balanced-split-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr79/scripts/experiments/balanced_split_engine.py b/references/frame-compiler/pr79/scripts/experiments/balanced_split_engine.py new file mode 100644 index 0000000000..e1a9883726 --- /dev/null +++ b/references/frame-compiler/pr79/scripts/experiments/balanced_split_engine.py @@ -0,0 +1,278 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + _graph = _graphs[h] + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/references/frame-compiler/pr79/scripts/experiments/binary_frame_math.py b/references/frame-compiler/pr79/scripts/experiments/binary_frame_math.py new file mode 100644 index 0000000000..b87855e808 --- /dev/null +++ b/references/frame-compiler/pr79/scripts/experiments/binary_frame_math.py @@ -0,0 +1,87 @@ +"""Exact rational helpers extracted without body changes from pinned PR48 verify.py. +Credits: icekylinx PR32/36, Dominik Scholz PR35, Zhihao Chen PR29/23, +Paureel/Aurel Prosz, Swapnil Jain, Rohan Arun PR25/31, RaD/hipotures, +Chafik Boukhalfa and inherited notices in references/frame-compiler/pr48. +Prepared with OpenAI Codex assistance; no formal theorem claim. +""" +from fractions import Fraction as Q +from functools import lru_cache +from math import comb, factorial, isqrt, prod + +def js(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):js(v)for k,v in x.items()} + if isinstance(x,(list,tuple)):return [js(v)for v in x] + return x + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def mersenne(exponent): + require(exponent >= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr79/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr79/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr79/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr79/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr79/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr79/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'balanced-split-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from balanced_split_compose import check_sources + manifest_path = ROOT/'research/balanced-split/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/balanced-split-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import balanced_split_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_all_threshold_dependent_bridge_fields_are_checked(self): + from balanced_split_compose import finite_bridge, validate_bridge + expected = finite_bridge(134126064) + self.assertTrue(validate_bridge(expected, 134126064)) + for section,key in (('bit','wire_bits'),('rows','coefficient'),('rows','degree'),('rows','degree_gap'),('rows','suffix_slope')): + changed = deepcopy(expected) + changed[section][key] = Fraction(changed[section][key])+1 + with self.subTest(field=section+'.'+key), self.assertRaisesRegex(AssertionError, 'Stale finite bridge'): + validate_bridge(changed, 134126064) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('balanced_split_graph.py', 'balanced_split_engine.py', 'balanced_split_compiler.py', 'split_pair_arithmetic.py', 'balanced_split_exchange_engine.py', 'balanced_split_compose.py', 'verify_balanced_split.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr79/tests/test_balanced_split_pending.py b/references/frame-compiler/pr79/tests/test_balanced_split_pending.py new file mode 100644 index 0000000000..cce267112e --- /dev/null +++ b/references/frame-compiler/pr79/tests/test_balanced_split_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/balanced_split_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/balanced-split-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main() diff --git a/references/frame-compiler/pr82/FETCH.json b/references/frame-compiler/pr82/FETCH.json new file mode 100644 index 0000000000..0dccc67c62 --- /dev/null +++ b/references/frame-compiler/pr82/FETCH.json @@ -0,0 +1,43 @@ +{ + "commit": "3410b940aa26e5876202152dfa7c4f66451ee22c", + "files": { + "LICENSE": { + "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64", + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4" + }, + "NOTICE": { + "git_blob": "8a6bef1613ee24ca140ea612af48fb51d8cd9000", + "sha256": "ef6c74f5103d624f1a9910668d4124b213775e9b7e24edde089d9f4d1377abbb" + }, + "research/envelope-balanced/README.md": { + "git_blob": "77486a38c26058fa5690952254a056c1035b6e30", + "sha256": "ed0a825837ca352dda60fc6d0bf977881466d2edeb2c906983d9b2678a34bd12" + }, + "research/envelope-balanced/SOURCE.json": { + "git_blob": "6b7fbca6d08b8da17bb79439a93bbd0f5262e330", + "sha256": "ede836ef555e700601810f4beea31057af88ce7ff4dae21fceba44918be26551" + }, + "research/envelope-balanced/compiler.py": { + "git_blob": "b4d43e88aaa65aad4b3d83decd3f34947b4b6962", + "sha256": "1716168a06fa5385c41232b40f343a98b322dec3718cb641f0042aa8f5610738" + }, + "research/envelope-balanced/flag_engine.py": { + "git_blob": "d210d9336bf92edf03eb9b6d89b9e66b22a15a54", + "sha256": "e42a43947c8d575b764683d88ddc26a290618ac79028337b3b50daedc8475183" + }, + "research/envelope-balanced/order-23.json": { + "git_blob": "035f01df59be3312e30ec692754d3a331a766799", + "sha256": "def92cd69f3fba2986c7a230ece45f9eb63fd38fef512d055bf0adffe9edfa82" + }, + "research/envelope-balanced/order-25.json": { + "git_blob": "ec2a8aa14c0b0c07de47b7314b535aa1385c0756", + "sha256": "47632a745319452f4237754ccb1793e7d0ae455654b68c6a31eb2a79a0f98b9f" + }, + "research/envelope-balanced/verify.py": { + "git_blob": "e74b03c41417c914bcf0e4e8fd0150a27e61aaef", + "sha256": "bd767d460a85414ca320a449705860a376bee42cb8ce0734233a8e9706ad4fc5" + } + }, + "repo": "rohanarun/integer-mult-bounds", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/82" +} diff --git a/references/frame-compiler/pr82/LICENSE b/references/frame-compiler/pr82/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/pr82/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/references/frame-compiler/pr82/NOTICE b/references/frame-compiler/pr82/NOTICE new file mode 100644 index 0000000000..8a6bef1613 --- /dev/null +++ b/references/frame-compiler/pr82/NOTICE @@ -0,0 +1,337 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Balanced coarse split composition (2026-10-08) +--------------------------------------------- +Eumemic / @eumemic supplied PR69's balanced coarse sums, with OpenAI Codex +assistance. Alejandro Zarzuelo Urdiales / @alejandrozu supplied PR70's bounded +carry-exchange strategy with the AI disclosures retained in the source archive. +Chafik Boukhalfa / @chafreaky, with OpenAI Codex assistance, selected the row/ +half-plane coarse rules, future-compatible unit completion, exact integer-price +carry adaptation, composition and this certificate package. The PR71 anchored +split vector, schedules, arithmetic, pending controls and their contributor +chain are retained as credited above. Original PR69/70 sources, licenses and +notices and the complete published PR71 baseline are preserved under +references/frame-compiler. All earlier notices remain applicable. diff --git a/references/frame-compiler/pr82/SOURCE.json b/references/frame-compiler/pr82/SOURCE.json new file mode 100644 index 0000000000..99c32c3c37 --- /dev/null +++ b/references/frame-compiler/pr82/SOURCE.json @@ -0,0 +1,17 @@ +{ + "commit": "3410b940aa26e5876202152dfa7c4f66451ee22c", + "files": { + "FETCH.json": "e3c49a0759e5539c0c6d665278dae83cd9f0c4f614f322b76df5abc4e2404d0b", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "ef6c74f5103d624f1a9910668d4124b213775e9b7e24edde089d9f4d1377abbb", + "research/envelope-balanced/README.md": "ed0a825837ca352dda60fc6d0bf977881466d2edeb2c906983d9b2678a34bd12", + "research/envelope-balanced/SOURCE.json": "ede836ef555e700601810f4beea31057af88ce7ff4dae21fceba44918be26551", + "research/envelope-balanced/compiler.py": "1716168a06fa5385c41232b40f343a98b322dec3718cb641f0042aa8f5610738", + "research/envelope-balanced/flag_engine.py": "e42a43947c8d575b764683d88ddc26a290618ac79028337b3b50daedc8475183", + "research/envelope-balanced/order-23.json": "def92cd69f3fba2986c7a230ece45f9eb63fd38fef512d055bf0adffe9edfa82", + "research/envelope-balanced/order-25.json": "47632a745319452f4237754ccb1793e7d0ae455654b68c6a31eb2a79a0f98b9f", + "research/envelope-balanced/verify.py": "bd767d460a85414ca320a449705860a376bee42cb8ce0734233a8e9706ad4fc5" + }, + "pr": 82, + "scope": "Exact credited coordinate-aware pricing source and notices; reported foreign witness accepted without producer replay." +} diff --git a/references/frame-compiler/pr82/research/envelope-balanced/README.md b/references/frame-compiler/pr82/research/envelope-balanced/README.md new file mode 100644 index 0000000000..77486a38c2 --- /dev/null +++ b/references/frame-compiler/pr82/research/envelope-balanced/README.md @@ -0,0 +1,127 @@ +# Envelope ordering inside balanced split compilation + +The finite conditional witness gives **kappa = 5203279888519/100000000000000000 = 5.2032798885190e-05**, +0.49049670% above PR80. Bit saving is 13008876609597/250000000000000000. +This is a draft pending the full expanded repository verification. + +PR80 selected already-compiled axes from PR76 and PR79. Here we compose +their construction methods before compilation on both axes: PR79's balanced +coarse graph and future-compatible unit completion; PR76/PR74's envelope +node ordering; three passes of PR79/PR70's bounded carry exchanges; and +PR78's geometric coordinate flags. h23 uses the half-plane coarse choice +and cover-core schedule; h25 uses row coarse sums and reverse-node schedule. +Both retain the anchored [1,1,2] split vector and exact next-use profile costs. +All archived sources are unchanged. `compiler.py` is the portable composition. +At h25 the discovery oracle receives coordinate-permuted frame masks, so its +costs refer to the final flag rather than the original coordinate order. +`flag_engine.py` differs from PR79's engine only in that oracle frame writer +and an attribution comment; operations, eligibility, independence and dirty +checks are unchanged. This changes only heuristic selection among legal +choices. Its final word is still independently replayed and exactly priced. +At h23 oracle pricing retains the original coordinate order. + +| Quantity | PR80 | This witness | +|---|---:|---:| +| h23 auxiliary roles | 27256 | 27075 | +| h25 auxiliary roles | 35684 | 35500 | +| Physical width | 134031764 | 133289600 | +| Total recursive rank | 77066417400 | 76639673100 | +| Deficit | 1846900 | 1846900 | + +## General compatibility argument + +Balanced coarse parenthesization changes only how the same Cartesian-product +edge sums are evaluated. The weighted scalar identities and recursively +contracting anchored partition are inherited from PR79's proof. Envelope +ordering then applies a bijection to non-source scalar node IDs, grouping +nodes by (core, cover), preserving the order inside each group and every +argument, output and provenance reference. It changes no scalar linear form +or frame. The graph verifier is rerun after this relabeling. Dependency and +carrier-eligibility checks in the compiler remain enabled. + +Future-compatible completion chooses independent unit rows after the desired +outputs and retained carriers. Any accepted independent completion is a full +invertible basis; the unchanged synthesis emits its literal XOR operations. +Bounded carrier exchanges preserve matching cardinality, unique uses and +independence of the output-plus-retained-input rows. These choices can change +each other's costs, so the words are recompiled and every profile recomputed; +we do not add reported savings or assume independent numerical gains. + +All clearing targets and controls remain charged. Both frame-containment +checks for pending controls remain enabled. The compiler and independent +replay verify the full arbitrary-dirty-role wrapper in both orientations. +Independent axis implementations expose the same source triple lines, fixed +I+J basis, terminal frames and scatter identity. Hence the complete tensor/data +construction is unchanged. Every endpoint/copy/data-growth/complex term is +retained exactly once. The fixed-width bridge is derived from the actual W. + +## General relabeling argument + +Let P be a permutation matrix on the h coordinates. It commutes with J, +so P commutes with the fixed basis L = I+J and preserves the form I-J/9. +For a core/cover frame F(C,U), the relabeled projector is +P F(C,U) P^-1 = F(P C,P U). Consequently, every frame inclusion, rank, +nondegeneracy condition, projector denominator bound and elementary role +operation is preserved. The existing exact CRT bounds apply unchanged. + +Relabel each input triple T to P T, each output (c,T) to (P c,P T), +each frame mask by P, and each scatter row by the induced triple permutation. +The role slots and literal XOR operations do not change. This conjugates +the complete linear word by the input/output permutation and therefore +preserves its identity on every ordinary input and arbitrary dirty role. +The verifier independently replays that identity in both orientations. + +The data component sums over every pair of source triples. Independent +coordinate permutations on the two axes induce a bijection on that complete +Cartesian product. Hence its existing complete histogram, copied-center +costs and endpoint corrections are unchanged. This argument uses the full +case set; it would not justify retaining a selected subset's histogram. + +North-east corner rank profiles depend on the fixed coordinate order. +Conjugating by P can change which adjacent pivots form a recursive block, +even though total rank is unchanged. We regenerate these profiles from the +actual relabeled words rather than assuming their costs are invariant. +Both dimensions use the selected orders in order-23.json and order-25.json. + +## Reproduction and validation + +From the repository root with assert-enabled Python 3.11+ and C++17: + +```sh +python3 research/envelope-balanced/verify.py --regenerate +(cd research/envelope-balanced && python3 -m unittest test_controls -v) +make verify +``` + +The regeneration option launches two isolated compiler processes and requires +both original words to reproduce byte-for-byte. The verifier then regenerates +the coordinate-permuted words, performs independent full input/dirty replay, +reconstructs all transitions, and regenerates exact bounded-minor/CRT profiles. +The complete paid child list is reconstructed; independent rational moment +bounds, 47 strict inequalities, seven margins and both next-grid exclusions +are checked. The complete PR76, PR79 and PR80 child lists are each excluded at +the new bit saving using their own width. Six physical/coordinate failure +controls and three stale bridge controls run separately. A dedicated +three-version CI workflow retains every inherited workflow. + +The bounded searches are not proofs of global optimality. All inherited +all-size residual compiler, routing, recovery, prime selection, finite +alphabet/tape, precision and analytic transfer interfaces remain hypotheses. +No unconditional multiplication theorem or practical speedup is claimed. + +## Attribution + +Thomas DiFiore (PR74) introduced the envelope ordering; Dominik Scholz +(PR76) composed it with carried exchanges; Chafik Boukhalfa (PR79/71) +provided balanced/future/exchange and anchored split compilation; eumemic +(PR69/57) provided balanced coarse sums and reversible compilation; +Alejandro Zarzuelo Urdiales (PR70) supplied the carry-exchange strategy; +Rohan Arun (PR78/80/65/67) supplied coordinate flags, axis selection, +schedules and profile-cost reclamation. This new pre-compilation composition +and finite selection were prepared by Rohan Arun with OpenAI Codex assistance. + +Credit also Rohan Garg, Avi Eisenberg, icekylinx, James Chang, Zhihao Chen, +Aurel Prosz/Paureel, Swapnil Jain, RaD/hipotures, Douglas Colkitt, OpenAI, +Harvey–van der Hoeven and all inherited contributors. Original licenses, +author and AI-assistance notices remain preserved. Tested PR75 zero-circuit +variants were not selected for this witness and are not claimed as its method. diff --git a/references/frame-compiler/pr82/research/envelope-balanced/SOURCE.json b/references/frame-compiler/pr82/research/envelope-balanced/SOURCE.json new file mode 100644 index 0000000000..6b7fbca6d0 --- /dev/null +++ b/references/frame-compiler/pr82/research/envelope-balanced/SOURCE.json @@ -0,0 +1,304 @@ +{ + "parent_pr80": "a9ed157ff106fd35557b5896197f66a1272f7f13", + "files": { + ".gitattributes": "5f257f4e9e574ad5767f902242f519dad19cc455d6858f49234d0ccc345cabf1", + ".github/workflows/combined-flags.yml": "53d0f33c83356b2764f3cb332892690ff74ffa0e68b9ae1203fe837979c15396", + ".github/workflows/envelope-balanced.yml": "d658c2f91e1377eac5288cff7725ae1e573efdff70dac5472e6a4060085ab7fc", + ".github/workflows/verify.yml": "1a9cccd742ba2a5aa5a5ac38c1b7559bc0dec46b23d3ce3ff3e26c3137e6c3a2", + "Makefile": "1bf5b63d413280a68fc2b91a7e83a6172632e50c8177ca097d9622af669ee8d6", + 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Composition by Rohan Arun +with OpenAI Codex assistance. Apache-2.0; finite conditional witness only. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2] +sys.path.insert(0,str(ROOT/'scripts/experiments')) +import balanced_split_graph as graph +import balanced_split_exchange_engine as baseline_engine +import flag_engine +sys.path.insert(0,str(ROOT/'references/frame-compiler/pr76/research/round7-scheduling')) +from schedule_variant import reorder +import argparse,gzip,json,subprocess,os,shlex + +def check_flag_engine(): + original=(ROOT/'scripts/experiments/balanced_split_exchange_engine.py').read_text() + before="for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank']))" + after="for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank']))" + assert original.count(before)==1 + expected='# Coordinate-conjugated oracle pricing by Rohan Arun with OpenAI Codex.\n'+original.replace(before,after) + assert (Path(__file__).parent/'flag_engine.py').read_text()==expected,'Flag engine contains changes beyond oracle coordinate pricing' + +def compile_axis(h,work): + check_flag_engine() + engine=flag_engine if h==25 else baseline_engine + if h==25: + cfg=json.loads((ROOT/f'research/envelope-balanced/order-{h}.json').read_text()) + assert sorted(cfg['order'])==list(range(h)) + engine.COORD_MAP={int(k):v for k,v in cfg['mapping'].items()} + assert engine.COORD_MAP=={old:new for new,old in enumerate(cfg['order'])} + work.mkdir(parents=True,exist_ok=True) + oracle=work/'oracle' + subprocess.run([*shlex.split(os.environ.get('CXX','c++')),'-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/profile_oracle.cpp'),'-o',str(oracle)],check=True) + engine.graph=lambda dimension:reorder(graph.graph(dimension)) + engine.build=graph.ordered_build(engine.build,h) + engine.ORACLE_EXE=str(oracle);engine.ORACLE_INPUT=str(work/'oracle.bin');engine.PENDING_COST=True;engine.oracles=[] + try:result,word=engine.compile_(h,matching=True,reclaim=True,dirty=True) + finally: + for process in engine.oracles: + process.stdin.close();assert process.wait(timeout=10)==0 + result.pop('seconds',None);result['scalar']=engine.graph(h).verify() + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + (work/'word.json.gz').write_bytes(gzip.compress(raw,mtime=0)) + (work/'compiler.json').write_text(json.dumps(result,indent=2)+'\n') + print('PASS compiled envelope-balanced axis',h,result['roles'],flush=True) + +if __name__=='__main__': + p=argparse.ArgumentParser();p.add_argument('--h',type=int,choices=(23,25),required=True);p.add_argument('--work',type=Path,required=True);args=p.parse_args();compile_axis(args.h,args.work) diff --git a/references/frame-compiler/pr82/research/envelope-balanced/flag_engine.py b/references/frame-compiler/pr82/research/envelope-balanced/flag_engine.py new file mode 100644 index 0000000000..d210d9336b --- /dev/null +++ b/references/frame-compiler/pr82/research/envelope-balanced/flag_engine.py @@ -0,0 +1,312 @@ +# Coordinate-conjugated oracle pricing by Rohan Arun with OpenAI Codex. +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(index[int(i)]):s for i,s in word['sources'].items()} + v=word['v'];word['scatter']=[[v+index[a-v],b] for a,b in word['scatter']] + word['outputs']=[[s,g,perm[c],sorted(perm[x] for x in triple)] for s,g,c,triple in word['outputs']] + return word + +def exact(profiles): + cert=json.loads((HERE/'certificate.json').read_text()) + N=comb(23,3)*comb(25,3);m=575;W=2*N+sum(N//p['v']*p['R'] for p in profiles) + L=sum(N//p['v']*p['loss'] for p in profiles) + rows=Counter({1:19*N,21:2*N,17:2*N,481:2*N}) + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 and p['v']==comb(h,3) + assert sum(t*n for t,n in enumerate(p['blocks']))==h*p['R']+h*(h-1)==p['rank_sum'] + rows.update({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + rows[h]+=bank;rows[m-2*h]+=bank;rows[1]+=2*N;rows[h-2]+=2*N + bit=dict(m=m,N=N,W=W,L=L,total_rank=sum(t*n for t,n in rows.items()),child_multiplicities=dict(sorted(rows.items()))) + assert bit['total_rank']==m*W-N+L + assert arithmetic.js(bit)==cert['bit'] + saving=Q(cert['bit_saving']);moment=refine.exact_moment(m,W,rows,saving) + rejected=refine.exact_moment(m,W,rows,saving+Q(1,10**18)) + assert moment['upper']<11 + assert Q(cert['kappa'])>Q(old['kappa']) + print('PASS exact conditional kappa',result['kappa'],'47 constraints, seven margins, independent bounds and next-grid controls') + +def verify(regenerate=False): + sources();profiles=[] + with tempfile.TemporaryDirectory(prefix='coordinate-flags-') as directory: + work=Path(directory);exe=work/'profiles' + subprocess.run(['c++','-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'scripts/experiments/binary_frame_profiles.cpp'),'-o',str(exe)],check=True) + if regenerate: + jobs=[] + for h in (23,25): + axis=work/str(h);axis.mkdir() + jobs.append(subprocess.Popen([sys.executable,str(HERE/'compiler.py'),'--h',str(h),'--work',str(axis)])) + for job in jobs:assert job.wait()==0,'Portable compiler regeneration failed' + for h in (23,25): + assert gzip.decompress((work/str(h)/'word.json.gz').read_bytes())==gzip.decompress(original_path(h).read_bytes()),'Regenerated physical word changed' + print('PASS portable deterministic regeneration of both unpermuted words',flush=True) + for h in (23,25): + original=json.loads(gzip.decompress((original_path(h)).read_bytes())) + config=json.loads((HERE/f'order-{h}.json').read_text());word=relabel(original,config) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + assert raw==gzip.decompress((HERE/f'word-{h}.json.gz').read_bytes()) + path=work/f'word-{h}.json';path.write_bytes(raw);checked=replay(path) + stored=json.loads((HERE/f'replay-{h}.json').read_text());assert arithmetic.js(checked)==stored['replay'] + trans=work/f'transitions-{h}.bin';receipt=prepare(path,trans);assert arithmetic.js(receipt)==stored['transitions'] + subprocess.run([str(exe),str(trans)],check=True) + profile=json.loads(Path(str(trans)+'.profiles.json').read_text());assert profile==json.loads((HERE/f'profiles-{h}.json').read_text()) + profiles.append(profile);print('PASS complete relabelled physical word and profile',h,flush=True) + exact(profiles) +if __name__=='__main__': + import argparse + parser=argparse.ArgumentParser();parser.add_argument('--regenerate',action='store_true');args=parser.parse_args();verify(args.regenerate) diff --git a/references/frame-compiler/pr84/.gitattributes b/references/frame-compiler/pr84/.gitattributes new file mode 100644 index 0000000000..6ef147f1f0 --- /dev/null +++ b/references/frame-compiler/pr84/.gitattributes @@ -0,0 +1,23 @@ +* text=auto eol=lf +*.pdf binary +# Unified diffs require a leading space on blank context lines. +*.patch -whitespace +# Preserve the exact upstream bytes, including original whitespace. +upstream/** -whitespace +# Preserve the exact pinned third-party proof snapshots and notices. +references/copied-centers/pr29/** -whitespace +references/copied-centers/pr33/** -whitespace +references/semantic-bulk/** -whitespace + +# Immutable contributor archives retain original CRLF and whitespace bytes. +references/frame-compiler/pr69/** -text -whitespace +references/frame-compiler/pr70/** -text -whitespace +references/frame-compiler/pr71/** -text -whitespace + +# Preserve original contributor and frozen discovery bytes. +references/frame-compiler/pr74/** -text -whitespace +references/frame-compiler/pr78/** -text -whitespace +references/frame-compiler/pr79/** -text -whitespace +references/frame-compiler/indexed-r5/** -text -whitespace +# Byte-identical credited PR74 extracts retain original trailing blank lines. +scripts/experiments/indexed_cycle_nodeops.py -whitespace diff --git a/references/frame-compiler/pr84/.github/workflows/verify.yml b/references/frame-compiler/pr84/.github/workflows/verify.yml new file mode 100644 index 0000000000..58b21a1373 --- /dev/null +++ b/references/frame-compiler/pr84/.github/workflows/verify.yml @@ -0,0 +1,63 @@ +name: Verify research artifacts + +on: + push: + pull_request: + workflow_dispatch: + +permissions: + contents: read + +jobs: + verify: + runs-on: ubuntu-24.04 + timeout-minutes: 20 + strategy: + fail-fast: false + matrix: + python-version: ['3.11', '3.13', '3.14'] + group: [community, producers, certificates, ternary, research, tests, strips, clones, positive, joint, pair, balanced, indexed] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: ${{ matrix.python-version }} + - name: Install headers for the exact enlarged-frame profiler + if: matrix.group == 'positive' + run: | + if ! test -f /usr/include/boost/multiprecision/cpp_int.hpp; then + sudo apt-get update + sudo apt-get install -y libboost-dev + fi + - name: Check arithmetic, source hashes, finite identities, and patches + run: make verify-${{ matrix.group }} + - name: Require reproducible certificates and patches + run: git diff --exit-code + + formal: + runs-on: ubuntu-24.04 + timeout-minutes: 30 + strategy: + fail-fast: false + matrix: + package: [historical, gaussian, matrix] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: '3.13' + - name: Install elan; each project pins its Lean toolchain + run: | + curl --proto '=https' --tlsv1.2 -sSf https://raw.githubusercontent.com/leanprover/elan/0e36a07b9bbcc5381fa6250df109f9a4f94d7bac/elan-init.sh -o /tmp/elan-init.sh + sh /tmp/elan-init.sh -y --default-toolchain none + echo "$HOME/.elan/bin" >> "$GITHUB_PATH" + - name: Fetch pinned Mathlib build cache + if: matrix.package == 'historical' + working-directory: formal/lean + run: lake exe cache get + - name: Check formal package and theorem axiom dependencies + run: make formal-${{ matrix.package }}-verify diff --git a/references/frame-compiler/pr84/LICENSE b/references/frame-compiler/pr84/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/pr84/LICENSE @@ 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Keep local verification sequential: +# different groups regenerate certificates that another group may read. +verify: + $(MAKE) verify-community + $(MAKE) verify-producers + $(MAKE) verify-certificates + $(MAKE) verify-ternary + $(MAKE) verify-research + $(MAKE) verify-strips + $(MAKE) verify-clones + $(MAKE) verify-positive + $(MAKE) verify-joint + $(MAKE) verify-pair + $(MAKE) verify-balanced + $(MAKE) verify-indexed + $(MAKE) verify-tests + +verify-community: community-audit-check community-followup-check copied-reversed-producer copied-reversed-check copied-fixed-reversed-producer copied-fixed-reversed-check + $(MAKE) copied-fixed-verify + $(MAKE) climbed-48-verify + +verify-producers: + $(MAKE) copied-centers-verify + $(MAKE) structured-bulk-verify + $(MAKE) endpoint-gauge-producer endpoint-gauge-certificate + $(MAKE) partial-swap-producer partial-swap-certificate + +verify-certificates: + python3 scripts/prime_field_network.py + python3 scripts/complex_network.py + python3 scripts/fast_gaussian.py + $(MAKE) batched-certificate batched-patch + python3 scripts/certify.py + python3 scripts/search_network.py + python3 scripts/make_patch.py + python3 scripts/nonadjacent.py + python3 scripts/make_nonadjacent_patch.py + python3 scripts/tune_routing.py + python3 scripts/research_networks.py + python3 scripts/search_network_variants.py + python3 scripts/block_label_targets.py + python3 scripts/audit_block_labels.py + python3 scripts/audit_additive_labels.py + python3 scripts/small_block_witness.py + python3 scripts/incidence_network.py + python3 scripts/make_incidence_patch.py + python3 scripts/search_incidence_partitions.py + python3 scripts/dag_network.py + python3 scripts/make_dag_patch.py + python3 scripts/shared_point_network.py + python3 scripts/make_shared_point_patch.py + python3 scripts/paired_network.py + python3 scripts/make_paired_patch.py + python3 scripts/prepare_layers.py + python3 scripts/audit_sparse_fusion.py + python3 scripts/audit_fused_block.py + python3 scripts/audit_short_guards.py + python3 scripts/audit_gather_schedules.py + python3 scripts/audit_coded_carries.py + python3 scripts/audit_cancellation.py + python3 scripts/audit_joint_frames.py + python3 scripts/audit_compact_controls.py + python3 scripts/compact_control_layer.py + python3 scripts/make_compact_control_patch.py + python3 scripts/audit_scratch_pooling.py + python3 scripts/reuse_network.py + python3 scripts/make_reuse_patch.py + +verify-ternary: + python3 scripts/complex_compression.py + python3 scripts/make_complex_compression_patch.py + python3 scripts/audit_ternary_side.py + python3 scripts/make_ternary_patch.py + +verify-tests: + python3 scripts/run_isolated_tests.py + git apply --check --directory=upstream patches/frozen-154.patch + git apply --check --directory=upstream patches/balanced-153.patch + git apply --check --directory=upstream patches/same-network-129.patch + git apply --check --directory=upstream patches/h46-111.patch + git apply --check --directory=upstream patches/h46-109.patch + git apply --check --directory=upstream patches/h46-108.patch + git apply --check --directory=upstream patches/h46-rational.patch + git apply --check --directory=upstream patches/nonadjacent-layout.patch + git apply --check --directory=upstream patches/frozen-nonadjacent-107.patch + git apply --check --directory=upstream patches/h46-nonadjacent-78.patch + git apply --check --directory=upstream patches/h46-nonadjacent-76.patch + git apply --check --directory=upstream patches/h46-shared-side-75.patch + git apply --check --directory=upstream patches/h46-incidence-67.patch + git apply --check --directory=upstream patches/h46-dag-63.patch + git apply --check --directory=upstream patches/h46-shared-point.patch + git apply --check --directory=upstream patches/h50-paired-59.patch + git apply --check --directory=upstream patches/compact-control-34.patch + git apply --check --directory=upstream patches/complex-compression-31.patch + git apply --check --directory=upstream patches/ternary-30.patch + git apply --check --directory=upstream patches/batched-23.patch + +note: + mkdir -p artifacts + tectonic --outdir artifacts notes/parameter-note.tex + +audit-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/nonadjacent-axis-note.tex + +tuned-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/routing-tuned-note.tex + +reuse-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/stage-reuse-note.tex + +incidence-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/incidence-note.tex + +dag-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/dag-note.tex + +shared-point-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/shared-point-note.tex + +paired-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/paired-note.tex + +compact-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/compact-control-note.tex + +complex-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/complex-compression-note.tex + +ternary-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/ternary-note.tex + +fetch: + python3 scripts/fetch_upstream.py + +.PHONY: batched-certificate batched-patch batched-note +PDFLATEX ?= pdflatex +TEX_ENGINE ?= pdflatex +TECTONIC ?= tectonic + +batched-certificate: + python3 scripts/controlled_bit_rank_moment.py --output certificates/controlled-bit-rank-moment.json > /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify + +.PHONY: balanced-split-verify verify-balanced +balanced-split-verify: + python3 scripts/experiments/verify_balanced_split.py + python3 scripts/experiments/audit_balanced_split_completion.py + python3 scripts/experiments/audit_balanced_split_exchange.py + python3 -m unittest discover -s tests -p 'test_balanced_split*.py' -v + +verify-balanced: balanced-split-verify + +.PHONY: indexed-cycle-verify verify-indexed +indexed-cycle-verify: + python3 scripts/experiments/verify_indexed_cycle.py + python3 scripts/experiments/audit_indexed_cycle_completion.py + python3 scripts/experiments/audit_indexed_cycle_exchange.py + python3 scripts/experiments/audit_indexed_cycle_cycles.py + python3 scripts/experiments/audit_indexed_cycle_retired.py + python3 scripts/experiments/audit_indexed_cycle_pending.py + python3 -m unittest discover -s tests -p 'test_indexed_cycle*.py' -v + +verify-indexed: indexed-cycle-verify diff --git a/references/frame-compiler/pr84/NOTICE b/references/frame-compiler/pr84/NOTICE new file mode 100644 index 0000000000..70f4d45ed6 --- /dev/null +++ b/references/frame-compiler/pr84/NOTICE @@ -0,0 +1,339 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Balanced coarse split composition (2026-10-08) +--------------------------------------------- +Eumemic / @eumemic supplied PR69's balanced coarse sums, with OpenAI Codex +assistance. Alejandro Zarzuelo Urdiales / @alejandrozu supplied PR70's bounded +carry-exchange strategy with the AI disclosures retained in the source archive. +Chafik Boukhalfa / @chafreaky, with OpenAI Codex assistance, selected the row/ +half-plane coarse rules, future-compatible unit completion, exact integer-price +carry adaptation, composition and this certificate package. The PR71 anchored +split vector, schedules, arithmetic, pending controls and their contributor +chain are retained as credited above. Original PR69/70 sources, licenses and +notices and the complete published PR71 baseline are preserved under +references/frame-compiler. All earlier notices remain applicable. + +Indexed two-cycle composition (2026-10-08): Chafik Boukhalfa with OpenAI Codex assistance. Thomas DiFiore (@tomdif, PR74) supplied exact node ordering and coordinate relabeling, including the selected h25 permutation. Rohan Arun (@rohanarun, PR78) supplied the coordinate-flag search idea. Balanced multi-splits, exact retired/pending indices, bounded two-cycles, late-output routing and selected-coordinate certification compose inherited PR57/59/60/62/63/65/67/68/69/70/71/79 work. All original authorship, Apache-2.0 and AI disclosures remain in unchanged contributor archives. diff --git a/references/frame-compiler/pr84/README.md b/references/frame-compiler/pr84/README.md new file mode 100644 index 0000000000..d48659c758 --- /dev/null +++ b/references/frame-compiler/pr84/README.md @@ -0,0 +1,188 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: balanced coarse split frames + +The [balanced-split proof and reproduction guide](research/balanced-split/README.md) +gives **κ=25872812736433/500000000000000000=5.1745625472866e-5**, approximately +**0.6437453019850683%** above the complete published PR71 witness. It composes +PR69 balanced coarse sums and a bounded PR70 carry exchange with PR71's +anchored split graph, future unit completion and profile-cost pending controls. +All actual words, dirty inputs, paid profiles and 47 strict assembly constraints +are checked by `make balanced-split-verify`. This finite conditional construction +retains the inherited all-size hypotheses and contributor notices. Chafik +Boukhalfa prepared the selected composition with OpenAI Codex assistance. + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. + +### Indexed two-cycle finite witness + +[Indexed-cycle proof and evidence](research/indexed-cycle/README.md) gives κ = 261356445457/5000000000000000 with W=132466108. It combines attributed balanced multi-splits, exact frame indexes, bounded carry two-cycles, PR74 node ordering and coordinate flags; all-size transfer remains inherited. Verify with `make indexed-cycle-verify`. The comparison is to pinned historical PR74/PR79 witnesses observed 2026-10-08. diff --git a/references/frame-compiler/pr84/SOURCE.json b/references/frame-compiler/pr84/SOURCE.json new file mode 100644 index 0000000000..ba5e23e8a1 --- /dev/null +++ b/references/frame-compiler/pr84/SOURCE.json @@ -0,0 +1,597 @@ +{ + "commit": "88ca39571907343a49e97f328971ec7bcd26fbfd", + "files": { + ".gitattributes": "2d77b30caac667f81591f6afa49898e4ada61fe6d0cff83341bae986b5ebfa45", + ".github/workflows/verify.yml": "e3adcf09259520d3460ad41496ef4b2efd3046b6ece2c91e5aa35a2b9b2a38ae", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "Makefile": "11d9bd93941ff079c0d63c715253392c30a503b2975ccb2c3ab6df39a305a3a1", + "NOTICE": "7d59d255960091cbd1c62ec1e7439023599687cdfdb7059904fe56578dac2333", + "README.md": "1bf17c27f5a2142812a1002a0f50833a105d0b6cefbaa3438fb024b2bbf4262b", + "certificates/indexed-cycle-compiler.json": 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25 + }, + "word_sha256": "ec153b2cd0ef6edeb626dbb2831abc5ce7a59c99870ec6a5e08afb5a1530c845", + "copied_centers": 25, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr84/certificates/indexed-cycle-two-cycle-validation.json b/references/frame-compiler/pr84/certificates/indexed-cycle-two-cycle-validation.json new file mode 100644 index 0000000000..4a80e9d18b --- /dev/null +++ b/references/frame-compiler/pr84/certificates/indexed-cycle-two-cycle-validation.json @@ -0,0 +1,7 @@ +{ + "accepted_cycles_checked": 231, + "cases": 1204, + "duplicate_group_use_key_rejected": true, + "source_sha256": "a4a582339430662e13c905d5a4701f4e488ff1830a72dc1c71da57066ad2ea38", + "status": "PASS actual atomic two-cycle legality and adverse fixtures" +} diff --git a/references/frame-compiler/pr84/certificates/indexed-cycle-validation.json b/references/frame-compiler/pr84/certificates/indexed-cycle-validation.json new file mode 100644 index 0000000000..68d9bc8540 --- /dev/null +++ b/references/frame-compiler/pr84/certificates/indexed-cycle-validation.json @@ -0,0 +1,237 @@ +{ + "axes": { + "23": { + "profile": { + "R": 26834, + "blocks": [ + 0, + 360947, + 18308, + 10287, + 5376, + 3976, + 3779, + 2686, + 2296, + 1754, + 1371, + 1322, + 902, + 790, + 495, + 433, + 233, + 96, + 102, + 0, + 90, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 5567, + "distinct_matrices": 38555, + "field_prime": 2305843009213693951, + "frames": 65728, + "h": 23, + "loss": 506, + "rank_sum": 617688, + "v": 1771 + }, + "replay": { + "elementary_xors": 176951, + "full_basis_vectors": 30376, + "h": 23, + "histogram": { + "0": 192243, + "1": 73048, + "2": 78597, + "3": 9345, + "4": 14768, + "5": 5655, + "6": 2630, + "7": 906, + "8": 1692, + "9": 1014, + "10": 793, + "11": 207, + "12": 370, + "13": 104, + "14": 1219, + "15": 400, + "16": 493, + "17": 1036, + "18": 2643, + "19": 5609, + "21": 384, + "22": 23 + }, + "output_roles": 5336, + "rank_mass": 617688, + "roles": 26834, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 732598 + }, + "transitions": { + "R": 26834, + "copied_centers": 23, + "distinct_transitions": 163929, + "frames": 65728, + "h": 23, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 83674, + "2": 73284, + "3": 9345, + "4": 14768, + "5": 5655, + "6": 2630, + "7": 906, + "8": 1692, + "9": 1014, + "10": 793, + "11": 207, + "12": 370, + "13": 104, + "14": 1219, + "15": 400, + "16": 493, + "17": 1036, + "18": 2643, + "19": 5609, + "21": 384, + "22": 23 + }, + "rank_mass": 617688, + "singles": 15939, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 1771, + "word_sha256": "c67fb6efa490db56814c743a48044c99397f3067f0038ce80673930c2f0ed829" + } + }, + "25": { + "profile": { + "R": 35348, + "blocks": [ + 0, + 492700, + 23012, + 12086, + 6121, + 4924, + 5649, + 4980, + 3550, + 2660, + 2408, + 2123, + 1685, + 1370, + 958, + 775, + 544, + 438, + 260, + 97, + 130, + 0, + 126, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 7465, + "distinct_matrices": 48221, + "field_prime": 2305843009213693951, + "frames": 86507, + "h": 25, + "loss": 600, + "rank_sum": 884300, + "v": 2300 + }, + "replay": { + "elementary_xors": 234549, + "full_basis_vectors": 39948, + "h": 25, + "histogram": { + "0": 255645, + "1": 78977, + "2": 122604, + "3": 13298, + "4": 15384, + "5": 8687, + "6": 1876, + "7": 609, + "8": 2952, + "9": 849, + "10": 987, + "11": 156, + "12": 1101, + "13": 318, + "14": 575, + "15": 208, + "16": 1351, + "17": 472, + "18": 673, + "19": 779, + "20": 4243, + "21": 8332, + "23": 495, + "24": 25 + }, + "output_roles": 6925, + "rank_mass": 884300, + "roles": 35348, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 970396 + }, + "transitions": { + "R": 35348, + "copied_centers": 25, + "distinct_transitions": 215055, + "frames": 86507, + "h": 25, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 92777, + "2": 115704, + "3": 13298, + "4": 15384, + "5": 8687, + "6": 1876, + "7": 609, + "8": 2952, + "9": 849, + "10": 987, + "11": 156, + "12": 1101, + "13": 318, + "14": 575, + "15": 208, + "16": 1351, + "17": 472, + "18": 673, + "19": 779, + "20": 4243, + "21": 8332, + "23": 495, + "24": 25 + }, + "rank_mass": 884300, + "singles": 20700, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 2300, + "word_sha256": "ec153b2cd0ef6edeb626dbb2831abc5ce7a59c99870ec6a5e08afb5a1530c845" + } + } + }, + "bit_saving": "408390793141/7812500000000000", + "certificate_sha256": "c2ca8f70fd7bfc962b675d4784941a93d4d756530d7b4ec26a116bdb2c6f8315", + "kappa": "261356445457/5000000000000000", + "margins": 7, + "producer_words_regenerated_and_matched": true, + "scope": "Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.", + "source_binding": "Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.", + "status": "PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly", + "strict_constraints": 47 +} diff --git a/references/frame-compiler/pr84/certificates/indexed-cycle-word-23.json.gz b/references/frame-compiler/pr84/certificates/indexed-cycle-word-23.json.gz new file mode 100644 index 0000000000..3260f9aef6 Binary files /dev/null and b/references/frame-compiler/pr84/certificates/indexed-cycle-word-23.json.gz differ diff --git a/references/frame-compiler/pr84/certificates/indexed-cycle-word-25.json.gz b/references/frame-compiler/pr84/certificates/indexed-cycle-word-25.json.gz new file mode 100644 index 0000000000..074ec5c508 Binary files /dev/null and b/references/frame-compiler/pr84/certificates/indexed-cycle-word-25.json.gz differ diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/EXPERIMENT.txt b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/EXPERIMENT.txt new file mode 100644 index 0000000000..ad69d585b0 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/EXPERIMENT.txt @@ -0,0 +1 @@ +Compose Thomas DiFiore PR74 exact node-envelope renumbering with independently audited two-cycle matching, future completion, exact indexed reclamation, and selected h25 late output-use routing. Test six grouping structures and three coarse-sum orientations per dimension. Canary retains unchanged earlier cycles112 graph/schedule and hashes. Every new scalar graph and dirty physical word is independently checked and CPU CRT profiles/certificates are rebuilt. Imported PR74 functions and source/credits are preserved exactly. No imported claim is re-verified as a gate. diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/LICENSE b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. 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a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/profiles.json b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/profiles.json new file mode 100644 index 0000000000..7baddf40c6 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/profiles.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27285,"loss":506,"rank_sum":628061,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38513,"crt_matrices":5538,"crt_disagreements":0,"blocks":[0,356669,20912,7996,5407,4043,3702,3146,2579,1990,1706,1444,980,839,542,483,239,205,49,97,0,23,0,0]} diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/replay.json b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/replay.json new file mode 100644 index 0000000000..d37ffd1add --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/replay.json @@ -0,0 +1,34 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27285, + "output_roles": 5336, + "elementary_xors": 160435, + "word_length": 666534, + "full_basis_vectors": 30827, + "rank_mass": 628061, + "histogram": { + "1": 58281, + "0": 171307, + "2": 80793, + "4": 14511, + "3": 10007, + "5": 6429, + "6": 2036, + "8": 1110, + "10": 535, + "9": 471, + "12": 661, + "14": 1868, + "13": 193, + "16": 431, + "11": 120, + "17": 574, + "18": 3412, + "15": 334, + "19": 6482, + "22": 23, + "21": 393, + "7": 627 + } +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/result.json b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/result.json new file mode 100644 index 0000000000..349e949822 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/result.json @@ -0,0 +1,19 @@ +{ + "h": 23, + "roles": 27285, + "stats": { + "augmentations": 13, + "regions": 59801, + "matched": 41730, + "multi_node_regions": 8694, + "carry_exchanges": 644, + "carry_two_cycles": 52, + "live_anchor_candidates": 72361, + "reclaimed": 2125, + "clearing_xors": 3916, + "live_anchor_xors": 76 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "word_sha256": "3f58db33edc2059ad6ca01cf8c36dd8cd8ae12149e1072e1f42757ca4ef17b82" +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/profiles.json b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/profiles.json new file mode 100644 index 0000000000..2be4368700 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/profiles.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35684,"loss":600,"rank_sum":892700,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":51168,"crt_matrices":7278,"crt_disagreements":0,"blocks":[0,491871,27309,10127,7839,5460,4947,4006,3802,2943,2456,2025,1787,1423,1124,867,560,478,221,170,46,59,0,25,0,0]} diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/replay.json b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/replay.json new file mode 100644 index 0000000000..3ec3c54dc6 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/replay.json @@ -0,0 +1,36 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 35684, + "output_roles": 6925, + "elementary_xors": 224161, + "word_length": 928844, + "full_basis_vectors": 40284, + "rank_mass": 892700, + "histogram": { + "1": 77041, + "0": 238437, + "2": 118217, + "3": 13314, + "4": 18459, + "6": 3215, + "5": 8388, + "7": 948, + "8": 1195, + "9": 721, + "10": 828, + "12": 708, + "13": 182, + "14": 653, + "16": 2171, + "18": 506, + "19": 981, + "17": 633, + "15": 187, + "11": 15, + "20": 4464, + "21": 8405, + "24": 25, + "23": 463 + } +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/result.json b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/result.json new file mode 100644 index 0000000000..50b259fcd7 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/result.json @@ -0,0 +1,19 @@ +{ + "h": 25, + "roles": 35684, + "stats": { + "augmentations": 16, + "regions": 84843, + "matched": 60971, + "multi_node_regions": 11575, + "carry_exchanges": 1000, + "carry_two_cycles": 62, + "live_anchor_candidates": 98464, + "reclaimed": 3263, + "clearing_xors": 6027, + "live_anchor_xors": 132 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "word_sha256": "7c60369042197c356dfac3516ae396d68dc92edbc5824b6078dce0e6676f7f79" +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/batch.py b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/batch.py new file mode 100644 index 0000000000..1f994fa396 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/batch.py @@ -0,0 +1,113 @@ +"""Durable independent CPU search over pinned current two-cycle construction. +Each accepted case regenerates and independently replays the literal word, +reconstructs paid frames, computes CPU CRT profiles and exact inequalities. +""" +from pathlib import Path +from hashlib import sha256 +from concurrent.futures import ProcessPoolExecutor,as_completed +import argparse,ast,cProfile,gzip,importlib.util,json,os,pstats,subprocess,sys,time,types +ROOT=Path(__file__).resolve().parent +sys.path.insert(0,str(ROOT/'scripts/experiments')) + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m + +def generate(h,groups,profile=False,mode="baseline"): + started=time.monotonic();out=ROOT/'results'/f'{h}-{groups}-{mode}';out.mkdir(parents=True,exist_ok=True) + compiler=load('search_compiler',ROOT/'scripts/experiments/compiler.py') + source=(ROOT/'research/pair-assembly/pair_graph.py').read_text() + donor=ROOT/'references/pr69/balanced_coarse_compiler.py' + constants={n.targets[0].id:ast.literal_eval(n.value) for n in ast.parse(donor.read_text()).body if isinstance(n,ast.Assign) and isinstance(n.targets[0],ast.Name) and n.targets[0].id in ('BEFORE','AFTER')} + replacement=constants['AFTER'];needle='columns = [self.total([e(a,b) for a in groups[i]]) for b in groups[j]]' + orientation=mode.removeprefix('envelope-') if mode.startswith('envelope-') else ('half' if h==23 else 'row') + if orientation=='half': + replacement=replacement.replace(needle,'columns = ([self.total([e(a,b) for a in groups[i]]) for b in groups[j]] if i+j < ng-1 else [self.total([e(a,b) for b in groups[j]]) for a in groups[i]])') + elif orientation=='row':replacement=replacement.replace(needle,'columns = [self.total([e(a,b) for b in groups[j]]) for a in groups[i]]') + assert source.count(constants['BEFORE'])==1 + graph=types.ModuleType('balanced_graph');graph.__file__=str(ROOT/'research/pair-assembly/pair_graph.py');exec(compile(source.replace(constants['BEFORE'],replacement),graph.__file__,'exec'),graph.__dict__) + original=graph.circuit_class + def subclass(dim): + parent=original(dim) + class Split(parent): + def grouping(self,points): + result=super().grouping(points);choices=[int(x) for x in groups];choice=choices[self._level] if self._level3 and choice: + first,mid,last=0,(len(result)-1)//2,len(result)-1 + requested={1:[first],2:[mid],3:[last],4:[first,mid],5:[first,last],6:[mid,last],7:[first,mid,last],8:[first,first+1],9:[last-1,last]}[choice] + chosen=[] + for k in requested: + if k not in chosen and 0<=k1:hi=mid + else:raise ArithmeticError('Enclosure inconclusive') + a=Q(lo,den);bridge=deepcopy(baseline['finite_bridge']);bridge['bit']['W']=p['W'] + bridge['bit']['wire_bits']=p['W'].bit_length() + bridge['rows']['coefficient']=sum(bridge[name]['halving_degree']*bridge[name]['wire_bits'] for name in ('bit','complex')) + bridge['rows']['degree_gap']=Q(bridge['rows']['degree'])-Q(51,25)*bridge['rows']['coefficient'] + bridge['rows']['suffix_slope']=4*bridge['rows']['degree'] + accepted=refine.exact_moment(m,p['W'],rows,a);rejected=refine.exact_moment(m,p['W'],rows,Q(hi,den));assert accepted['upper']<1prior and best['prior65_moment']['lower']>1 + for r in rows: + r['moment_at_best_bit']=refine.exact_moment(m,r['bit']['W'],r['bit']['child_multiplicities'],best['bit_saving']) + output={'verified_baseline':{'pr':65,'commit':'49e84f939d15b618b50714eb039cabf97c74256a','kappa':prior},'best':best,'rows':rows,'cases':len(rows)} + (HERE/'fine-pair-comparison.json').write_text(json.dumps(refine.arithmetic.js(output),indent=2,sort_keys=True)+'\n') + (HERE/'selected-exact-result.json').write_text(json.dumps(refine.arithmetic.js(best),indent=2,sort_keys=True)+'\n') + print('BEST',json.dumps({'pair':best['pair'],'kappa':str(best['kappa']),'bit_saving':str(best['bit_saving']),'W':best['bit']['W'],'gain_percent_vs_verified65':float(100*(best['kappa']/prior-1))},sort_keys=True),flush=True) diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/nodeops.py b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/nodeops.py new file mode 100644 index 0000000000..fa6164310d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/nodeops.py @@ -0,0 +1,40 @@ +# Exact function extracts from Thomas DiFiore PR74,3f78d8967c009153f2df5c6a6577b6ab1d37e2ca. Apache-2.0; original source and notices retained. + +def reorder(c): + groups={} + for x in sorted(c.active): + if c.args[x]: groups.setdefault((c.core[x],c.union[x]),[]).append(x) + def key(item): + (core,cover),nodes=item + return cover.bit_count()-core.bit_count(),-core,cover,min(nodes) + ids=list(range(len(c.inputs)+1))+[x for _,nodes in sorted(groups.items(),key=key) for x in nodes] + mapping={x:i for i,x in enumerate(ids)} + args,core,cover,provenance=c.args,c.core,c.union,c.provenance + c.args=[tuple(mapping[y] for y in args[x]) if args[x] else None for x in ids] + c.core=[core[x] for x in ids];c.union=[cover[x] for x in ids] + c.provenance=[provenance[x] for x in ids] + c.active={mapping[x] for x in c.active};c.outputs={k:mapping[v] for k,v in c.outputs.items()} + c.support_in.cache_clear() + c.verify() + return c + + +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/original/carry_cycle_compiler.py b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/original/carry_cycle_compiler.py new file mode 100644 index 0000000000..d883cbc71d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/original/carry_cycle_compiler.py @@ -0,0 +1,338 @@ +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path('/Users/chafreaky/Documents/personal/integer-mult-research-20261008/joint-reclaim/references/frame-compiler/pr48') +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": "41187950749917624099/1000000000000000000000000", + "cell_above_band": "666666666665666652937349833360791967/1333388250600666556832132000000000000", + "compact_leaf": "26927049500082375901/1000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "13729317166639208033/333347062650166639208033", + "epsilon_positive": "333333333333000000000000/333347062650166639208033", + "g1_above_kappa": "3408408254232349301008147/3333470626501666392080330000000000000", + "g2_above_kappa": "4241/2500000000000", + "g3_above_kappa": "74937627730682908927817/3333470626501666392080330000000000000", + "g4_above_kappa": "4241/2500000000000", + "g5_above_kappa": "5299956450675231223831763/13333882506006665568321320000000000000", + "g6_above_kappa": "11966897703678564007992423/13333882506006665568321320000000000000", + "g7_above_kappa": "3333196040161742016173902349301008147/3333470626501666392080330000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "13729317166639208033/333347062650166639208033", + "lambda_above_internal": "82375901/2000000000000000000000000", + "lambda_above_sigma": "61024099000082375901/2000000000000000000000000", + "lambda_above_tau": "82375901/2000000000000000000000000", + "lambda_prime_above_lambda": "82375901/2000000000000000000000000", + "lambda_prime_below_one": "41187950499917624099/1000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "21966907133275670202633360791967/533355300240266622732852800000000000", + "phase_leaf_above_bit": "53854099/2000000000000", + "phase_local": "109834536999766601613833360791967/2666776501201333113664264000000000000", + "prime_interval_packing": "13729317166639208033/333347062650166639208033", + "q_below_internal": "82375901/1000000000000000000000000", + "q_below_leaf": "26927049500082375901/1000000000000000000000000", + "q_below_reservations": "1/4000000000000", + "q_positive": "41187950499917624099/1000000000000000000000000", + "record_suffix": "13729317166639208033/333347062650166639208033", + "row_product_gap": "6548/25", + "short_record_fallback": "666639206901368489075295096355187267/666694125300333278416066000000000000", + "small_field_exposure": "1/1000000000000" + }, + "finite_bridge": { + "bit": { + "W": 177530859, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000000000, + "cutoff_log2_input": { + "alpha": 5956134977, + "compact": 23824539905, + "geometry": 3999930893196446780, + "guard": 4283152, + "log_p": 25, + "normalization": 14000000000000000000, + "period": 47649079809, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000000000, + "powers": { + "alpha": { + "exponent": 725614180574271, + "rhs": 112000000000000154416, + "rhs_bits": 67 + }, + "compact": { + "exponent": 725614180574271, + "rhs": 448000000000000617600, + "rhs_bits": 69 + }, + "leaf": { + "exponent": 666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 725614180574271, + "rhs": 224000000000000308760, + "rhs_bits": 68 + }, + "rows": { + "exponent": 725614180574271, + "rhs": 112000000000000154416000, + "rhs_bits": 77 + } + } + }, + { + "log2_input": 28000000000000000000, + "powers": { + "alpha": { + "exponent": 1451228361148543, + "rhs": 224000000000000154416, + "rhs_bits": 68 + }, + "compact": { + "exponent": 1451228361148543, + "rhs": 896000000000000617600, + "rhs_bits": 70 + }, + "leaf": { + "exponent": 1333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1451228361148543, + "rhs": 448000000000000308760, + "rhs_bits": 69 + }, + "rows": { + "exponent": 1451228361148543, + "rhs": 224000000000000154416000, + "rhs_bits": 78 + } + } + }, + { + "log2_input": 56000000000000000000, + "powers": { + "alpha": { + "exponent": 2902456722297087, + "rhs": 448000000000000154416, + "rhs_bits": 69 + }, + "compact": { + "exponent": 2902456722297087, + "rhs": 1792000000000000617600, + "rhs_bits": 71 + }, + "leaf": { + "exponent": 2666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2902456722297087, + "rhs": 896000000000000308760, + "rhs_bits": 70 + }, + "rows": { + "exponent": 2902456722297087, + "rhs": 448000000000000154416000, + "rhs_bits": 79 + } + } + }, + { + "log2_input": 112000000000000000000, + "powers": { + "alpha": { + "exponent": 5804913444594174, + "rhs": 896000000000000154416, + "rhs_bits": 70 + }, + "compact": { + "exponent": 5804913444594174, + "rhs": 3584000000000000617600, + "rhs_bits": 72 + }, + "leaf": { + "exponent": 5333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5804913444594174, + "rhs": 1792000000000000308760, + "rhs_bits": 71 + }, + "rows": { + "exponent": 5804913444594174, + "rhs": 896000000000000154416000, + "rhs_bits": 80 + } + } + }, + { + "log2_input": 224000000000000000000, + "powers": { + "alpha": { + "exponent": 11609826889188348, + "rhs": 1792000000000000154416, + "rhs_bits": 71 + }, + "compact": { + "exponent": 11609826889188348, + "rhs": 7168000000000000617600, + "rhs_bits": 73 + }, + "leaf": { + "exponent": 10666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11609826889188348, + "rhs": 3584000000000000308760, + "rhs_bits": 72 + }, + "rows": { + "exponent": 11609826889188348, + "rhs": 1792000000000000154416000, + "rhs_bits": 81 + } + } + }, + { + "log2_input": 448000000000000000000, + "powers": { + "alpha": { + "exponent": 23219653778376697, + "rhs": 3584000000000000154416, + "rhs_bits": 72 + }, + "compact": { + "exponent": 23219653778376697, + "rhs": 14336000000000000617600, + 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witness; inherited all-size transfer remains assumed" +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/check.py b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/check.py new file mode 100644 index 0000000000..0630cfc19a --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/check.py @@ -0,0 +1,104 @@ +#!/usr/bin/env python3 +"""Screen complete paid profiles from independently replayed axis constructions.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions required') +from pathlib import Path +from collections import Counter +from fractions import Fraction as Q +import importlib.util,argparse,json,subprocess,tempfile,hashlib,os,shlex +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +from producer import check_sources +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m +exact=load('candidate_exact',ROOT/'research/rank-pair-refinement/refine.py') +balanced=load('candidate_assembly',DEP/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') + +def profile(path): + v=json.loads(Path(path).read_text()) + return v['profile'] if 'profile' in v else v + +def calculate(first,second): + profiles=[profile(first),profile(second)] + N=4073300;m=575 + assert [p['h'] for p in profiles]==[23,25] + W=2*N+sum(N//p['v']*p['R'] for p in profiles) + parts={'data':Counter({1:18*N,21:2*N,17:2*N,481:2*N}),'endpoint_copy':Counter({1:N})} + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 + assert p['rank_sum']==h*p['R']+p['loss']==sum(t*n for t,n in enumerate(p['blocks'])) + assert p['loss']==h*(h-1) + parts[f'internal_{h}']=Counter({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + parts[f'exterior_{h}']=Counter({h:bank,m-2*h:bank}) + parts[f'growth_{h}']=Counter({1:2*N,h-2:2*N}) + rows=sum(parts.values(),Counter());assert sum(t*n for t,n in rows.items())==m*W-1846900 + lo,hi,grid=1,71700000000000,10**18 + while lo+11 + result.update(status='Verified finite conditional witness; inherited all-size transfer remains assumed', + source_manifest_sha256=hashlib.sha256((HERE/'SOURCE.json').read_bytes()).hexdigest(), + axes=axes,eventual_bounds=balanced.cutoffs(result['finite_bridge'],result['assembly']), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113',pr71_kappa=Q(previous['kappa']), + relative_gain_pr71=result['kappa']/Q(previous['kappa'])-1, + pr71_complete_profile_exclusion_lower=old_lower)) + result=arithmetic.js(result) + path=HERE/'certificate.json' + if record:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:assert result==json.loads(path.read_text()) + print('PASS exact moment, next-grid exclusions, 47 inequalities and seven margins',flush=True) + return result + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--record',action='store_true');args=parser.parse_args();generate(args.record) diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/producer.py b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/producer.py new file mode 100644 index 0000000000..8d68303a3b --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/producer.py @@ -0,0 +1,132 @@ +#!/usr/bin/env python3 +"""Balanced coarse sums + anchored split/live frames + core ordering and coordinates. + +Composition for Thomas DiFiore with OpenAI Codex assistance. Apache-2.0. +PR69 coarse sums: eumemic. PR71 split/live composition: Chafik Boukhalfa. +Graph: Avi Eisenberg PR62; split operation: Rohan Garg PR59; reclamation: +Rohan Arun PR65/67, Dominik Scholz PR63/68, eumemic PR57. Original notices +and exact sources are retained under references/frame-compiler/pr69 and pr71. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +from hashlib import sha256 +import argparse,ast,gzip,importlib.util,json,types +from concurrent.futures import ProcessPoolExecutor +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +import split_pair_graph as provider +import split_pair_compiler as ancestor +from binary_frame_replay import replay + + +def check_sources(): + for folder in (DEP,ROOT/'references/frame-compiler/pr69'): + manifest=json.loads((folder/'SOURCE.json').read_text()) + for name,digest in manifest['files'].items(): + assert sha256((folder/name).read_bytes()).hexdigest()==digest,name + manifest=json.loads((HERE/'SOURCE.json').read_text()) + required={str((HERE/name).relative_to(ROOT)) for name in ('producer.py','check.py','graph_audit.py','independent_check.py','selection.json')} + assert required <= set(manifest['files']), 'Incomplete selected source closure' + for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + + +def reorder(c): + groups={} + for x in sorted(c.active): + if c.args[x]: groups.setdefault((c.core[x],c.union[x]),[]).append(x) + def key(item): + (core,cover),nodes=item + return cover.bit_count()-core.bit_count(),-core,cover,min(nodes) + ids=list(range(len(c.inputs)+1))+[x for _,nodes in sorted(groups.items(),key=key) for x in nodes] + mapping={x:i for i,x in enumerate(ids)} + args,core,cover,provenance=c.args,c.core,c.union,c.provenance + c.args=[tuple(mapping[y] for y in args[x]) if args[x] else None for x in ids] + c.core=[core[x] for x in ids];c.union=[cover[x] for x in ids] + c.provenance=[provenance[x] for x in ids] + c.active={mapping[x] for x in c.active};c.outputs={k:mapping[v] for k,v in c.outputs.items()} + c.support_in.cache_clear() + c.verify() + return c + + +def graph(h,ordered=True): + source=Path(provider._graph.__file__).read_text() + original=ROOT/'references/frame-compiler/pr69/scripts/experiments/balanced_coarse_compiler.py' + replacements={} + for node in ast.parse(original.read_text()).body: + if isinstance(node,ast.Assign): + for target in node.targets: + if isinstance(target,ast.Name) and target.id in ('BEFORE','AFTER'): + replacements[target.id]=ast.literal_eval(node.value) + assert source.count(replacements['BEFORE'])==1 + module=types.ModuleType('balanced_split_private_graph');module.__file__=provider._graph.__file__ + exec(compile(source.replace(replacements['BEFORE'],replacements['AFTER']),module.__file__+':balanced-coarse','exec'),module.__dict__) + previous=provider._graph + try: + provider._graph=module + c=provider.graph(h) + finally: + provider._graph=previous + return reorder(c) if ordered else c + + +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + +def compile_axis(h): + check_sources() + config=json.loads((HERE/'selection.json').read_text())['axes'][str(h)] + previous_graph,previous_order=provider.graph,provider.ordered_build + # graph() calls the original provider; keep that callable private while + # the inherited driver resolves the selected composed graph dynamically. + original_graph=previous_graph + def selected_graph(dimension): + provider.graph=original_graph + try:return graph(dimension) + finally:provider.graph=selected_graph + try: + provider.graph=selected_graph + provider.ordered_build=lambda original,dimension:original + compiled,word=ancestor.compile_axis(h) + finally: + provider.graph,provider.ordered_build=previous_graph,previous_order + compiled['graph_configuration']=config + word=relabel(word,config['coordinate_permutation']) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + path=HERE/f'word-{h}.json.gz' + with path.open('wb') as stream: + with gzip.GzipFile(filename='',fileobj=stream,mode='wb',mtime=0) as archive:archive.write(raw) + receipt=replay(path) + assert sha256(raw).hexdigest()==config['expected_word_sha256'] + axis=dict(configuration=config,compiled=compiled,replay=receipt, + word_sha256=sha256(raw).hexdigest(),gzip_sha256=sha256(path.read_bytes()).hexdigest()) + (HERE/f'axis-{h}.json').write_text(json.dumps(axis,indent=2)+'\n') + print(f'PASS fresh balanced/split/core word h={h}, roles={receipt["roles"]}',flush=True) + + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--h',type=int,choices=(23,25));args=parser.parse_args() + if args.h:compile_axis(args.h) + else: + with ProcessPoolExecutor(max_workers=2) as pool:list(pool.map(compile_axis,(23,25))) diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-23.json b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-23.json new file mode 100644 index 0000000000..013f4e59c7 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27136,"loss":506,"rank_sum":624634,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38292,"crt_matrices":5488,"crt_disagreements":0,"blocks":[0,355721,21666,6948,6524,3093,4314,2400,3266,1501,2094,1008,1374,586,732,353,307,139,62,16,0,23,0,0]} diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-25.json b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-25.json new file mode 100644 index 0000000000..1e3b6b89aa --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35744,"loss":600,"rank_sum":894200,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52202,"crt_matrices":7623,"crt_disagreements":0,"blocks":[0,490052,26188,13531,7191,4637,5355,4229,3705,2610,2620,2080,1814,1357,1070,868,612,463,233,56,141,0,71,25,0,0]} diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/selection.json b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/selection.json new file mode 100644 index 0000000000..57cf3b6b65 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/selection.json @@ -0,0 +1,86 @@ +{ + "source_pr71": "1bef94fd40a746452548c84a4a8f8834670a3113", + "source_pr69": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "axes": { + "23": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 22, + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 20, + 19, + 21 + ], + "expected_word_sha256": "8dc6696a274e70ca0af3fc49c4bdede362adaedc8dc322f335e3dab499f1ed48" + }, + "25": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 2, + 1, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "expected_word_sha256": "2c923afe366219ee3fffc9db063c91e44cdf7cbbdb62246b8e6a297dc440b577" + } + } +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/arithmetic/refine.py b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": 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0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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"scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1", + "scripts/partial_swap/graph.py": "fd8c567759e26a10d2bad05508fd0355eb70fb116664d4e06e1858d0d8cb2ef9", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + } + }, + "status": "Conditional exact arithmetic witness; general transfer proofs are dependencies" +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py b/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis 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"scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + }, + "integration_note": "Against main d55bcd62, binary_io.hpp adds only six standard-library includes. Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + } + }, + "gzip_sha256": "4629d45d5074f87706db46be3aa3cd369071cd215bc6560d641115aadcce54a0", + "word_sha256": "bd0cbf73756f2e4f8d3879ec6c7a194990eb9ec40aaf3580bdded6994798d920" + }, + "25": { + "compiled": { + "h": 25, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 36586, + "baseline_pr48_roles": 48329, + "histogram": { + "1": 55478, + "0": 416276, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + }, + "rank_mass": 915250, + "elementary_xors": 205650, + "stats": { + "augmentations": 286, + "regions": 73695, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json new file mode 100644 index 0000000000..346cf87ea3 --- /dev/null +++ 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mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": 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}, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr84/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + "exponent": 5333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5715743812, + "rhs": 1792000000313576, + "rhs_bits": 51 + }, + "rows": { + "exponent": 5715743812, + "rhs": 896000000156824000, + "rhs_bits": 60 + } + } + }, + { + "log2_input": 224000000000000, + "powers": { + "alpha": { + "exponent": 11431487624, + "rhs": 1792000000156824, + "rhs_bits": 51 + }, + "compact": { + "exponent": 11431487624, + "rhs": 7168000000627232, + "rhs_bits": 53 + }, + "leaf": { + "exponent": 10666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11431487624, + "rhs": 3584000000313576, + "rhs_bits": 52 + }, + "rows": { + "exponent": 11431487624, + "rhs": 1792000000156824000, + "rhs_bits": 61 + } + } + }, + { + "log2_input": 448000000000000, + "powers": { + "alpha": { + "exponent": 22862975248, + "rhs": 3584000000156824, + "rhs_bits": 52 + }, + "compact": { + "exponent": 22862975248, + "rhs": 14336000000627232, + "rhs_bits": 54 + }, + "leaf": { + "exponent": 21333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 22862975248, + "rhs": 7168000000313576, + "rhs_bits": 53 + }, + "rows": { + "exponent": 22862975248, + "rhs": 3584000000156824000, + "rhs_bits": 62 + } + } + } + ], + "practical_runtime_claim": false + }, + "kappa": "40827/800000000", + "next_kappa": "318961/6250000000", + "next_kappa_rejection": "{'g1_above_kappa': '-25408022593116799041/7102635201420453820506250000000', 'g3_above_kappa': '-5201705247125960457841/1136421632227272611281000000000000', 'g5_above_kappa': '-7640875416065173165777/1818274611563636178049600000000000', 'g6_above_kappa': '-33658690551416775383761/9091373057818180890248000000000000'}", + "original_enclosure_control": { + "accepted_upper": 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a/references/frame-compiler/pr84/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr84/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 at the new bit saving, +and the new complete profile has exact upper moment <1. All47 strict assembly +conditions and seven margins pass. **53 Lean endpoints** pass:34 new universal, +15 concrete,4 reused rational-helper lemmas. No omitted proof, project axiom or +native decision shortcut. The math scope includes dirty-word/complement safety, +coordinate conjugacy, fresh-kernel clearing, actual finite rounding and old-profile +rejection. It does not formalize the Python/C++ compiler or the all-size theorem. + +## Reproduce the accepted words + +Use an external checkout of frozen PR62 commit +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No newer sources are consumed. +See `verification/README.md` to compile its exact C++17 profiler, then run: + +``` +python verification/verify_words.py --upstream UPSTREAM --profiler PROFILER --word23 words/word-23.json.gz --word25 words/word-25.json.gz --output work/recheck +python verification/check_guards.py words/word-23.json.gz +python verification/check_guards.py words/word-25.json.gz +cd math +lake build Frozen62Research +``` + +The verifier checks immutable sources and its own adapter hashes, full input/dirty +bases in both orientations, exact source/scatter inventory, every literal frame +transition and all fixed-I+J profiles with bounded-minor and CRT checks. It rejects +optimized Python assertion mode. Use the supplied words for authoritative replay; +floating discovery prices propose candidates and have no trusted-proof role. +Discovery source snapshots, exact oracle fixtures (gzip-compressed) and matching +seeds retain original byte hashes. `discovery/SEARCH.md` explains the algorithms, +heuristic boundary and experimental commands. Historical workspace paths in the +source-generation receipts identify the original run; the accepted-word replay +uses the explicit upstream argument and needs no private directory layout. +Portable discovery regeneration: + +``` +python discovery/regenerate_portable.py --upstream UPSTREAM --work work/regenerate +``` + +This rewrites workspace paths only and checks both raw words and deterministic +gzip against the accepted words. Floating discovery is outside the trusted +certificate; the independent word/profile verifier establishes acceptance. + +The one-hour session froze information through #62. The unchanged data geometry +and its rational recovery are inherited; selected physical words/profile checks +are fresh. All-size analytic, compiler/frame transfer, finite-alphabet tape, +routing, prime selection/recovery and eventual-threshold contracts remain +conditional. No practical runtime or global-optimality claim is made. + +Alejandro Zarzuelo Urdiales is the human author/developer, following earlier +Archivara and personal July/October matrix/parity work developed with multiple +AI tools. This synthesis involved substantial OpenAI Codex assistance. Known +linear algebra, matroid exchange, dirty uncomputation and concavity principles +retain prior-work status. The finite construction credits Avi Eisenberg/ikeboy +(#62 interval/core-aware graph), eumemic (#57 frame compiler), Chafik Boukhalfa +(#60 ranking and earlier exact profiling), Rohan Arun and other retained notices. +The prior matrix/parity source is in `../matrix-exponent-synthesis/` and prior +Gaussian work in PR45. Its product counts retain their separate arithmetic scope. +The paper is supplied as LaTeX source; no newly compiled PDF is claimed. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md b/references/frame-compiler/pr84/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md new file mode 100644 index 0000000000..b8dd669634 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md @@ -0,0 +1,136 @@ +# Local frame-compiler search, frozen through PR62 + +All experiments in this directory use the pinned PR62 pair graph at +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No later community source is consumed. +The original checkout is unchanged. Each emitted word and compiler copy has +a SHA256 recorded in its `compiled.json`; changed words are sent separately +to the independent literal replay and profile verifier. + +## New dependency-circuit choices + +The inherited compiler reduces retired fresh-signal rows against the current +live anchors and an echelon basis of compatible retired rows. Instead of +accepting the first dependent retired row, the new selectors collect the +available fundamental dependency circuits and choose a circuit by one of: + +- total charged target/provider rank growth (`all_growth`); +- number and rank growth of other retired providers (`all_collateral`); +- anchor-only dependence before general retired dependence (`anchor_first`); +- actual physical transition child-profile moment cost (`profile_cost*`). + +Every clearing XOR and every target/provider frame promotion is still emitted +and charged. A zero fresh-signal row can contain arbitrary physical dirty state; +its reuse is justified by the complete reversible word, not by claiming that +the physical register is initialized to zero. The compiler runs both complete +dirty-basis orientations, and the independent verifier repeats them. + +For the last selector let `C(A,B) = sum_t n_t(A,B) F_t`, where the `n_t` are +the exact inherited fixed-I+J pivot-run profile of the physical frame transition +and `F_t = t exp(a log(m/t))`. A candidate target `s` at old frame `A_s`, cleared +into frame `G` with providers `z`, is priced by + +``` +C(A_s,G) - C(A_s,I) + + sum_z [C(A_z,G) + C(G,I) - C(A_z,I)]. +``` + +This accounts for immediate promotions and the change in deferred cleanup, +assuming each other retired provider remains retired until cleanup. Future +reuse couples decisions, so this is a discovery heuristic, not an additive +global optimality certificate. Linear rank mass cancels between candidates; +`t*expm1(a*log(m/t))` avoids cancellation in floating discovery prices. +Missing transition profiles are recorded and collected for the next iteration. +Once a run has zero missing pairs, every local price uses an actual transition +profile. The final saving is accepted only through exact rational whole-profile +moment bounds and all assembly gates. + +`build_pair_oracle.py` is a local adaptation of the frozen C++ profiler that +additionally exports each transition histogram. It preserves the projector, +pivot, bounded-minor and three-prime CRT routines. Its synthetic transition-list +input is an oracle request, not a physical executable word. Each immutable +profile dump and the source/header hashes are recorded. + +## Moment-ordered carry selection + +The `--weighted` experiment orders the inherited linear/partition-matroid +candidate edges by their physical transition moment change before the original +greedy initialization and augmenting paths. For a value produced at `P`, +preserved through donor frame `G`, and carried to future target `T`, its +no-reclamation child-cost change is + +``` +C(G,T) - C(G,I) - C(0,P) - C(P,T). +``` + +At fixed cardinality, role and external-volume corrections are common to all +edge choices in the same axis. The inherited augmenting algorithm still seeks +maximum cardinality; it does not optimize the weights globally. Reclamation +adds coupling, so only the changed whole-word profile can establish an actual +improvement. This experiment makes no minimum-cost matroid claim. + +The `--exchange` variant starts from the frozen original maximum-cardinality +matching and tries bounded improving one-edge exchanges. A new edge may replace +the old donor of the same use when its donor block stays linearly independent; +or it may replace a selected edge in the same donor block and serve an unused +use. Both preserve cardinality and distinct-use constraints. The `--cycle` +variant additionally tests two-edge donor/use cycles, checking the independence +of both changed blocks. No improving two-edge cycle was found in the tested +native-price instance; this is not a proof that longer cycles cannot improve it. + +## Joint basis and schedule search + +`--basis shift1` profiles all candidate physical transitions after the point +permutation `i -> (i+1) mod h`, while preserving their original frame IDs. +Matching and reclamation are then priced in that basis. The emitted word is +renamed by `relabel_word.py`: all frame masks, canonical source/output triples, +common points and scatter port indices change together. Scratch slots and +literal XOR instructions are retained. The complete triple family and the +permutation-invariant `I+J` basis are inherited; every final renamed word still +gets fresh full-basis and actual physical-profile verification. + +This joint search differs from merely relabeling an already selected schedule: +the selected carries and clearing circuits are optimized under the new ordered +pivot-run prices. It remains a bounded discovery heuristic. + +## Regeneration + +The frozen graph/matching setup and a moment-cost exchange run are generated by: + +``` +python -S collect_matching_pairs.py --h 23 +python -S build_pair_oracle.py --h 23 --strategy matching_collect +python -S run_strategy.py --h 23 --strategy profile_cost --exchange +``` + +Repeat at `h=25`. For joint search, add `--basis shift1` to the oracle and +strategy commands. Reclamation may encounter transitions absent from the +initial carry-edge inventory. Run the oracle again on the emitted strategy +directory with `--incremental`, then run a new strategy label. The new label +must start with `profile_cost`; output directories are never overwritten. +`compiled.json` records the exact oracle dump hash, missing-pair count, word +hashes and source pin. Immutable earlier oracle dumps are retained by SHA256. +Use `--oracle path/to/the-immutable-dump.jsonl` to reproduce the prices of a +specific recorded run instead of consuming the subsequently enlarged cache. +The initial compiler matching cache is accepted only if its complete candidate +edge list matches the current frozen graph and every restored selected block +passes the same linear-independence check. + +The runner saves an immutable source copy and its hash for later runs. Floating +`expm1` prices at discovery saving `a=0.00005103` select proposals only. Neither +those prices nor their reported local gains are used as an arithmetic witness. + +## Acceptance boundary + +The independent verifier checks all input and dirty basis vectors in both +orientations, exact literal-scatter incidences, causal nested physical frames, +event equality reconstructed from the actual XOR word, rank mass, actual child +profiles and CRT agreement. It then computes the whole mixed-axis recurrence +and exact rational moment/assembly witnesses. Existing all-size geometry, +analytic envelopes, compiler/tape arguments and the surrounding reduction are +inherited from frozen PR62. A finite profile improvement does not by itself +formally prove those inherited hypotheses. + +Reduced XOR count alone is not accepted as an exponent improvement. In this +search `all_collateral` and `anchor_first` reduced clearing XORs but worsened +the certified characteristic. Actual child-size distributions decide the +saving, even when both physical-role counts and total rank mass are unchanged. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py b/references/frame-compiler/pr84/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py new file mode 100644 index 0000000000..7c154b1a29 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py @@ -0,0 +1,275 @@ +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +import sys;sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'matrix-synthesis/bridge/pr62/references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s,add=True): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>s&1;e^=1<=prices[f]-1e-14:continue + if not can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:-prices[z])if prices[e] /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/NOTICE b/references/frame-compiler/pr84/references/frame-compiler/pr71/NOTICE new file mode 100644 index 0000000000..8adab44ba3 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/NOTICE @@ -0,0 +1,324 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/README.md b/references/frame-compiler/pr84/references/frame-compiler/pr71/README.md new file mode 100644 index 0000000000..4a9b481aa3 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/README.md @@ -0,0 +1,172 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/SOURCE.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/SOURCE.json new file mode 100644 index 0000000000..c8cc31f3d0 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/SOURCE.json @@ -0,0 +1,120 @@ +{ + "commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "Makefile": "6e9e48a677b2f66643226840f574a6535e3564ffb0c72284b60302684a5dfbe4", + "NOTICE": "1e0702aa665673508fa91169163c5785d680637fff636fda01f36e3b127c3ee0", + "README.md": "24817241fcad7f0a294ec6ad9666ee552ed9057e8d89e3c1d27e8fa2c7fe4229", + "certificates/split-pair-compiler.json": 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Original upstream sources and notices are preserved byte-for-byte. Actual inherited dependencies are additionally checked through the shared PR48 manifest.", + "shared_dependency_manifest": "../pr48/SOURCE.json", + "shared_dependency_manifest_sha256": "6ccc673f88d3650d75ed600b082fe2fc2866dd88a172d182a38c1d0cd27d24b3" + }, + "pr67": { + "author": "Rohan Arun with OpenAI assistance", + "commit": "b3745601e947a94316bf25c2c6263d93c06e3364", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "5931cb7d43e09380594b113018cac70258fb66e0673b91f706b01ea482c1be1a", + "research/slot-cost-rank-pair/README.md": "e0fcd8e732c8b8becb3d860eb83dc979ed5e6b33ba16caf9dca1e44f7929c340", + "research/slot-cost-rank-pair/arithmetic/certificate.json": "e66f955f1b76ce3db7ecb84294993a072f42f972b8f3040015c12e6dc953d698", + "research/slot-cost-rank-pair/compiler.py": "29296211e0532aaf19101a6b2f2ceaebe374af95ae3acd63e63656db0afef7ae", + "research/slot-cost-rank-pair/frame-compiler.json": "eb5c0b401e677d3958ecfcd6d8de3bc825c4fb66d1cf79c3fcbcf23938ca6e69", + "research/slot-cost-rank-pair/paired-candidate.json": "be0322ad60f73923953f242eaffaf114ff12438e8617dae38888b77fa03184cc", + "research/slot-cost-rank-pair/profile_oracle.cpp": "d1f6b650de9fb5842b412595369271d9eeb6f54045c76c0fb5cad29854955c35", + "research/slot-cost-rank-pair/verify.py": "3c1d2eac9d3d2f13b60503deaa84e11ab2975aa84af71c8ad74584c5902b2d77" + }, + "repo": "rohanarun/integer-mult-bounds", + "scope": "Preserved immutable source and reported complete baseline profile/arithmetic for all-rank profile-cost reclamation. This package verifies its own composed words, actual paid profile and exact improvement.", + "shared_dependency_manifest": "../pr48/SOURCE.json", + "shared_dependency_manifest_sha256": "6ccc673f88d3650d75ed600b082fe2fc2866dd88a172d182a38c1d0cd27d24b3" + }, + "pr68": { + "author": "Dominik Scholz with OpenAI assistance", + "commit": "734c58e225e9d2254570c3b50296ed96943f62ea", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "d9db68e85db965bf7037d535ddc354b096b7c3b8f4cb0eb4887dc61eba5eae23", + "research/global-anchor-screen/PROOF.md": "3023c8c039acb3afc2a1e0c2ee55dcffaa4a1a2961076222ae20b03d0f3c6a38", + "research/global-anchor-screen/SOURCE.json": "f6249b8f91c7721a59ecc6d43a3f2ec65162578203bd430ef76732a3937399f3", + "research/global-anchor-screen/compiler-frozen.py": "12d646fa9ad69e4f3c532fe69080d8fe1509cde0968a6ab52a9d60273803adc0", + "research/global-anchor-screen/selected-manifest.json": "97bd86fc20fb3aee2d1adacd6a485b12e918b7340d2d3ca70e1318889e13e3a0", + "research/global-anchor-screen/selected_compile.py": "86bdfcf599c6b131e376773fe177bca57a9f63c9b60bad5de8aa00982d779b22" + }, + "repo": "DominikScholz/integer-mult-bounds", + "scope": "Preserved original pending live-carrier compiler, selected driver, proof and source provenance. This package composes the pending lifecycle and both containment checks with PR67 profile-cost selection and its own next-use scoring.", + "shared_dependency_manifest": "../pr48/SOURCE.json", + "shared_dependency_manifest_sha256": "6ccc673f88d3650d75ed600b082fe2fc2866dd88a172d182a38c1d0cd27d24b3" + }, + "split_operation": { + "author": "Rohan Garg / rohangar1 with OpenAI Codex assistance", + "commit": "641f22e52913db784f3b6ff1176b0c2945aae45b", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "f85437ee441f2a028660dd5e8dbdc0ec7b52bb55c04ea34fa4829c154bfd0ac1", + "research/split-skip/SOURCE.json": "7c2b4646a3ecfef6f881da5c43e4bd0fa9a4d1b00548b8ab458d897e16735134", + "research/split-skip/split_graph.py": "9b16ba907cbd58611fb64bfb9211be7809d54822d44c78fc6167cf4ba79eb905" + }, + "repo": "CrocSwap/integer-mult-bounds", + "scope": "Preserved original split-pair operation and attribution. These files document the adapted grouping operation; they are not imported by this producer. Actual imported source closure is PR65 plus shared PR48." + } + }, + "status": "Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed" +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-profiles-23.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-profiles-23.json new file mode 100644 index 0000000000..bf40dc76b4 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-profiles-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27455,"loss":506,"rank_sum":631971,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38745,"crt_matrices":5750,"crt_disagreements":0,"blocks":[0,357148,21253,8022,5466,4156,3835,3250,2612,2109,1750,1529,1008,863,555,461,234,149,40,9,0,23,0,0]} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-profiles-25.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-profiles-25.json new file mode 100644 index 0000000000..2f4bb6b9e9 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-profiles-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":36015,"loss":600,"rank_sum":900975,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52075,"crt_matrices":7444,"crt_disagreements":0,"blocks":[0,492698,27869,10467,7897,5674,5027,4110,3809,3047,2490,2047,1814,1443,1151,898,567,470,271,163,47,13,0,25,0,0]} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-transitions-23.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-transitions-23.json new file mode 100644 index 0000000000..1a389c32fd --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27455, + "frames": 59803, + "distinct_transitions": 152272, + "singles": 15939, + "rank_mass": 631971, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69190, + "2": 73632, + "3": 10224, + "4": 15382, + "5": 6461, + "6": 1593, + "7": 694, + "8": 1229, + "9": 411, + "10": 539, + "11": 98, + "12": 671, + "13": 254, + "14": 1927, + "15": 439, + "16": 440, + "17": 487, + "18": 3417, + "19": 6882, + "21": 171, + "22": 23 + }, + "word_sha256": "b0379d99fd6c10307da0d0fc526ed6171f19105a47bae61730fc3745ef60bd9e", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-transitions-25.json 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a/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-validation.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-validation.json new file mode 100644 index 0000000000..471a5bed88 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-validation.json @@ -0,0 +1,237 @@ +{ + "axes": { + "23": { + "profile": { + "R": 27455, + "blocks": [ + 0, + 357148, + 21253, + 8022, + 5466, + 4156, + 3835, + 3250, + 2612, + 2109, + 1750, + 1529, + 1008, + 863, + 555, + 461, + 234, + 149, + 40, + 9, + 0, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 5750, + "distinct_matrices": 38745, + "field_prime": 2305843009213693951, + "frames": 59803, + "h": 23, + "loss": 506, + "rank_sum": 631971, + "v": 1771 + }, + "replay": { + "elementary_xors": 162103, + "full_basis_vectors": 30997, + "h": 23, + "histogram": { + "0": 175253, + "1": 58564, + "2": 78945, + "3": 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4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "output_roles": 6925, + "rank_mass": 900975, + "roles": 36015, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 935228 + }, + "transitions": { + "R": 36015, + "copied_centers": 25, + "distinct_transitions": 212584, + "frames": 84845, + "h": 25, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 91026, + "2": 108047, + "3": 13560, + "4": 19874, + "5": 8387, + "6": 2967, + "7": 1127, + "8": 1443, + "9": 664, + "10": 791, + "11": 38, + "12": 758, + "13": 149, + "14": 681, + "15": 167, + "16": 2265, + "17": 680, + "18": 566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "rank_mass": 900975, + "singles": 20700, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 2300, + "word_sha256": "4c956749f0ec72c61875c51099afdf23e69ccea268a9b43b8d46da2ffdb24903" + } + } + }, + "bit_saving": 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and b/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-word-23.json.gz differ diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-word-25.json.gz b/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-word-25.json.gz new file mode 100644 index 0000000000..da9935d15a Binary files /dev/null and b/references/frame-compiler/pr84/references/frame-compiler/pr71/certificates/split-pair-word-25.json.gz differ diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/SOURCE.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/SOURCE.json new file mode 100644 index 0000000000..4e38e34dc8 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/SOURCE.json @@ -0,0 +1,16 @@ +{ + "files": { + "research/copied-fixed/balanced_assembly.py": "4d27575dcad2b45a281a34054d311409ecd954f373c0c3a62c29bcc843f06a86", + "research/copied-fixed/certificate.json": "33b3373c04e18a7f4cee33ba68da6ed71934acc3e0179cca6197696be4befa22", + "research/copied-fixed/changed_graph.py": "375a7ca6cac6d153c1880fd5ea5b4525e5dca9d4ee3018d24d679c219b59c5b3", + "research/copied-fixed/profiles.cpp": "b9fbd71c746609948b60c441ba4601e88436956fe636d1810f270ce4ce6a63a6", + "research/copied-fixed/verify.py": "44932182ce6c4d39776650311262ef0ac1ea9b5da7220bc0f728e2789881f84a", + "scripts/exclusion_circuit.py": "b253f9d7318becda1c1f3b24e2287ed44a9c27fcea00cf9d531afb950d0457a0", + "scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34" + }, + "head": "b7194b8586844956904b33e9fe18f0c75606c11b", + "scope": "Unmodified producer inputs for experimental frame compiler; attribution retained in each file", + "source_pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/48" +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py new file mode 100644 index 0000000000..c7fd42867d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py @@ -0,0 +1,196 @@ +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit', 'complex'): + data = finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + 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b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "PR48": { + "author": "Chafik Boukhalfa", + "commit": "b7194b8586844956904b33e9fe18f0c75606c11b", + 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Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + } + }, + "gzip_sha256": "4629d45d5074f87706db46be3aa3cd369071cd215bc6560d641115aadcce54a0", + "word_sha256": "bd0cbf73756f2e4f8d3879ec6c7a194990eb9ec40aaf3580bdded6994798d920" + }, + "25": { + "compiled": { + "h": 25, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 36586, + "baseline_pr48_roles": 48329, + "histogram": { + "1": 55478, + "0": 416276, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + }, + "rank_mass": 915250, + "elementary_xors": 205650, + "stats": { + "augmentations": 286, + "regions": 73695, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json new file mode 100644 index 0000000000..346cf87ea3 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json @@ -0,0 +1,1087 @@ +{ + "accepted_moment": { + "degree": 8, + "lower": "34287951499999999998997315662315085394575263036671/34287951500000000000000000000000000000000000000000", + "rounding_denominator": 10000000000000000000000000000000000000000, + "saving": "5103158916233/100000000000000000", + "strict_gap": "2278828040192983762647964739/77927162500000000000000000000000000000000000000", + "terms": { + "1": { + "exp_lower": "5001621630918375893019301295747281962987/5000000000000000000000000000000000000000", + "exp_upper": "10003243261836751786038602591494564437549/10000000000000000000000000000000000000000", + "log_lower": "3177185020398675220004135749131/500000000000000000000000000000", + "log_upper": "6354370040797350440008271498263/1000000000000000000000000000000", + "weight": "61988/2833715" + 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rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.", + "All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.", + "Neither global optimality nor measured practical speedup is claimed." + ], + "rejected_moment": { + "degree": 8, + "lower": "8571987875000000003683551653063012975552828889113/8571987875000000000000000000000000000000000000000", + "rounding_denominator": 10000000000000000000000000000000000000000, + "saving": "51031589162331/1000000000000000000", + "strict_gap": "-920887913265753353254538048853/2142996968750000000000000000000000000000000000000", + "terms": { + "1": { + "exp_lower": "2000648652367350369920582377063597092877/2000000000000000000000000000000000000000", + "exp_upper": "250081081545918796240072797132949649399/250000000000000000000000000000000000000", + "log_lower": "3177185020398675220004135749131/500000000000000000000000000000", + "log_upper": 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b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json new file mode 100644 index 0000000000..42958fc74b --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json @@ -0,0 +1,195 @@ +{ + "artifact_sha256": { + "frame-profiles-23.json": "fec377bcf1512a427674983256b900229d4133026445b6e680c6e1e6dde5af7d", + "frame-profiles-25.json": 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orientations PASS", + "word_length": 621342 + }, + "schedule": "cover-core", + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4" + }, + "25": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 48329, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 41186, + "elementary_xors": 205977, + "h": 25, + "histogram": { + "0": 416741, + "1": 55478, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "2": 115781, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 915250, + "roles": 36586, + "stats": { + "augmentations": 286, + "clearing_xors": 2154, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "regions": 73695 + } + }, + "gzip_sha256": 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"3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "research/reordered-rank-pair/test_negative.py": "88832242e6f74e3fe08d109d4f21ff188a9ca0ae50c3e8f31da0243fe9501510", + "research/reordered-rank-pair/verify.py": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352", + "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3", + "scripts/experiments/binary_frame_profiles.cpp": "8e2e391d3ee57cbb1372c68e4aa031e1b861321536eabd642ada54e12e678669", + "scripts/experiments/binary_frame_replay.py": "392e78e62d7685c99a5888a7da743ea6c3dcad631af4a743c91e0c09348442bc", + "scripts/experiments/rank_pair_compiler.py": "9984aaccf880e4840402322d76678bfddb33ce7e494af78430a43429f51b85fd" + }, + "status": "Exact topological scheduling of unchanged PR63 graph/compiler; both physical orientations and fixed profiles checked" +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json new file mode 100644 index 0000000000..3b648dbe21 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "loss": 506, + "rank_sum": 642620, + "field_prime": 2305843009213693951, + "frames": 52475, + "distinct_matrices": 36399, + "crt_matrices": 6049, + "crt_disagreements": 0, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json new file mode 100644 index 0000000000..19cc34b4ca --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json @@ -0,0 +1,40 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "loss": 600, + "rank_sum": 915250, + "field_prime": 2305843009213693951, + "frames": 73697, + "distinct_matrices": 50394, + "crt_matrices": 8127, + "crt_disagreements": 0, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json new file mode 100644 index 0000000000..2883a5f7c9 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "frames": 52475, + "distinct_transitions": 138016, + "singles": 15939, + "rank_mass": 642620, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 53320, + "2": 77409, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "21": 165, + "22": 23 + }, + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json new file mode 100644 index 0000000000..3b4bc33ff6 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json @@ -0,0 +1,35 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "frames": 73697, + "distinct_transitions": 190838, + "singles": 20700, + "rank_mass": 915250, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69278, + "2": 108881, + "3": 14362, + "4": 16908, + 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a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz new file mode 100644 index 0000000000..6a239a3e9f Binary files /dev/null and b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz differ diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + 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a/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) ++ slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();pending={};stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): +@@ -149,7 +151,8 @@ + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 +- return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) ++ endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 ++ return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} +@@ -161,6 +164,9 @@ + old,e=bb[p];row^=old;expr^=e + return expr + for s in anchors:ins(s) ++ for s,target in pending.items(): ++ if contains(blocks[frames[s]]['frame'],blocks[g]['frame']) and contains(blocks[g]['frame'],blocks[target]['frame']): ++ ins(s);stats['live_anchor_candidates']+=1 + best=None + # Inspect every eligible dependent candidate across all retired ranks. + # Rank the actual fixed-basis growth/cleanup profiles by an integer entropy score. +@@ -176,7 +182,9 @@ + if best is None or key= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and kappa > previous_kappa + bridge = json.loads((OLD/'certificate.json').read_text())['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/split-pair/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr67_commit='b3745601e947a94316bf25c2c6263d93c06e3364', + pr67_kappa=previous_kappa, ratio_pr67=kappa/previous_kappa, + absolute_gain_pr67=kappa-previous_kappa, + pr67_complete_profile_exclusion_lower=prior65_lower, + full_pr67_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected split-pair partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'split-pair-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py new file mode 100644 index 0000000000..1290ef2eb8 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py @@ -0,0 +1,275 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py new file mode 100644 index 0000000000..7908c963a4 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py @@ -0,0 +1,78 @@ +#!/usr/bin/env python3 +"""Replay the aligned split-pair/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from split_pair_compose import compose, check_sources +from split_pair_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'split-pair-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='split-pair-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + 'c++', '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'split-pair-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'split-pair-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'split-pair-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'split-pair-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'split-pair-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/tests/test_split_pair.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/tests/test_split_pair.py new file mode 100644 index 0000000000..5088cff133 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/tests/test_split_pair.py @@ -0,0 +1,238 @@ +"""Physical and exact-arithmetic controls for the aligned split/pair witness.""" +from copy import deepcopy +from fractions import Fraction +from itertools import combinations +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile +import unittest +from unittest.mock import patch + +ROOT = Path(__file__).resolve().parents[1] +EXPERIMENTS = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXPERIMENTS)) +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from binary_frame_math import moment + + +class SplitPairControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.words = {h: json.loads(gzip.decompress((ROOT/f'certificates/split-pair-word-{h}.json.gz').read_bytes())) + for h in (23,25)} + + def reject_mutation(self, mutate, checker='both'): + for h, original in self.words.items(): + with self.subTest(h=h), tempfile.TemporaryDirectory() as directory: + changed = deepcopy(original) + mutate(changed) + path = Path(directory)/'word.json' + path.write_text(json.dumps(changed, separators=(',', ':'))+'\n') + with self.assertRaises((AssertionError, ValueError, IndexError, KeyError)): + if checker != 'transitions': + replay(path) + if checker != 'replay': + prepare(path, Path(directory)/'transitions.bin') + + def test_selected_words_pass_independent_replay(self): + recorded = json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + actual = replay(ROOT/f'certificates/split-pair-word-{h}.json.gz') + self.assertEqual(json.loads(json.dumps(actual)), recorded['axes'][str(h)]['replay']) + + def test_omitted_literal_xor_is_rejected(self): + self.reject_mutation(lambda word: word['ops'].pop(0)) + + def test_self_xor_is_rejected(self): + def mutate(word): + word['ops'][0][1] = word['ops'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_non_nested_operation_frame_is_rejected(self): + def mutate(word): + narrow = next(i for i,(core,cover) in enumerate(word['frames']) if core == cover) + operation = next(op for op in word['ops'] if word['frames'][op[2]][0] != word['frames'][op[2]][1]) + operation[2] = narrow + self.reject_mutation(mutate) + + def test_aliased_terminal_role_is_rejected(self): + def mutate(word): + word['outputs'][1][0] = word['outputs'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_missing_copied_center_is_rejected(self): + def mutate(word): + index = next(i for i,(_,_,_,target) in enumerate(word['outputs']) if len(target) == 1) + word['outputs'].pop(index) + self.reject_mutation(mutate) + + def test_omitted_transition_cannot_reduce_paid_profile(self): + self.reject_mutation(lambda word: word['events'].pop(0), 'transitions') + + def test_understated_physical_width_is_rejected(self): + def mutate(word): + word['R'] -= 1 + self.reject_mutation(mutate) + + def test_complete_pr67_profile_fails_new_bit_saving(self): + from split_pair_arithmetic import refine + previous = json.loads((ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/paired-candidate.json').read_text())['bit'] + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + result = refine.exact_moment(previous['m'], previous['W'], {int(t): n for t,n in previous['child_multiplicities'].items()}, Fraction(current['bit_saving'])) + self.assertGreater(result['lower'], 1) + self.assertGreater(Fraction(current['kappa']), Fraction(current['comparison']['pr67_kappa'])) + + def test_private_import_preserves_path_and_arithmetic_module(self): + import split_pair_graph as provider + import split_pair_arithmetic as arithmetic + sentinel = object() + existing = sys.modules.get('refine', sentinel) + previous_path = sys.path[:] + graph, schedule = provider._private_modules() + refine, audit = arithmetic.private_arithmetic() + self.assertIs(audit.refine, refine) + self.assertIs(sys.modules.get('refine', sentinel), existing) + self.assertEqual(sys.path, previous_path) + + def test_failed_graph_build_restores_original_providers(self): + import split_pair_graph as provider + previous_class, previous_points = provider._graph.circuit_class, provider._graph.alternating_points + with patch.object(provider._graph, 'graph', side_effect=RuntimeError('deliberate graph failure')): + with self.assertRaises(RuntimeError): + provider.graph(23) + self.assertIs(provider._graph.circuit_class, previous_class) + self.assertIs(provider._graph.alternating_points, previous_points) + + def test_failed_compilation_restores_engine_graph_and_schedule(self): + import split_pair_compiler as producer + previous_graph, previous_build = producer.compiler.graph, producer.compiler.build + missing = object() + runtime = {name:getattr(producer.compiler,name,missing) for name in ('PENDING_COST','ORACLE_EXE','ORACLE_INPUT','oracles')} + with patch.object(producer.compiler, 'compile_', side_effect=RuntimeError('deliberate compiler failure')): + with self.assertRaises(RuntimeError): + producer.compile_axis(23) + self.assertIs(producer.compiler.graph, previous_graph) + self.assertIs(producer.compiler.build, previous_build) + for name,value in runtime.items(): + self.assertIs(getattr(producer.compiler,name,missing),value) + + def test_uncertified_configurations_are_rejected(self): + import split_pair_graph as provider + wrong_anchor = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_anchor['anchor'] = False + boolean_group = deepcopy(provider.EXPECTED_CONFIGS[23]); boolean_group['groups'][0] = True + changed_schedule = deepcopy(provider.EXPECTED_CONFIGS[23]); changed_schedule['schedule'] = 'reverse-node' + for changed in (wrong_anchor, boolean_group, changed_schedule): + with self.subTest(configuration=changed), patch.object(provider.json, 'loads', return_value=changed): + with self.assertRaises(ValueError): + provider.configuration(23) + for dimension in (True, 22, 24, '23'): + with self.subTest(dimension=dimension), self.assertRaises(ValueError): + provider.configuration(dimension) + + def test_recursive_weighted_exclusions_and_contraction(self): + import split_pair_graph as provider + for h in (23,25): + block_sizes = [] + parent = provider._graph.circuit_class(h) + selected = provider.split_class(parent, provider.configuration(h)['groups']) + case = self + class Audited(selected): + def grouping(self, points): + groups = super().grouping(points) + case.assertEqual([x for group in groups for x in group], list(points)) + case.assertLess(len(groups), len(points)) + return groups + + def _block(self, points, edges, weights, level): + def expected(omitted): + values = [value for pair,value in edges.items() if not set(pair) & omitted] + values += [value for point,value in weights.items() if point not in omitted] + support = 0 + for value in values: + case.assertEqual(support & self.support[value], 0) + support |= self.support[value] + return support + total, single, pairs = super()._block(points, edges, weights, level) + case.assertEqual(self.support[total], expected(set())) + case.assertEqual(set(single), set(points)) + for a in points: + case.assertEqual(self.support[single[a]], expected({a})) + case.assertEqual(set(pairs), set(combinations(points,2))) + for a,b in combinations(points,2): + case.assertEqual(self.support[pairs[a,b]], expected({a,b})) + block_sizes.append(len(points)) + return total, single, pairs + local = Audited(h-1) + block_sizes.clear() + local.pair(list(range(h-1))) + self.assertEqual(sorted(block_sizes, reverse=True), [h-1, 12 if h==23 else 13, 7 if h==23 else 8, 5, 3, 2]) + + def test_next_fine_grid_points_and_old_assembly_controls_reject(self): + from split_pair_arithmetic import refine + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + bit = current['bit']; saving = Fraction(current['bit_saving']); kappa = Fraction(current['kappa']) + grid = Fraction(1,10**18) + rows = {int(t): n for t,n in bit['child_multiplicities'].items()} + self.assertLess(refine.exact_moment(bit['m'],bit['W'],rows,saving)['upper'], 1) + self.assertGreater(refine.exact_moment(bit['m'],bit['W'],rows,saving+grid)['lower'], 1) + for label, variant in ( + ('next_kappa', dict(kappa=kappa+grid)), + ('zero_backoff', dict(h=Fraction())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))): + call = dict(a_bit=saving, kappa=kappa, h=Fraction(1,10**12));call.update(variant) + with self.subTest(control=label), self.assertRaises(refine.balanced.InvalidAssembly): + refine.balanced.assembly(current['finite_bridge'], **call) + + def test_mass_preserving_profile_mutation_is_rejected(self): + from split_pair_compose import check_sources + profile_path = ROOT/'certificates/split-pair-profiles-23.json' + changed = json.loads(profile_path.read_text()) + before = sum(t*n for t,n in enumerate(changed['blocks'])) + changed['blocks'][2] += 3; changed['blocks'][3] -= 2 + self.assertTrue(all(n >= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'split-pair-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from split_pair_compose import check_sources + manifest_path = ROOT/'research/split-pair/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/split-pair-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import split_pair_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('split_pair_graph.py', 'split_pair_engine.py', 'split_pair_compiler.py', 'split_pair_arithmetic.py', 'split_pair_compose.py', 'verify_split_pair.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr71/tests/test_split_pair_pending.py b/references/frame-compiler/pr84/references/frame-compiler/pr71/tests/test_split_pair_pending.py new file mode 100644 index 0000000000..e6d63f72a4 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr71/tests/test_split_pair_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/split_pair_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr74/FETCH.json b/references/frame-compiler/pr84/references/frame-compiler/pr74/FETCH.json new file mode 100644 index 0000000000..92196075e8 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr74/FETCH.json @@ -0,0 +1,72 @@ +{ + "pr": 74, + "commit": "3f78d8967c009153f2df5c6a6577b6ab1d37e2ca", + "files": [ + { + "path": "research/balanced-split-frames/producer.py", + "blob_sha": "8d68303a3be4ba2f15f3b54a74560c4310b0fc69", + "sha256": "ec94e4b7af370f7e921fffa3679e80d081a672dbd3ff198043edfb0dc7a9cc9d", 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Rank-first reclamation on interval-strip pair assembly, 8 October 2026 +Composition and exact profile witness: Dominik Scholz, with substantial OpenAI +GPT-6 Astra / Codex assistance. The PR #60 descending-frame-rank compiler by +Chafik Boukhalfa is reused unchanged on Avi Eisenberg's PR #62 scalar graph. +The joint frame compiler and paid reclamation are eumemic's PR #57, developed +with OpenAI Codex assistance. PR #62 records Anthropic Claude assistance. +This composition improves actual fixed-basis block profiles with unchanged +role counts; no new slot-priority rule or scalar graph is claimed. All prior +contributors, licenses, compiler arguments and conditional analytic/tape +interfaces remain credited. See research/rank-pair/PROOF.md. + +Ordered scalar frames, minimum-raise reclamation and coordinate relabeling +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. +The new finite construction and exact arithmetic certificates are in +research/ordered-frames, with an earlier parameter refinement in +research/rank-pair-refinement. These build on Dominik Scholz's PR #63 +composition, Chafik Boukhalfa's PR #60 reclamation compiler, Avi Eisenberg's +PR #62 scalar graph and eumemic's PR #57 reversible frame compiler. +Concurrent PR #65/#67 work is acknowledged in the proof. All inherited +licenses, author notices and conditional proof boundaries remain in force. + +Balanced split frames with core node ordering and coordinate relabeling +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. +This composition combines eumemic's PR69 coarse column sums, Chafik Boukhalfa's +PR71 anchored split/next-use-live compiler, and the earlier PR74 node ordering +and coordinate relabeling. Rohan Garg's PR59 split operation, Avi Eisenberg's +PR62 scalar graph, Rohan Arun's PR65/67 schedules and profile-cost selection, +Dominik Scholz's PR63/68 composition and pending controls, and eumemic's PR57 +compiler remain credited. Original source closures and notices are preserved +under references/frame-compiler/pr69 and pr71; all preceding licenses apply. +See research/balanced-split-frames/PROOF.md for the finite conditional scope. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr74/SOURCE.json b/references/frame-compiler/pr84/references/frame-compiler/pr74/SOURCE.json new file mode 100644 index 0000000000..87bd75428a --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr74/SOURCE.json @@ -0,0 +1,19 @@ +{ + "commit": "3f78d8967c009153f2df5c6a6577b6ab1d37e2ca", + "files": { + "FETCH.json": "4aee950c461d4b46ca42d323d7a7041118ba2b1002d7a867616f3c7ea4d66c1c", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "c087c747998243c96db63203920affd28cec880b702c36017c40a3eb29947fa9", + "research/balanced-split-frames/PROOF.md": "f7a908eea56fdab2f2e8f4ce694a0132c37844ae1cb657962b6549f585bfcdfb", + "research/balanced-split-frames/README.md": "f620b1a18df2b6c0f5d179ebf50f90e630270bba90e14c0d4bff189e3056ee49", + "research/balanced-split-frames/SOURCE.json": "c933a96c636f1e22e02be6fb775a9da2cd14c11fa2d07ba75af17c7e99f00049", + "research/balanced-split-frames/certificate.json": "cec62c4ca612e458b638982056c80be8741ed634904077a5c220427e23cc3edd", + "research/balanced-split-frames/check.py": "45fb95cb2a6b0573efbe37938c149936f4aa4fff1a88425380af7bc59239b4ae", + "research/balanced-split-frames/producer.py": "ec94e4b7af370f7e921fffa3679e80d081a672dbd3ff198043edfb0dc7a9cc9d", + "research/balanced-split-frames/profile-23.json": "7f61525499f56ccc3a183a2741ef823cce30423475fa586ba7d36610b5b66844", + "research/balanced-split-frames/profile-25.json": "9b4d0647e3667af963c164c048c6ea750d90397b046336ede5a5b6902a9f6473", + "research/balanced-split-frames/selection.json": "cbc616540af0ff5b63a90a920c70acd660fbb67052e4dc19889fe0443f2129f4" + }, + "pr": 74, + "scope": "Exact attributed contributor inputs and reported comparison certificate, not a new audit of the entire foreign claim." +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/PROOF.md b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/PROOF.md new file mode 100644 index 0000000000..7244811413 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/PROOF.md @@ -0,0 +1,145 @@ +# A paid composition of balanced coarse sums, split recursion and frame order + +## Statement and boundary + +The complete finite profile below certifies + +`kappa = 10366199626713/200000000000000000` + +for the inherited conditional bound `T(n)=O(n(log n)^(1-kappa))`. +The all-size compiler, analytic transfer, fixed-alphabet tape simulation, +precision, routing, prime selection and exact recovery hypotheses are inherited. +Finite source checks and arithmetic do not establish those general hypotheses. + +## 1. Pinned ingredients + +PR #71 is frozen at `1bef94fd40a746452548c84a4a8f8834670a3113` in +`references/frame-compiler/pr71/`, including its complete consumed source +closure, selected words, data interfaces, licenses, notices and root documents. +Its own source manifest is preserved without re-pinning. PR #69's original +coarse-sum compiler and notices are frozen at +`91aa1f17e6e3fc063241686a41a34ddd0dc24c50` in the adjacent `pr69/` archive. + +The new producer reads PR #69's literal BEFORE/AFTER replacement, applies it +exactly once to the archived PR #62 scalar graph consumed by PR #71, and keeps +PR #71's `[1,1,2]` split choices and lowest-intact-pair anchoring. The original +source files are unchanged. After reordering, it uses the archived PR #71 +compiler and its next-use profile-cost selection unchanged. + +## 2. Shared intermediate sums preserve the scalar map + +For two disjoint groups A and B, replace the chain forming +`sum_{a in A,b in B} e(a,b)` by +`sum_{b in B} (sum_{a in A} e(a,b))`. +Each operand support occurs exactly once. The nested sums are disjoint, +so this is an equality over the inherited scalar field. Existing node +interning shares the column intermediates with later strip computations. +The singleton cases and strictly decreasing recursive partitions retain the +same identity. No negative coefficient or cancellation is introduced. + +`graph_audit.py` reconstructs dense global triple-coordinate supports using +its own recurrence. For each dimension it checks every input, addition, +core, cover and prescribed output, and compares the complete output support +inventory with original PR #71. This checks 67,460 / 94,993 additions and +5,336 / 6,925 outputs. Original PR #71 has 68,771 / 96,718 additions. + +## 3. Legal node order and fully charged live reclamation + +Keep source IDs fixed. Group remaining active nodes by their original +(core, cover), retaining their original order within each group. Sort groups +lexicographically by + +`(popcount(cover)-popcount(core), -core, cover, first_original_node)`. + +Remap every operand and output ID, clear support caches indexed by old IDs, +and verify again. The independent audit proves that each literal edge and +output is preserved, every operand precedes its consumer, every envelope is +unchanged, and this is exactly the selected renumbering. Matching is recomputed +on the resulting graph and the compiler uses its natural region order. + +PR #71's unchanged pending live controls enter a clearing basis only when +their current frame is contained in the present frame and that frame is +contained in their next-use frame. Controls retain their values. The complete +word contains every chosen clearing XOR and every required frame raise. +The discovery score is never substituted for the actual charged profile. + +Both complete words are regenerated with dirty-basis checks enabled. A +separate serialized-word checker replays every input and arbitrary dirty +basis column in both orientations. The final roles are 27,136 / 35,744. + +## 4. Coordinate relabeling and the data family + +Apply each selected permutation to the frame core/cover masks, source-triple +indices, scatter target-triple indices, output common points and output +triples. Literal XORs, scratch IDs and frame IDs remain unchanged. The complete +permutations are frozen in `selection.json`; both relabeled words are replayed. + +For permutation matrix P, both fixed bases `I+J` and the inverse metric +`I-J/9` commute with P. Envelope projectors therefore transform by conjugation. +Containment and every legal incidence remain valid. Ordered contiguous child +profiles can change, and every one is regenerated from the literal word +using the inherited exact bounded-minor/CRT profiler, with zero disagreements. + +Each coordinate permutation induces a bijection on the complete triple set. +Consequently the complete two-axis data-block family is only reindexed: its +aggregate inherited profile and rational recovery cases remain valid. Copied +centers, endpoints and data growth remain explicitly charged. + +## 5. Complete recurrence and assembly + +Let `N=4073300`, `m=575`, and let `R_h` and `b_{h,t}` be the verified role count +and exact internal profile. The physical width is + +`W = 2N + (N/1771)R_23 + (N/2300)R_25 = 133862024`. + +The complete child multiset includes: + +- data: `18N` children of size 1 and `2N` each of sizes 21, 17 and 481; +- paid endpoint copies: `N` additional size-1 children; +- internal axis h: `(N/binom(h,3))*b_{h,t}` children of size t; +- exterior axis h: `(N/binom(h,3))*R_h` each of sizes h and `m-2h`; +- data growth per axis: `2N` each of sizes 1 and `h-2`. + +The total rank is `76968816900 = mW-1846900`; maximum child size is 529. +The exact characteristic is +`M(a)=sum_t (t*n_t/(mW))*exp(a*log(m/t))`. +At `a=25916842362591/500000000000000000`, a rigorous upper bound is below 1. +At `a+10^-18`, a rigorous lower bound is above 1. Positive logarithms make +the characteristic increasing. The complete original PR #71 profile is +separately excluded at the new accepted saving. + +Production arithmetic uses the retained rational logarithm/exponential +helper. The independent checker derives the complete paid multiset and uses +40 exact atanh terms for logarithms and Taylor degree 10 with a geometric +exponential tail. It imports no production arithmetic and checks each of the +47 assembly slacks and seven margins independently. The next kappa grid value +is rejected. Negative controls reject omitted paid children, fabricated slacks +and incorrect source hashes. + +Use positive backoff `10^-18`. Since W is below `2^27`, its `bit_length()` is +27. The product-row coefficient becomes `9*27+20*30=843`. Keeping degree 2000 +and suffix slope 8000 gives degree gap `2000-(51/25)*843=7007/25`. +These values are derived and checked; no stale predecessor constants remain. +Arithmetic cutoff bounds are not complete operational runtime thresholds. + +## Credits + +The composition, core-order continuation, coordinate choices, packaging and +independent audits were prepared for Thomas DiFiore with substantial OpenAI +Codex assistance. Coarse-sum reassociation is eumemic's PR #69. Anchored split +frames and next-use-aware live selection are Chafik Boukhalfa's PR #71. +Rohan Garg supplied the split operation (#59); Avi Eisenberg supplied interval +strips and core-aware pair assembly (#62); Rohan Arun supplied region schedules +and profile-cost selection (#65/#67); Dominik Scholz supplied ranked composition +and pending live controls (#63/#68); eumemic supplied the reversible compiler +and physical/profile checking interfaces (#57). Our earlier PR #74 supplied the +core node ordering and coordinate-relabeling continuation used here. + +The preserved archives retain all earlier credits, including RaD/hipotures, +icekylinx, James Chang, Zhihao Chen, Aurel Prosz, Swapnil Jain, Alejandro Zarzuelo +Urdiales, Douglas Colkitt, OpenAI and Harvey–van der Hoeven, and predecessor +AI-assistance disclosures. No predecessor authorship or endorsement of this +composition is implied. Existing licenses and notices remain in force. + +Concurrent PR #75–#79 contributions, including carry exchanges, balanced split +constructions and coordinate flags, are acknowledged. No priority claim is made. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/README.md b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/README.md new file mode 100644 index 0000000000..5784b8b928 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/README.md @@ -0,0 +1,70 @@ +# Balanced split frames with shared sums and reusable live controls + +**κ = 10366199626713 / 200000000000000000 = 0.000051830998133565** + +The conditional bound is `T(n) = O(n (log n)^(1-kappa))`. +This is **0.9788258% above our original PR #74 result**, **0.8097927% above +pinned PR #71**, and **0.8082664% above PR #75's claim observed on 8 October +2026**. The later PR #79 claim `5.1745625472866e-5`, observed at 19:55 UTC on the same +date, is also below this result by **0.1649853%**. These compare asymptotic exponent savings; they are not measured +multiplication speedups. + +| Quantity | Original PR #74 | Pinned PR #71 | This composition | +| --- | ---: | ---: | ---: | +| h23 auxiliary roles | 27,698 | 27,455 | 27,136 | +| h25 auxiliary roles | 36,310 | 36,015 | 35,744 | +| Physical width | 136,157,010 | 135,075,665 | 133,862,024 | +| Conditional κ | 5.132858076595e-5 | 5.1414646104039e-5 | 5.1830998133565e-5 | + +## Construction + +Compose eumemic's PR #69 column-balanced coarse sums with Chafik Boukhalfa's +PR #71 anchored split recursion and next-use-aware live reclamation. Apply +our original-envelope node order before carrier matching, then relabel the +geometric coordinates and recompute the actual fixed-basis profiles. + +The balanced graph has 67,460 / 94,993 active additions, compared with +PR #71's 68,771 / 96,718. Every prescribed output is unchanged. The complete +physical words pay for all XORs, frame raises, copied centers and data blocks. +The width now lies below `2^27`; its role-logarithm and product-row constants +are recomputed in the exact certificate. + +## Evidence and reproduction + +- [Proof, scope and contributor credits](PROOF.md) +- [Exact certificate](certificate.json) +- [Selected graph and coordinate choices](selection.json) +- [Immutable source manifest](SOURCE.json) +- [Independent dense scalar audit](graph-audit.json) +- [Independent exact arithmetic audit](independent-audit.json) +- [Verification receipt](validation.json) and [raw log](verification.log) + +Use Python 3.11 or newer and a C++17 compiler with unsigned 128-bit support: + +```sh +make balanced-split-frames-verify +``` + +This regenerates both words from pinned sources, checks their selected raw +hashes, audits the complete scalar graph, independently replays every input +and dirty basis vector in both orientations, reconstructs every literal frame +transition and exact profile, and checks the full paid recurrence and assembly. +The two replay dimensions contain 30,678 / 40,344 basis coordinates. +Both profiles have zero CRT disagreements. Independent arithmetic verifies +all 47 strict inequalities, seven margins, adjacent-grid rejection, and +exclusion of the complete pinned PR #71 profile at the new bit saving. + +The earlier full-suite receipt in `../ordered-frames/validation.json` covers +that historical source state. Current upstream checks and formal packages +remain separate CI jobs. The new source archives retain original notices +and original root documentation so predecessor pins remain unchanged. + +All inherited analytic, all-size compiler, fixed-tape, precision, routing, +prime-selection and recovery hypotheses remain assumed. This is a verified +finite conditional witness, with no global-optimality or practical-speed claim. + +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. Original +PR #74 remains available in `../ordered-frames/`; all predecessor credits and +licenses remain applicable. + +Concurrent PR #75–#79 work is acknowledged; no priority claim is made. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/SOURCE.json b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/SOURCE.json new file mode 100644 index 0000000000..06404d9283 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/SOURCE.json @@ -0,0 +1,21 @@ +{ + "files": { + "references/frame-compiler/pr69/SOURCE.json": "928fa8cce0964a6894af3f40cbde6d983aac395336e5277f751c9cbf1b07957f", + "references/frame-compiler/pr71/SOURCE.json": "1c79309362044dd386f72946ccb2e258e98d07d7239ea89d8a8646338d24228a", + "research/balanced-split-frames/check.py": "45fb95cb2a6b0573efbe37938c149936f4aa4fff1a88425380af7bc59239b4ae", + "research/balanced-split-frames/graph_audit.py": "b95cf9269fbcaf7f7b9732b28d7a8b790feefc262e86a36de33a92ab7906a8b3", + "research/balanced-split-frames/independent_check.py": "02dd998ebe68f111a42657e1591416b28b618a8d58bbd4fb0686d3afd929db1a", + "research/balanced-split-frames/producer.py": "ec94e4b7af370f7e921fffa3679e80d081a672dbd3ff198043edfb0dc7a9cc9d", + "research/balanced-split-frames/profile-23.json": "7f61525499f56ccc3a183a2741ef823cce30423475fa586ba7d36610b5b66844", + "research/balanced-split-frames/profile-25.json": "9b4d0647e3667af963c164c048c6ea750d90397b046336ede5a5b6902a9f6473", + "research/balanced-split-frames/selection.json": "cbc616540af0ff5b63a90a920c70acd660fbb67052e4dc19889fe0443f2129f4", + "research/balanced-split-frames/transitions-23.json": "0e9b6bbb1f9f08b34077bb93a60b39c2d61cf8f1329c884fd47326bf32bfac60", + "research/balanced-split-frames/transitions-25.json": "3bffd56836edefb309825f4ba303dc27ae88455aa7c8fc918af3ef24d82caee3", + "research/balanced-split-frames/word-23.json.gz": "956b886339ccbd3d599c5e0ec403b870958d052f3442067e8f12a56318e9525d", + "research/balanced-split-frames/word-25.json.gz": "ea090af1c4b56b7dae31d1f0d3fece4417677160f07c372e0455d7f8ac31c7b0", + "research/rank-pair-refinement/refine.py": "a19a79ea064fe66cb5f4e2971d6ab277cdfd452975c539e23066174533430691" + }, + "pr69_commit": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "pr71_commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "scope": "Selected sources and finite inputs. The archived PR69 and PR71 manifests bind the complete inherited source closure; generated axis receipts and arithmetic/audit certificates are checked outputs." +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/certificate.json b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/certificate.json new file mode 100644 index 0000000000..6a3cfa48df --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/certificate.json @@ -0,0 +1,740 @@ +{ + "W": 133862024, + "accepted": { + "lower": "99999999999999999979924873504956311258242134978917/100000000000000000000000000000000000000000000000000", + "strict_gap": "20075126495043683558076755370663/100000000000000000000000000000000000000000000000000", + "terms": { + "1": { + "lower": "578243869104998674370968149468068831065643870861/25000000000000000000000000000000000000000000000000", + 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python3 +"""Screen complete paid profiles from independently replayed axis constructions.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions required') +from pathlib import Path +from collections import Counter +from fractions import Fraction as Q +import importlib.util,argparse,json,subprocess,tempfile,hashlib,os,shlex +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +from producer import check_sources +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m +exact=load('candidate_exact',ROOT/'research/rank-pair-refinement/refine.py') +balanced=load('candidate_assembly',DEP/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') + +def profile(path): + v=json.loads(Path(path).read_text()) + return v['profile'] if 'profile' in v else v + +def calculate(first,second): + profiles=[profile(first),profile(second)] + N=4073300;m=575 + assert [p['h'] for p in profiles]==[23,25] + W=2*N+sum(N//p['v']*p['R'] for p in profiles) + parts={'data':Counter({1:18*N,21:2*N,17:2*N,481:2*N}),'endpoint_copy':Counter({1:N})} + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 + assert p['rank_sum']==h*p['R']+p['loss']==sum(t*n for t,n in enumerate(p['blocks'])) + assert p['loss']==h*(h-1) + parts[f'internal_{h}']=Counter({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + parts[f'exterior_{h}']=Counter({h:bank,m-2*h:bank}) + parts[f'growth_{h}']=Counter({1:2*N,h-2:2*N}) + rows=sum(parts.values(),Counter());assert sum(t*n for t,n in rows.items())==m*W-1846900 + lo,hi,grid=1,71700000000000,10**18 + while lo+11 + result.update(status='Verified finite conditional witness; inherited all-size transfer remains assumed', + source_manifest_sha256=hashlib.sha256((HERE/'SOURCE.json').read_bytes()).hexdigest(), + axes=axes,eventual_bounds=balanced.cutoffs(result['finite_bridge'],result['assembly']), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113',pr71_kappa=Q(previous['kappa']), + relative_gain_pr71=result['kappa']/Q(previous['kappa'])-1, + pr71_complete_profile_exclusion_lower=old_lower)) + result=arithmetic.js(result) + path=HERE/'certificate.json' + if record:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:assert result==json.loads(path.read_text()) + print('PASS exact moment, next-grid exclusions, 47 inequalities and seven margins',flush=True) + return result + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--record',action='store_true');args=parser.parse_args();generate(args.record) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/producer.py b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/producer.py new file mode 100644 index 0000000000..8d68303a3b --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/producer.py @@ -0,0 +1,132 @@ +#!/usr/bin/env python3 +"""Balanced coarse sums + anchored split/live frames + core ordering and coordinates. + +Composition for Thomas DiFiore with OpenAI Codex assistance. Apache-2.0. +PR69 coarse sums: eumemic. PR71 split/live composition: Chafik Boukhalfa. +Graph: Avi Eisenberg PR62; split operation: Rohan Garg PR59; reclamation: +Rohan Arun PR65/67, Dominik Scholz PR63/68, eumemic PR57. Original notices +and exact sources are retained under references/frame-compiler/pr69 and pr71. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +from hashlib import sha256 +import argparse,ast,gzip,importlib.util,json,types +from concurrent.futures import ProcessPoolExecutor +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +import split_pair_graph as provider +import split_pair_compiler as ancestor +from binary_frame_replay import replay + + +def check_sources(): + for folder in (DEP,ROOT/'references/frame-compiler/pr69'): + manifest=json.loads((folder/'SOURCE.json').read_text()) + for name,digest in manifest['files'].items(): + assert sha256((folder/name).read_bytes()).hexdigest()==digest,name + manifest=json.loads((HERE/'SOURCE.json').read_text()) + required={str((HERE/name).relative_to(ROOT)) for name in ('producer.py','check.py','graph_audit.py','independent_check.py','selection.json')} + assert required <= set(manifest['files']), 'Incomplete selected source closure' + for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + + +def reorder(c): + groups={} + for x in sorted(c.active): + if c.args[x]: groups.setdefault((c.core[x],c.union[x]),[]).append(x) + def key(item): + (core,cover),nodes=item + return cover.bit_count()-core.bit_count(),-core,cover,min(nodes) + ids=list(range(len(c.inputs)+1))+[x for _,nodes in sorted(groups.items(),key=key) for x in nodes] + mapping={x:i for i,x in enumerate(ids)} + args,core,cover,provenance=c.args,c.core,c.union,c.provenance + c.args=[tuple(mapping[y] for y in args[x]) if args[x] else None for x in ids] + c.core=[core[x] for x in ids];c.union=[cover[x] for x in ids] + c.provenance=[provenance[x] for x in ids] + c.active={mapping[x] for x in c.active};c.outputs={k:mapping[v] for k,v in c.outputs.items()} + c.support_in.cache_clear() + c.verify() + return c + + +def graph(h,ordered=True): + source=Path(provider._graph.__file__).read_text() + original=ROOT/'references/frame-compiler/pr69/scripts/experiments/balanced_coarse_compiler.py' + replacements={} + for node in ast.parse(original.read_text()).body: + if isinstance(node,ast.Assign): + for target in node.targets: + if isinstance(target,ast.Name) and target.id in ('BEFORE','AFTER'): + replacements[target.id]=ast.literal_eval(node.value) + assert source.count(replacements['BEFORE'])==1 + module=types.ModuleType('balanced_split_private_graph');module.__file__=provider._graph.__file__ + exec(compile(source.replace(replacements['BEFORE'],replacements['AFTER']),module.__file__+':balanced-coarse','exec'),module.__dict__) + previous=provider._graph + try: + provider._graph=module + c=provider.graph(h) + finally: + provider._graph=previous + return reorder(c) if ordered else c + + +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + +def compile_axis(h): + check_sources() + config=json.loads((HERE/'selection.json').read_text())['axes'][str(h)] + previous_graph,previous_order=provider.graph,provider.ordered_build + # graph() calls the original provider; keep that callable private while + # the inherited driver resolves the selected composed graph dynamically. + original_graph=previous_graph + def selected_graph(dimension): + provider.graph=original_graph + try:return graph(dimension) + finally:provider.graph=selected_graph + try: + provider.graph=selected_graph + provider.ordered_build=lambda original,dimension:original + compiled,word=ancestor.compile_axis(h) + finally: + provider.graph,provider.ordered_build=previous_graph,previous_order + compiled['graph_configuration']=config + word=relabel(word,config['coordinate_permutation']) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + path=HERE/f'word-{h}.json.gz' + with path.open('wb') as stream: + with gzip.GzipFile(filename='',fileobj=stream,mode='wb',mtime=0) as archive:archive.write(raw) + receipt=replay(path) + assert sha256(raw).hexdigest()==config['expected_word_sha256'] + axis=dict(configuration=config,compiled=compiled,replay=receipt, + word_sha256=sha256(raw).hexdigest(),gzip_sha256=sha256(path.read_bytes()).hexdigest()) + (HERE/f'axis-{h}.json').write_text(json.dumps(axis,indent=2)+'\n') + print(f'PASS fresh balanced/split/core word h={h}, roles={receipt["roles"]}',flush=True) + + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--h',type=int,choices=(23,25));args=parser.parse_args() + if args.h:compile_axis(args.h) + else: + with ProcessPoolExecutor(max_workers=2) as pool:list(pool.map(compile_axis,(23,25))) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/profile-23.json b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/profile-23.json new file mode 100644 index 0000000000..013f4e59c7 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/profile-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27136,"loss":506,"rank_sum":624634,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38292,"crt_matrices":5488,"crt_disagreements":0,"blocks":[0,355721,21666,6948,6524,3093,4314,2400,3266,1501,2094,1008,1374,586,732,353,307,139,62,16,0,23,0,0]} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/profile-25.json b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/profile-25.json new file mode 100644 index 0000000000..1e3b6b89aa --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/profile-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35744,"loss":600,"rank_sum":894200,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52202,"crt_matrices":7623,"crt_disagreements":0,"blocks":[0,490052,26188,13531,7191,4637,5355,4229,3705,2610,2620,2080,1814,1357,1070,868,612,463,233,56,141,0,71,25,0,0]} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/selection.json b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/selection.json new file mode 100644 index 0000000000..57cf3b6b65 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/selection.json @@ -0,0 +1,86 @@ +{ + "source_pr71": "1bef94fd40a746452548c84a4a8f8834670a3113", + "source_pr69": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "axes": { + "23": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 22, + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 20, + 19, + 21 + ], + "expected_word_sha256": "8dc6696a274e70ca0af3fc49c4bdede362adaedc8dc322f335e3dab499f1ed48" + }, + "25": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 2, + 1, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "expected_word_sha256": "2c923afe366219ee3fffc9db063c91e44cdf7cbbdb62246b8e6a297dc440b577" + } + } +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr78/FETCH.json b/references/frame-compiler/pr84/references/frame-compiler/pr78/FETCH.json new file mode 100644 index 0000000000..4db82db4a1 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr78/FETCH.json @@ -0,0 +1,48 @@ +{ + "pr": 78, + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf", + "files": [ + { + "path": "research/coordinate-flags/verify.py", + "blob_sha": "216ccd3d58c1331fffdb008df7547982cb43d2ae", + "sha256": "b59a5345c8684bb67a5ea666d5de11422c45cdf19f2c13de1520623a71bae7e1", + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf" + }, + { + "path": "research/coordinate-flags/order-23.json", + "blob_sha": "035f01df59be3312e30ec692754d3a331a766799", + "sha256": "def92cd69f3fba2986c7a230ece45f9eb63fd38fef512d055bf0adffe9edfa82", + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf" + }, + { + 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Coordinate-flag relabeling and finite verification: Rohan Arun with OpenAI Codex assistance. Based on Chafik Boukhalfa PR71 and the inherited contributions credited in research/coordinate-flags/README.md. Existing contributor originals are preserved. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr78/SOURCE.json b/references/frame-compiler/pr84/references/frame-compiler/pr78/SOURCE.json new file mode 100644 index 0000000000..15f08e2813 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr78/SOURCE.json @@ -0,0 +1,15 @@ +{ + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf", + "files": { + "FETCH.json": "79d6b40af23f03d6737be9a072ebca4f96aa6a663895cffdee4052432b5d13b8", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "0a0e0314b9d1e23a193e92aa633fc50c432b6e3ea326f40d5cbb1ea538823149", + "research/coordinate-flags/README.md": "cbc4f20613e1dfafcce7c5f82c274fdd48898cc968d14fbea7bf9b1a47607e85", + "research/coordinate-flags/SOURCE.json": "c0ec88783c06431d95e1e8efabbb2928857f1d4ca8d0ada10206e99322ae78e2", + "research/coordinate-flags/order-23.json": "def92cd69f3fba2986c7a230ece45f9eb63fd38fef512d055bf0adffe9edfa82", + "research/coordinate-flags/order-25.json": "209dee5fac04fa91a5bf63ed0307a56e849cc6800fa543254590045e0c95d6a5", + "research/coordinate-flags/verify.py": "b59a5345c8684bb67a5ea666d5de11422c45cdf19f2c13de1520623a71bae7e1" + }, + "pr": 78, + "scope": "Exact attributed contributor inputs and reported comparison certificate, not a new audit of the entire foreign claim." +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/README.md b/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/README.md new file mode 100644 index 0000000000..950f4eaa2d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/README.md @@ -0,0 +1,68 @@ +# Coordinate flags for the split-pair witness + +This finite conditional witness gives kappa = 12857195906507 / 250000000000000000 += 5.1428783626028e-5, about 0.02750% above PR71's 5.1414646104039e-5. +The bit saving is 25715714341 / 500000000000000. Roles, physical width, +recursive rank mass, scalar operations, paid clearing and copied endpoints +remain those of PR71. The changed object is the coordinate flag used to +decompose internal frame transitions into consecutive pivot blocks. + +## General relabeling argument + +Let P be a permutation matrix on the h coordinates. It commutes with J, +so P commutes with the fixed basis L = I+J and preserves the form I-J/9. +For a core/cover frame F(C,U), the relabeled projector is +P F(C,U) P^-1 = F(P C,P U). Consequently, every frame inclusion, rank, +nondegeneracy condition, projector denominator bound and elementary role +operation is preserved. The existing exact CRT bounds apply unchanged. + +Relabel each input triple T to P T, each output (c,T) to (P c,P T), +each frame mask by P, and each scatter row by the induced triple permutation. +The role slots and literal XOR operations do not change. This conjugates +the complete linear word by the input/output permutation and therefore +preserves its identity on every ordinary input and arbitrary dirty role. +The verifier independently replays that identity in both orientations. + +The data component sums over every pair of source triples. Independent +coordinate permutations on the two axes induce a bijection on that complete +Cartesian product. Hence its existing complete histogram, copied-center +costs and endpoint corrections are unchanged. This argument uses the full +case set; it would not justify retaining a selected subset's histogram. + +North-east corner rank profiles depend on the fixed coordinate order. +Conjugating by P can change which adjacent pivots form a recursive block, +even though total rank is unchanged. We regenerate these profiles from the +actual relabeled words rather than assuming their costs are invariant. +Both dimensions use the selected orders in order-23.json and order-25.json. + +## Verification and scope + +Run `make coordinate-flags-verify`. It checks source closure, regenerates +both words byte for byte, replays every ordinary and dirty basis vector in +both orientations, reconstructs physical transitions, and recomputes all +fixed-I+J profiles with the inherited exact CRT bounds. Six negative controls +reject inconsistent coordinates, missing source/output relabeling, missing +operations and aliased terminal roles. + +The complete paid child list is rebuilt independently. Directed rational +moment bounds, an independent logarithm/exponential computation, 47 strict +constraints, seven margins, both next-grid rejections and exclusion of +PR71's complete profile at the new saving are checked. + +The search used structured coordinate orders and bounded adjacent swaps. +No global optimum or practical speedup is claimed. This remains conditional +on the inherited all-size residual compiler, routing, recovery, prime +selection, fixed finite-alphabet multitape simulation and analytic transfer. +The full expanded repository rerun is pending; this package is a draft. + +## Credit + +Chafik Boukhalfa's PR71 supplies the split-pair graph and next-use scoring. +Rohan Garg introduced the split operation (PR59); Avi Eisenberg supplied +interval/pair assembly (PR62); Dominik Scholz supplied ranked frames and +pending controls (PR63/68); Rohan Arun supplied schedule and profile-cost +search (PR65/67); eumemic supplied the reversible compiler and physical +checkers (PR57). Credit also icekylinx, James Chang, Zhihao Chen, Aurel +Prosz/Paureel, Swapnil Jain, Alejandro Zarzuelo Urdiales, RaD/hipotures, +Douglas Colkitt, OpenAI and all inherited contributors. Existing sources, +licenses and notices are retained. 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b/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/order-23.json @@ -0,0 +1,53 @@ +{ + "h": 23, + "order": [ + 1, + 3, + 2, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 21, + 20, + 22, + 0 + ], + "mapping": { + "1": 0, + "3": 1, + "2": 2, + "4": 3, + "5": 4, + "6": 5, + "7": 6, + "8": 7, + "9": 8, + "10": 9, + "11": 10, + "12": 11, + "13": 12, + "14": 13, + "15": 14, + "16": 15, + "17": 16, + "18": 17, + "19": 18, + "21": 19, + "20": 20, + "22": 21, + "0": 22 + } +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/order-25.json b/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/order-25.json new file mode 100644 index 0000000000..7c06a68e6e --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/order-25.json @@ -0,0 +1,57 @@ +{ + "h": 25, + "order": [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 23, + 22, + 24, + 0 + ], + "mapping": { + "1": 0, + "2": 1, + "3": 2, + "4": 3, + "5": 4, + "6": 5, + "7": 6, + "8": 7, + "9": 8, + "10": 9, + "11": 10, + "12": 11, + "13": 12, + "14": 13, + "15": 14, + "16": 15, + "17": 16, + "18": 17, + "19": 18, + "20": 19, + "21": 20, + "23": 21, + "22": 22, + "24": 23, + "0": 24 + } +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/verify.py b/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/verify.py new file mode 100644 index 0000000000..216ccd3d58 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/verify.py @@ -0,0 +1,89 @@ +"""Rebuild the coordinate-permuted PR71 words and their exact paid bound.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2];HERE=Path(__file__).resolve().parent +sys.path.insert(0,str(ROOT/'scripts/experiments')) +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +from split_pair_arithmetic import refine,audit +import binary_frame_math as arithmetic +from pin_split_pair_sources import required_paths +from fractions import Fraction as Q +from collections import Counter +from itertools import combinations +from math import comb +from hashlib import sha256 +import gzip,json,subprocess,tempfile + +def required(): + names=required_paths()|{'research/split-pair/SOURCE.json','certificates/split-pair-kappa.json', + '.github/workflows/verify.yml'} + names.update(str(p.relative_to(ROOT)) for p in HERE.iterdir() if p.is_file() and p.name not in ('SOURCE.json','validation.json')) + return names + +def sources(): + manifest=json.loads((HERE/'SOURCE.json').read_text()) + assert required()<=set(manifest['files']),'Source closure incomplete' + for name,digest in manifest['files'].items():assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + +def relabel(word,config): + h=word['h'];order=config['order'];assert sorted(order)==list(range(h)) + perm={old:new for new,old in enumerate(order)} + assert perm=={int(k):v for k,v in config['mapping'].items()} + triples=list(combinations(range(h),3));lookup={t:i for i,t in enumerate(triples)} + index={i:lookup[tuple(sorted(perm[x] for x in triple))] for i,triple in enumerate(triples)} + def mask(m):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(index[int(i)]):s for i,s in word['sources'].items()} + v=word['v'];word['scatter']=[[v+index[a-v],b] for a,b in word['scatter']] + word['outputs']=[[s,g,perm[c],sorted(perm[x] for x in triple)] for s,g,c,triple in word['outputs']] + return word + +def exact(profiles): + cert=json.loads((HERE/'certificate.json').read_text());baseline=json.loads((HERE/'baseline-pr71.json').read_text()) + N=comb(23,3)*comb(25,3);m=575;W=2*N+sum(N//p['v']*p['R'] for p in profiles) + L=sum(N//p['v']*p['loss'] for p in profiles) + rows=Counter({1:19*N,21:2*N,17:2*N,481:2*N}) + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 and p['v']==comb(h,3) + assert sum(t*n for t,n in enumerate(p['blocks']))==h*p['R']+h*(h-1)==p['rank_sum'] + rows.update({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + rows[h]+=bank;rows[m-2*h]+=bank;rows[1]+=2*N;rows[h-2]+=2*N + bit=dict(m=m,N=N,W=W,L=L,total_rank=sum(t*n for t,n in rows.items()),child_multiplicities=dict(sorted(rows.items()))) + assert bit['total_rank']==m*W-N+L + assert arithmetic.js(bit)==cert['bit'] + saving=Q(cert['bit_saving']);moment=refine.exact_moment(m,W,rows,saving) + rejected=refine.exact_moment(m,W,rows,saving+Q(1,10**18)) + assert moment['upper']<11 + print('PASS exact conditional kappa',result['kappa'],'47 constraints, seven margins, independent bounds and next-grid controls') + +def verify(): + sources();profiles=[] + with tempfile.TemporaryDirectory(prefix='coordinate-flags-') as directory: + work=Path(directory);exe=work/'profiles' + subprocess.run(['c++','-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'scripts/experiments/binary_frame_profiles.cpp'),'-o',str(exe)],check=True) + for h in (23,25): + original=json.loads(gzip.decompress((ROOT/f'certificates/split-pair-word-{h}.json.gz').read_bytes())) + config=json.loads((HERE/f'order-{h}.json').read_text());word=relabel(original,config) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + assert raw==gzip.decompress((HERE/f'word-{h}.json.gz').read_bytes()) + path=work/f'word-{h}.json';path.write_bytes(raw);checked=replay(path) + stored=json.loads((HERE/f'replay-{h}.json').read_text());assert arithmetic.js(checked)==stored['replay'] + trans=work/f'transitions-{h}.bin';receipt=prepare(path,trans);assert arithmetic.js(receipt)==stored['transitions'] + subprocess.run([str(exe),str(trans)],check=True) + profile=json.loads(Path(str(trans)+'.profiles.json').read_text());assert profile==json.loads((HERE/f'profiles-{h}.json').read_text()) + profiles.append(profile);print('PASS complete relabelled physical word and profile',h,flush=True) + exact(profiles) +if __name__=='__main__':verify() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/.gitattributes b/references/frame-compiler/pr84/references/frame-compiler/pr79/.gitattributes new file mode 100644 index 0000000000..48ba61f217 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/.gitattributes @@ -0,0 +1,15 @@ +* text=auto eol=lf +*.pdf binary +# Unified diffs require a leading space on blank context lines. +*.patch -whitespace +# Preserve the exact upstream bytes, including original whitespace. +upstream/** -whitespace +# Preserve the exact pinned third-party proof snapshots and notices. +references/copied-centers/pr29/** -whitespace +references/copied-centers/pr33/** -whitespace +references/semantic-bulk/** -whitespace + +# Immutable contributor archives retain original CRLF and whitespace bytes. +references/frame-compiler/pr69/** -text -whitespace +references/frame-compiler/pr70/** -text -whitespace +references/frame-compiler/pr71/** -text -whitespace diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/.github/workflows/verify.yml b/references/frame-compiler/pr84/references/frame-compiler/pr79/.github/workflows/verify.yml new file mode 100644 index 0000000000..33886a2cdf --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/.github/workflows/verify.yml @@ -0,0 +1,63 @@ +name: Verify research artifacts + +on: + push: + pull_request: + workflow_dispatch: + +permissions: + contents: read + +jobs: + verify: + runs-on: ubuntu-24.04 + timeout-minutes: 20 + strategy: + fail-fast: false + matrix: + python-version: ['3.11', '3.13', '3.14'] + group: [community, producers, certificates, ternary, research, tests, strips, clones, positive, joint, pair, balanced] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: ${{ matrix.python-version }} + - name: Install headers for the exact enlarged-frame profiler + if: matrix.group == 'positive' + run: | + if ! test -f /usr/include/boost/multiprecision/cpp_int.hpp; then + sudo apt-get update + sudo apt-get install -y libboost-dev + fi + - name: Check arithmetic, source hashes, finite identities, and patches + run: make verify-${{ matrix.group }} + - name: Require reproducible certificates and patches + run: git diff --exit-code + + formal: + runs-on: ubuntu-24.04 + timeout-minutes: 30 + strategy: + fail-fast: false + matrix: + package: [historical, gaussian, matrix] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: '3.13' + - name: Install elan; each project pins its Lean toolchain + run: | + curl --proto '=https' --tlsv1.2 -sSf https://raw.githubusercontent.com/leanprover/elan/0e36a07b9bbcc5381fa6250df109f9a4f94d7bac/elan-init.sh -o /tmp/elan-init.sh + sh /tmp/elan-init.sh -y --default-toolchain none + echo "$HOME/.elan/bin" >> "$GITHUB_PATH" + - name: Fetch pinned Mathlib build cache + if: matrix.package == 'historical' + working-directory: formal/lean + run: lake exe cache get + - name: Check formal package and theorem axiom dependencies + run: make formal-${{ matrix.package }}-verify diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/LICENSE b/references/frame-compiler/pr84/references/frame-compiler/pr79/LICENSE 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/Makefile b/references/frame-compiler/pr84/references/frame-compiler/pr79/Makefile new file mode 100644 index 0000000000..e2e2c38a36 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/Makefile @@ -0,0 +1,447 @@ +.PHONY: verify note audit-note tuned-note reuse-note incidence-note dag-note shared-point-note paired-note compact-note complex-note ternary-note fetch +.DEFAULT_GOAL := verify + +.PHONY: community-audit-check +community-audit-check: + python3 scripts/audit_community_candidate.py --check docs/research/community-audit-arithmetic.json + +.PHONY: community-followup-check +community-followup-check: + python3 scripts/audit_followup_candidate.py --candidate-root . --check docs/research/community-followup-arithmetic.json + +.PHONY: verify-community verify-producers verify-certificates verify-ternary verify-tests +# CI runs these in separate checkouts. Keep local verification sequential: +# different groups regenerate certificates that another group may read. +verify: + $(MAKE) verify-community + $(MAKE) verify-producers + $(MAKE) verify-certificates + $(MAKE) verify-ternary + $(MAKE) verify-research + $(MAKE) verify-strips + $(MAKE) verify-clones + $(MAKE) verify-positive + $(MAKE) verify-joint + $(MAKE) verify-pair + $(MAKE) verify-balanced + $(MAKE) verify-tests + +verify-community: community-audit-check community-followup-check copied-reversed-producer copied-reversed-check copied-fixed-reversed-producer copied-fixed-reversed-check + $(MAKE) copied-fixed-verify + $(MAKE) climbed-48-verify + +verify-producers: + $(MAKE) copied-centers-verify + $(MAKE) structured-bulk-verify + $(MAKE) endpoint-gauge-producer endpoint-gauge-certificate + $(MAKE) partial-swap-producer partial-swap-certificate + +verify-certificates: + python3 scripts/prime_field_network.py + python3 scripts/complex_network.py + python3 scripts/fast_gaussian.py + $(MAKE) batched-certificate batched-patch + python3 scripts/certify.py + python3 scripts/search_network.py + python3 scripts/make_patch.py + python3 scripts/nonadjacent.py + python3 scripts/make_nonadjacent_patch.py + python3 scripts/tune_routing.py + python3 scripts/research_networks.py + python3 scripts/search_network_variants.py + python3 scripts/block_label_targets.py + python3 scripts/audit_block_labels.py + python3 scripts/audit_additive_labels.py + python3 scripts/small_block_witness.py + python3 scripts/incidence_network.py + python3 scripts/make_incidence_patch.py + python3 scripts/search_incidence_partitions.py + python3 scripts/dag_network.py + python3 scripts/make_dag_patch.py + python3 scripts/shared_point_network.py + python3 scripts/make_shared_point_patch.py + python3 scripts/paired_network.py + python3 scripts/make_paired_patch.py + python3 scripts/prepare_layers.py + python3 scripts/audit_sparse_fusion.py + python3 scripts/audit_fused_block.py + python3 scripts/audit_short_guards.py + python3 scripts/audit_gather_schedules.py + python3 scripts/audit_coded_carries.py + python3 scripts/audit_cancellation.py + python3 scripts/audit_joint_frames.py + python3 scripts/audit_compact_controls.py + python3 scripts/compact_control_layer.py + python3 scripts/make_compact_control_patch.py + python3 scripts/audit_scratch_pooling.py + python3 scripts/reuse_network.py + python3 scripts/make_reuse_patch.py + +verify-ternary: + python3 scripts/complex_compression.py + python3 scripts/make_complex_compression_patch.py + python3 scripts/audit_ternary_side.py + python3 scripts/make_ternary_patch.py + +verify-tests: + python3 scripts/run_isolated_tests.py + git apply --check --directory=upstream patches/frozen-154.patch + git apply --check --directory=upstream patches/balanced-153.patch + git apply --check --directory=upstream patches/same-network-129.patch + git apply --check --directory=upstream patches/h46-111.patch + git apply --check --directory=upstream patches/h46-109.patch + git apply --check --directory=upstream patches/h46-108.patch + git apply --check --directory=upstream patches/h46-rational.patch + git apply --check --directory=upstream patches/nonadjacent-layout.patch + git apply --check --directory=upstream patches/frozen-nonadjacent-107.patch + git apply --check --directory=upstream patches/h46-nonadjacent-78.patch + git apply --check --directory=upstream patches/h46-nonadjacent-76.patch + git apply --check --directory=upstream patches/h46-shared-side-75.patch + git apply --check --directory=upstream patches/h46-incidence-67.patch + git apply --check --directory=upstream patches/h46-dag-63.patch + git apply --check --directory=upstream patches/h46-shared-point.patch + git apply --check --directory=upstream patches/h50-paired-59.patch + git apply --check --directory=upstream patches/compact-control-34.patch + git apply --check --directory=upstream patches/complex-compression-31.patch + git apply --check --directory=upstream patches/ternary-30.patch + git apply --check --directory=upstream patches/batched-23.patch + +note: + mkdir -p artifacts + tectonic --outdir artifacts notes/parameter-note.tex + +audit-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/nonadjacent-axis-note.tex + +tuned-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/routing-tuned-note.tex + +reuse-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/stage-reuse-note.tex + +incidence-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/incidence-note.tex + +dag-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/dag-note.tex + +shared-point-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/shared-point-note.tex + +paired-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/paired-note.tex + +compact-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/compact-control-note.tex + +complex-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/complex-compression-note.tex + +ternary-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/ternary-note.tex + +fetch: + python3 scripts/fetch_upstream.py + +.PHONY: batched-certificate batched-patch batched-note +PDFLATEX ?= pdflatex +TEX_ENGINE ?= pdflatex +TECTONIC ?= tectonic + +batched-certificate: + python3 scripts/controlled_bit_rank_moment.py --output certificates/controlled-bit-rank-moment.json > /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify + +.PHONY: balanced-split-verify verify-balanced +balanced-split-verify: + python3 scripts/experiments/verify_balanced_split.py + python3 scripts/experiments/audit_balanced_split_completion.py + python3 scripts/experiments/audit_balanced_split_exchange.py + python3 -m unittest discover -s tests -p 'test_balanced_split*.py' -v + +verify-balanced: balanced-split-verify diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/NOTICE b/references/frame-compiler/pr84/references/frame-compiler/pr79/NOTICE new file mode 100644 index 0000000000..8a6bef1613 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/NOTICE @@ -0,0 +1,337 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Balanced coarse split composition (2026-10-08) +--------------------------------------------- +Eumemic / @eumemic supplied PR69's balanced coarse sums, with OpenAI Codex +assistance. Alejandro Zarzuelo Urdiales / @alejandrozu supplied PR70's bounded +carry-exchange strategy with the AI disclosures retained in the source archive. +Chafik Boukhalfa / @chafreaky, with OpenAI Codex assistance, selected the row/ +half-plane coarse rules, future-compatible unit completion, exact integer-price +carry adaptation, composition and this certificate package. The PR71 anchored +split vector, schedules, arithmetic, pending controls and their contributor +chain are retained as credited above. Original PR69/70 sources, licenses and +notices and the complete published PR71 baseline are preserved under +references/frame-compiler. All earlier notices remain applicable. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/README.md b/references/frame-compiler/pr84/references/frame-compiler/pr79/README.md new file mode 100644 index 0000000000..1bd7139657 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/README.md @@ -0,0 +1,184 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: balanced coarse split frames + +The [balanced-split proof and reproduction guide](research/balanced-split/README.md) +gives **κ=25872812736433/500000000000000000=5.1745625472866e-5**, approximately +**0.6437453019850683%** above the complete published PR71 witness. It composes +PR69 balanced coarse sums and a bounded PR70 carry exchange with PR71's +anchored split graph, future unit completion and profile-cost pending controls. +All actual words, dirty inputs, paid profiles and 47 strict assembly constraints +are checked by `make balanced-split-verify`. This finite conditional construction +retains the inherited all-size hypotheses and contributor notices. Chafik +Boukhalfa prepared the selected composition with OpenAI Codex assistance. + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/SOURCE.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/SOURCE.json new file mode 100644 index 0000000000..6ba76e935b --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/SOURCE.json @@ -0,0 +1,257 @@ +{ + "commit": "9a58e62cf9e8954a4dde3c9b1372d733c276a6d1", + "files": { + ".gitattributes": "5f257f4e9e574ad5767f902242f519dad19cc455d6858f49234d0ccc345cabf1", + ".github/workflows/verify.yml": "1a9cccd742ba2a5aa5a5ac38c1b7559bc0dec46b23d3ce3ff3e26c3137e6c3a2", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "Makefile": "1bf5b63d413280a68fc2b91a7e83a6172632e50c8177ca097d9622af669ee8d6", + "NOTICE": 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No external claimed bound is imported as a proof." + }, + "split_operation": { + "author": "Rohan Garg / rohangar1 with OpenAI Codex assistance", + "commit": "641f22e52913db784f3b6ff1176b0c2945aae45b", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "f85437ee441f2a028660dd5e8dbdc0ec7b52bb55c04ea34fa4829c154bfd0ac1", + "research/split-skip/SOURCE.json": "7c2b4646a3ecfef6f881da5c43e4bd0fa9a4d1b00548b8ab458d897e16735134", + "research/split-skip/split_graph.py": "9b16ba907cbd58611fb64bfb9211be7809d54822d44c78fc6167cf4ba79eb905" + }, + "repo": "CrocSwap/integer-mult-bounds", + "scope": "Preserved original split-pair operation and attribution. These files document the adapted grouping operation; they are not imported by this producer. Actual imported source closure is PR65 plus shared PR48." + } + }, + "status": "Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed" +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-profiles-23.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-profiles-23.json new file mode 100644 index 0000000000..ee696ff2ba --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-profiles-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27297,"loss":506,"rank_sum":628337,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38540,"crt_matrices":5512,"crt_disagreements":0,"blocks":[0,357189,20828,8114,5378,4120,3708,3149,2526,2013,1694,1444,960,837,528,481,240,205,49,100,0,23,0,0]} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-profiles-25.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-profiles-25.json new file mode 100644 index 0000000000..b0d73f3327 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-profiles-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35684,"loss":600,"rank_sum":892700,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":51168,"crt_matrices":7278,"crt_disagreements":0,"blocks":[0,491995,27247,10127,7839,5460,4947,4006,3802,2943,2456,2025,1787,1423,1124,867,560,478,221,170,46,59,0,25,0,0]} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-repository-validation.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-repository-validation.json new file mode 100644 index 0000000000..8079dc012c --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-repository-validation.json @@ -0,0 +1,92 @@ +{ + "bit_saving": "51748303221339/1000000000000000000", + "certificate_sha256": "0c9ddf817a7198d597b65cd178873a36910188cfe9bdd2b22a3477ee84df5e88", + "ci": { + "required": "All twelve arithmetic groups on Python3.11/3.13/3.14 and all three inherited formal packages, plus any other triggered checks", + "status": "PENDING" + }, + "final_archive_binding": { + "all_staged_source_blobs_match_manifest": true, + "checked_utc": "2026-10-08T19:48:16.522765+00:00", + "controls_log_sha256": "e2e08dad6d7a59a4a8a8484510ce0717a32c6d5e8384c99c7cce614ef4e6a2a1", + "exact_composition_rechecked": true, + "focused_controls": 24, + "reason": "Preserve the original CRLF and whitespace bytes of the new contributor archives in Git; no graph, engine, physical word, profile or mathematical change.", + "source_manifest_sha256": 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/dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/SOURCE.json @@ -0,0 +1,16 @@ +{ + "files": { + "research/copied-fixed/balanced_assembly.py": "4d27575dcad2b45a281a34054d311409ecd954f373c0c3a62c29bcc843f06a86", + "research/copied-fixed/certificate.json": "33b3373c04e18a7f4cee33ba68da6ed71934acc3e0179cca6197696be4befa22", + "research/copied-fixed/changed_graph.py": "375a7ca6cac6d153c1880fd5ea5b4525e5dca9d4ee3018d24d679c219b59c5b3", + "research/copied-fixed/profiles.cpp": "b9fbd71c746609948b60c441ba4601e88436956fe636d1810f270ce4ce6a63a6", + "research/copied-fixed/verify.py": "44932182ce6c4d39776650311262ef0ac1ea9b5da7220bc0f728e2789881f84a", + "scripts/exclusion_circuit.py": "b253f9d7318becda1c1f3b24e2287ed44a9c27fcea00cf9d531afb950d0457a0", + "scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34" + }, + "head": "b7194b8586844956904b33e9fe18f0c75606c11b", + "scope": "Unmodified producer inputs for experimental frame compiler; attribution retained in each file", + "source_pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/48" +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py new file mode 100644 index 0000000000..c7fd42867d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py @@ -0,0 +1,196 @@ +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit', 'complex'): + data = finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + 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"scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1", + "scripts/partial_swap/graph.py": "fd8c567759e26a10d2bad05508fd0355eb70fb116664d4e06e1858d0d8cb2ef9", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + } + }, + "status": "Conditional exact arithmetic witness; general transfer proofs are dependencies" +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "PR48": { + "author": "Chafik Boukhalfa", + "commit": "b7194b8586844956904b33e9fe18f0c75606c11b", + 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Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + } + }, + "gzip_sha256": "4629d45d5074f87706db46be3aa3cd369071cd215bc6560d641115aadcce54a0", + "word_sha256": "bd0cbf73756f2e4f8d3879ec6c7a194990eb9ec40aaf3580bdded6994798d920" + }, + "25": { + "compiled": { + "h": 25, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 36586, + "baseline_pr48_roles": 48329, + "histogram": { + "1": 55478, + "0": 416276, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + }, + "rank_mass": 915250, + "elementary_xors": 205650, + "stats": { + "augmentations": 286, + "regions": 73695, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json new file mode 100644 index 0000000000..346cf87ea3 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json @@ -0,0 +1,1087 @@ +{ + "accepted_moment": { + "degree": 8, + "lower": "34287951499999999998997315662315085394575263036671/34287951500000000000000000000000000000000000000000", + "rounding_denominator": 10000000000000000000000000000000000000000, + "saving": "5103158916233/100000000000000000", + "strict_gap": "2278828040192983762647964739/77927162500000000000000000000000000000000000000", + "terms": { + "1": { + "exp_lower": "5001621630918375893019301295747281962987/5000000000000000000000000000000000000000", + "exp_upper": "10003243261836751786038602591494564437549/10000000000000000000000000000000000000000", + "log_lower": "3177185020398675220004135749131/500000000000000000000000000000", + "log_upper": "6354370040797350440008271498263/1000000000000000000000000000000", + "weight": "61988/2833715" + 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rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.", + "All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.", + "Neither global optimality nor measured practical speedup is claimed." + ], + "rejected_moment": { + "degree": 8, + "lower": "8571987875000000003683551653063012975552828889113/8571987875000000000000000000000000000000000000000", + "rounding_denominator": 10000000000000000000000000000000000000000, + "saving": "51031589162331/1000000000000000000", + "strict_gap": "-920887913265753353254538048853/2142996968750000000000000000000000000000000000000", + "terms": { + "1": { + "exp_lower": "2000648652367350369920582377063597092877/2000000000000000000000000000000000000000", + "exp_upper": "250081081545918796240072797132949649399/250000000000000000000000000000000000000", + "log_lower": "3177185020398675220004135749131/500000000000000000000000000000", + "log_upper": 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b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json new file mode 100644 index 0000000000..42958fc74b --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json @@ -0,0 +1,195 @@ +{ + "artifact_sha256": { + "frame-profiles-23.json": "fec377bcf1512a427674983256b900229d4133026445b6e680c6e1e6dde5af7d", + "frame-profiles-25.json": 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orientations PASS", + "word_length": 621342 + }, + "schedule": "cover-core", + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4" + }, + "25": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 48329, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 41186, + "elementary_xors": 205977, + "h": 25, + "histogram": { + "0": 416741, + "1": 55478, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "2": 115781, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 915250, + "roles": 36586, + "stats": { + "augmentations": 286, + "clearing_xors": 2154, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "regions": 73695 + } + }, + "gzip_sha256": 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"3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "research/reordered-rank-pair/test_negative.py": "88832242e6f74e3fe08d109d4f21ff188a9ca0ae50c3e8f31da0243fe9501510", + "research/reordered-rank-pair/verify.py": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352", + "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3", + "scripts/experiments/binary_frame_profiles.cpp": "8e2e391d3ee57cbb1372c68e4aa031e1b861321536eabd642ada54e12e678669", + "scripts/experiments/binary_frame_replay.py": "392e78e62d7685c99a5888a7da743ea6c3dcad631af4a743c91e0c09348442bc", + "scripts/experiments/rank_pair_compiler.py": "9984aaccf880e4840402322d76678bfddb33ce7e494af78430a43429f51b85fd" + }, + "status": "Exact topological scheduling of unchanged PR63 graph/compiler; both physical orientations and fixed profiles checked" +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json new file mode 100644 index 0000000000..3b648dbe21 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "loss": 506, + "rank_sum": 642620, + "field_prime": 2305843009213693951, + "frames": 52475, + "distinct_matrices": 36399, + "crt_matrices": 6049, + "crt_disagreements": 0, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json new file mode 100644 index 0000000000..19cc34b4ca --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json @@ -0,0 +1,40 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "loss": 600, + "rank_sum": 915250, + "field_prime": 2305843009213693951, + "frames": 73697, + "distinct_matrices": 50394, + "crt_matrices": 8127, + "crt_disagreements": 0, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json new file mode 100644 index 0000000000..2883a5f7c9 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "frames": 52475, + "distinct_transitions": 138016, + "singles": 15939, + "rank_mass": 642620, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 53320, + "2": 77409, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "21": 165, + "22": 23 + }, + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json new file mode 100644 index 0000000000..3b4bc33ff6 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json @@ -0,0 +1,35 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "frames": 73697, + "distinct_transitions": 190838, + "singles": 20700, + "rank_mass": 915250, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69278, + "2": 108881, + "3": 14362, + "4": 16908, + 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a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz new file mode 100644 index 0000000000..6a239a3e9f Binary files /dev/null and b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz differ diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + 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a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 at the new bit saving, +and the new complete profile has exact upper moment <1. All47 strict assembly +conditions and seven margins pass. **53 Lean endpoints** pass:34 new universal, +15 concrete,4 reused rational-helper lemmas. No omitted proof, project axiom or +native decision shortcut. The math scope includes dirty-word/complement safety, +coordinate conjugacy, fresh-kernel clearing, actual finite rounding and old-profile +rejection. It does not formalize the Python/C++ compiler or the all-size theorem. + +## Reproduce the accepted words + +Use an external checkout of frozen PR62 commit +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No newer sources are consumed. +See `verification/README.md` to compile its exact C++17 profiler, then run: + +``` +python verification/verify_words.py --upstream UPSTREAM --profiler PROFILER --word23 words/word-23.json.gz --word25 words/word-25.json.gz --output work/recheck +python verification/check_guards.py words/word-23.json.gz +python verification/check_guards.py words/word-25.json.gz +cd math +lake build Frozen62Research +``` + +The verifier checks immutable sources and its own adapter hashes, full input/dirty +bases in both orientations, exact source/scatter inventory, every literal frame +transition and all fixed-I+J profiles with bounded-minor and CRT checks. It rejects +optimized Python assertion mode. Use the supplied words for authoritative replay; +floating discovery prices propose candidates and have no trusted-proof role. +Discovery source snapshots, exact oracle fixtures (gzip-compressed) and matching +seeds retain original byte hashes. `discovery/SEARCH.md` explains the algorithms, +heuristic boundary and experimental commands. Historical workspace paths in the +source-generation receipts identify the original run; the accepted-word replay +uses the explicit upstream argument and needs no private directory layout. +Portable discovery regeneration: + +``` +python discovery/regenerate_portable.py --upstream UPSTREAM --work work/regenerate +``` + +This rewrites workspace paths only and checks both raw words and deterministic +gzip against the accepted words. Floating discovery is outside the trusted +certificate; the independent word/profile verifier establishes acceptance. + +The one-hour session froze information through #62. The unchanged data geometry +and its rational recovery are inherited; selected physical words/profile checks +are fresh. All-size analytic, compiler/frame transfer, finite-alphabet tape, +routing, prime selection/recovery and eventual-threshold contracts remain +conditional. No practical runtime or global-optimality claim is made. + +Alejandro Zarzuelo Urdiales is the human author/developer, following earlier +Archivara and personal July/October matrix/parity work developed with multiple +AI tools. This synthesis involved substantial OpenAI Codex assistance. Known +linear algebra, matroid exchange, dirty uncomputation and concavity principles +retain prior-work status. The finite construction credits Avi Eisenberg/ikeboy +(#62 interval/core-aware graph), eumemic (#57 frame compiler), Chafik Boukhalfa +(#60 ranking and earlier exact profiling), Rohan Arun and other retained notices. +The prior matrix/parity source is in `../matrix-exponent-synthesis/` and prior +Gaussian work in PR45. Its product counts retain their separate arithmetic scope. +The paper is supplied as LaTeX source; no newly compiled PDF is claimed. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md new file mode 100644 index 0000000000..b8dd669634 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md @@ -0,0 +1,136 @@ +# Local frame-compiler search, frozen through PR62 + +All experiments in this directory use the pinned PR62 pair graph at +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No later community source is consumed. +The original checkout is unchanged. Each emitted word and compiler copy has +a SHA256 recorded in its `compiled.json`; changed words are sent separately +to the independent literal replay and profile verifier. + +## New dependency-circuit choices + +The inherited compiler reduces retired fresh-signal rows against the current +live anchors and an echelon basis of compatible retired rows. Instead of +accepting the first dependent retired row, the new selectors collect the +available fundamental dependency circuits and choose a circuit by one of: + +- total charged target/provider rank growth (`all_growth`); +- number and rank growth of other retired providers (`all_collateral`); +- anchor-only dependence before general retired dependence (`anchor_first`); +- actual physical transition child-profile moment cost (`profile_cost*`). + +Every clearing XOR and every target/provider frame promotion is still emitted +and charged. A zero fresh-signal row can contain arbitrary physical dirty state; +its reuse is justified by the complete reversible word, not by claiming that +the physical register is initialized to zero. The compiler runs both complete +dirty-basis orientations, and the independent verifier repeats them. + +For the last selector let `C(A,B) = sum_t n_t(A,B) F_t`, where the `n_t` are +the exact inherited fixed-I+J pivot-run profile of the physical frame transition +and `F_t = t exp(a log(m/t))`. A candidate target `s` at old frame `A_s`, cleared +into frame `G` with providers `z`, is priced by + +``` +C(A_s,G) - C(A_s,I) + + sum_z [C(A_z,G) + C(G,I) - C(A_z,I)]. +``` + +This accounts for immediate promotions and the change in deferred cleanup, +assuming each other retired provider remains retired until cleanup. Future +reuse couples decisions, so this is a discovery heuristic, not an additive +global optimality certificate. Linear rank mass cancels between candidates; +`t*expm1(a*log(m/t))` avoids cancellation in floating discovery prices. +Missing transition profiles are recorded and collected for the next iteration. +Once a run has zero missing pairs, every local price uses an actual transition +profile. The final saving is accepted only through exact rational whole-profile +moment bounds and all assembly gates. + +`build_pair_oracle.py` is a local adaptation of the frozen C++ profiler that +additionally exports each transition histogram. It preserves the projector, +pivot, bounded-minor and three-prime CRT routines. Its synthetic transition-list +input is an oracle request, not a physical executable word. Each immutable +profile dump and the source/header hashes are recorded. + +## Moment-ordered carry selection + +The `--weighted` experiment orders the inherited linear/partition-matroid +candidate edges by their physical transition moment change before the original +greedy initialization and augmenting paths. For a value produced at `P`, +preserved through donor frame `G`, and carried to future target `T`, its +no-reclamation child-cost change is + +``` +C(G,T) - C(G,I) - C(0,P) - C(P,T). +``` + +At fixed cardinality, role and external-volume corrections are common to all +edge choices in the same axis. The inherited augmenting algorithm still seeks +maximum cardinality; it does not optimize the weights globally. Reclamation +adds coupling, so only the changed whole-word profile can establish an actual +improvement. This experiment makes no minimum-cost matroid claim. + +The `--exchange` variant starts from the frozen original maximum-cardinality +matching and tries bounded improving one-edge exchanges. A new edge may replace +the old donor of the same use when its donor block stays linearly independent; +or it may replace a selected edge in the same donor block and serve an unused +use. Both preserve cardinality and distinct-use constraints. The `--cycle` +variant additionally tests two-edge donor/use cycles, checking the independence +of both changed blocks. No improving two-edge cycle was found in the tested +native-price instance; this is not a proof that longer cycles cannot improve it. + +## Joint basis and schedule search + +`--basis shift1` profiles all candidate physical transitions after the point +permutation `i -> (i+1) mod h`, while preserving their original frame IDs. +Matching and reclamation are then priced in that basis. The emitted word is +renamed by `relabel_word.py`: all frame masks, canonical source/output triples, +common points and scatter port indices change together. Scratch slots and +literal XOR instructions are retained. The complete triple family and the +permutation-invariant `I+J` basis are inherited; every final renamed word still +gets fresh full-basis and actual physical-profile verification. + +This joint search differs from merely relabeling an already selected schedule: +the selected carries and clearing circuits are optimized under the new ordered +pivot-run prices. It remains a bounded discovery heuristic. + +## Regeneration + +The frozen graph/matching setup and a moment-cost exchange run are generated by: + +``` +python -S collect_matching_pairs.py --h 23 +python -S build_pair_oracle.py --h 23 --strategy matching_collect +python -S run_strategy.py --h 23 --strategy profile_cost --exchange +``` + +Repeat at `h=25`. For joint search, add `--basis shift1` to the oracle and +strategy commands. Reclamation may encounter transitions absent from the +initial carry-edge inventory. Run the oracle again on the emitted strategy +directory with `--incremental`, then run a new strategy label. The new label +must start with `profile_cost`; output directories are never overwritten. +`compiled.json` records the exact oracle dump hash, missing-pair count, word +hashes and source pin. Immutable earlier oracle dumps are retained by SHA256. +Use `--oracle path/to/the-immutable-dump.jsonl` to reproduce the prices of a +specific recorded run instead of consuming the subsequently enlarged cache. +The initial compiler matching cache is accepted only if its complete candidate +edge list matches the current frozen graph and every restored selected block +passes the same linear-independence check. + +The runner saves an immutable source copy and its hash for later runs. Floating +`expm1` prices at discovery saving `a=0.00005103` select proposals only. Neither +those prices nor their reported local gains are used as an arithmetic witness. + +## Acceptance boundary + +The independent verifier checks all input and dirty basis vectors in both +orientations, exact literal-scatter incidences, causal nested physical frames, +event equality reconstructed from the actual XOR word, rank mass, actual child +profiles and CRT agreement. It then computes the whole mixed-axis recurrence +and exact rational moment/assembly witnesses. Existing all-size geometry, +analytic envelopes, compiler/tape arguments and the surrounding reduction are +inherited from frozen PR62. A finite profile improvement does not by itself +formally prove those inherited hypotheses. + +Reduced XOR count alone is not accepted as an exponent improvement. In this +search `all_collateral` and `anchor_first` reduced clearing XORs but worsened +the certified characteristic. Actual child-size distributions decide the +saving, even when both physical-role counts and total rank mass are unchanged. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py new file mode 100644 index 0000000000..7c154b1a29 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py @@ -0,0 +1,275 @@ +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +import sys;sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'matrix-synthesis/bridge/pr62/references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s,add=True): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>s&1;e^=1<=prices[f]-1e-14:continue + if not can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:-prices[z])if prices[e] /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/NOTICE b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/NOTICE new file mode 100644 index 0000000000..8adab44ba3 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/NOTICE @@ -0,0 +1,324 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/README.md b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/README.md new file mode 100644 index 0000000000..4a9b481aa3 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/README.md @@ -0,0 +1,172 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/SOURCE.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/SOURCE.json new file mode 100644 index 0000000000..c8cc31f3d0 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/SOURCE.json @@ -0,0 +1,120 @@ +{ + "commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "Makefile": "6e9e48a677b2f66643226840f574a6535e3564ffb0c72284b60302684a5dfbe4", + "NOTICE": "1e0702aa665673508fa91169163c5785d680637fff636fda01f36e3b127c3ee0", + "README.md": 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566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "rank_mass": 900975, + "singles": 20700, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 2300, + "word_sha256": "4c956749f0ec72c61875c51099afdf23e69ccea268a9b43b8d46da2ffdb24903" + } + } + }, + "bit_saving": "12854322426487/250000000000000000", + "certificate_sha256": "0fcb53fa374273efab6370953c966e8fa065dbfdba43691843a4788cb2cda42e", + "kappa": "51414646104039/1000000000000000000", + "margins": 7, + "producer_words_regenerated_and_matched": true, + "scope": "Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.", + "source_binding": "Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.", + "status": "PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly", + 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a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py new file mode 100644 index 0000000000..c7fd42867d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py @@ -0,0 +1,196 @@ +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit', 'complex'): + data = finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": 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b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": "41187950749917624099/1000000000000000000000000", + "cell_above_band": "666666666665666652937349833360791967/1333388250600666556832132000000000000", + "compact_leaf": "26927049500082375901/1000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "13729317166639208033/333347062650166639208033", + "epsilon_positive": "333333333333000000000000/333347062650166639208033", + "g1_above_kappa": "3408408254232349301008147/3333470626501666392080330000000000000", + "g2_above_kappa": "4241/2500000000000", + "g3_above_kappa": "74937627730682908927817/3333470626501666392080330000000000000", + "g4_above_kappa": "4241/2500000000000", + "g5_above_kappa": "5299956450675231223831763/13333882506006665568321320000000000000", + "g6_above_kappa": "11966897703678564007992423/13333882506006665568321320000000000000", + "g7_above_kappa": "3333196040161742016173902349301008147/3333470626501666392080330000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "13729317166639208033/333347062650166639208033", + "lambda_above_internal": "82375901/2000000000000000000000000", + "lambda_above_sigma": "61024099000082375901/2000000000000000000000000", + "lambda_above_tau": "82375901/2000000000000000000000000", + "lambda_prime_above_lambda": "82375901/2000000000000000000000000", + "lambda_prime_below_one": "41187950499917624099/1000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "21966907133275670202633360791967/533355300240266622732852800000000000", + "phase_leaf_above_bit": "53854099/2000000000000", + "phase_local": "109834536999766601613833360791967/2666776501201333113664264000000000000", + "prime_interval_packing": "13729317166639208033/333347062650166639208033", + "q_below_internal": "82375901/1000000000000000000000000", + "q_below_leaf": "26927049500082375901/1000000000000000000000000", + "q_below_reservations": "1/4000000000000", + "q_positive": "41187950499917624099/1000000000000000000000000", + "record_suffix": "13729317166639208033/333347062650166639208033", + "row_product_gap": "6548/25", + "short_record_fallback": "666639206901368489075295096355187267/666694125300333278416066000000000000", + "small_field_exposure": "1/1000000000000" + }, + "finite_bridge": { + "bit": { + "W": 177530859, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "degree": 2000, + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": 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b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": 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Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 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"multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json 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b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json new file mode 100644 index 0000000000..42958fc74b --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json @@ -0,0 +1,195 @@ +{ + "artifact_sha256": { + "frame-profiles-23.json": "fec377bcf1512a427674983256b900229d4133026445b6e680c6e1e6dde5af7d", + "frame-profiles-25.json": "28b4b911e26fbc02dde0d2e1458ed16227f756126ab8144d6d45e164d1165262", + "frame-transitions-23.json": "86646f1110595294cccc15603c552f0a153574a690b69c3b144d84a449891103", + "frame-transitions-25.json": "c333c348665d12b95e168ca4fac48bfdca335104edd0f29c81fe94bec292e774", + "frame-word-23.json.gz": "a44e038e1c548ea8ac31dd04acc2bba7951b22e17df7b7ad3464ea2b504a8da4", + "frame-word-25.json.gz": "ad8b299697f90b185b6b791313b505586be97965519052100d097df6199e00c5", + "paired-candidate.json": "34a500d739537235dfc5d24325c22856ca4567b9eac998a3bce9b13db5501940" + }, + "axes": { + "23": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 36432, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 31460, + "elementary_xors": 149137, + "h": 23, + "histogram": { + "0": 302057, + "1": 42694, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "2": 82722, + "21": 165, + "22": 23, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 642620, + "roles": 27918, + "stats": { + "augmentations": 220, + "clearing_xors": 1577, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "regions": 52473 + } + }, + "gzip_sha256": "a44e038e1c548ea8ac31dd04acc2bba7951b22e17df7b7ad3464ea2b504a8da4", + "replay": { + "elementary_xors": 149137, + "full_basis_vectors": 31460, + "h": 23, + "histogram": { + "0": 162914, + "1": 42694, + "10": 442, + "11": 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orientations PASS", + "word_length": 856108 + }, + "schedule": "reverse-node", + "word_sha256": "a54443429f47c486016771ce0436effda098e142afc52861c20957e9ff8e086b" + } + }, + "source_sha256": { + "research/pair-assembly/frame/frame_verify.py": "fafe25d57166a747eeb847444a2e02dd7eed19038b93a2c495014d147d04a8fb", + "research/pair-assembly/pair_graph.py": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "research/reordered-rank-pair/test_negative.py": "88832242e6f74e3fe08d109d4f21ff188a9ca0ae50c3e8f31da0243fe9501510", + "research/reordered-rank-pair/verify.py": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352", + "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3", + "scripts/experiments/binary_frame_profiles.cpp": 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b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "loss": 506, + "rank_sum": 642620, + "field_prime": 2305843009213693951, + "frames": 52475, + "distinct_matrices": 36399, + "crt_matrices": 6049, + "crt_disagreements": 0, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json new file mode 100644 index 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b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json new file mode 100644 index 0000000000..2883a5f7c9 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "frames": 52475, + "distinct_transitions": 138016, + "singles": 15939, + "rank_mass": 642620, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 53320, + "2": 77409, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "21": 165, + "22": 23 + }, + "word_sha256": 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b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + "exponent": 5333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5715743812, + "rhs": 1792000000313576, + "rhs_bits": 51 + }, + "rows": { + "exponent": 5715743812, + "rhs": 896000000156824000, + "rhs_bits": 60 + } + } + }, + { + "log2_input": 224000000000000, + "powers": { + "alpha": { + "exponent": 11431487624, + "rhs": 1792000000156824, + "rhs_bits": 51 + }, + "compact": { + "exponent": 11431487624, + "rhs": 7168000000627232, + "rhs_bits": 53 + }, + "leaf": { + "exponent": 10666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11431487624, + "rhs": 3584000000313576, + "rhs_bits": 52 + }, + "rows": { + "exponent": 11431487624, + "rhs": 1792000000156824000, + "rhs_bits": 61 + } + } + }, + { + "log2_input": 448000000000000, + "powers": { + "alpha": { + "exponent": 22862975248, + "rhs": 3584000000156824, + "rhs_bits": 52 + }, + "compact": { + "exponent": 22862975248, + "rhs": 14336000000627232, + "rhs_bits": 54 + }, + "leaf": { + "exponent": 21333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 22862975248, + "rhs": 7168000000313576, + "rhs_bits": 53 + }, + "rows": { + "exponent": 22862975248, + "rhs": 3584000000156824000, + "rhs_bits": 62 + } + } + } + ], + "practical_runtime_claim": false + }, + "kappa": "40827/800000000", + "next_kappa": "318961/6250000000", + "next_kappa_rejection": "{'g1_above_kappa': '-25408022593116799041/7102635201420453820506250000000', 'g3_above_kappa': '-5201705247125960457841/1136421632227272611281000000000000', 'g5_above_kappa': '-7640875416065173165777/1818274611563636178049600000000000', 'g6_above_kappa': '-33658690551416775383761/9091373057818180890248000000000000'}", + "original_enclosure_control": { + "accepted_upper": "427922022655051425592169455669348999419009338821677321501934579031509793316011927849852932699225587520480274623290826519124585131702799274967695430254567113650998884459986946222692530282749027853246814000572815342011972280832203653626757194588235745687874105909336892415629002940540277569675953192803096179140323199169875932058482212840371519373866332987776983981442275480629595879092440778438065834410270423292532877965451564571150969903518733283745770147929604915103094966966240445718551419238205360172260389165815355293860586787487668007987689744585745259297708409486845374929838902410526770296527117452860612190765279746966315757114757646249443956020657651637850471083396567352186238660458491615294604389003317389825219053116168473153626947262543915434579501546193988862612230828605213616950127673267971569642351835151332191639228898384399684069201926146521990048728093044781289653532998958679374426311189560250341590145887508815021337226982815008224357898461730107482372032845888428476273500999760300211786400006201411895378711403441679516543048925021677151249124774565210588951830515783148269750340702961227551/427922022656065148722015624802653702889498564421131911283499341667573520226931037010841800905471906532344178836996138043716400845851217866305783744362952178488692163617667760947934446961428764096857095662125776648371730944750850740376437391609342381012534311915175448066736517476339673099556706774420618964194148648273392198066357729130169733561134843302857240883248026154958104699812690626052696940220399106081385425042375485602542555097186568052507330835744941604979041042724146442866160606543845260686788873587136675704407457814823973491248098778928607362558510538701395621352496475077156310639504247824069338077266718928997258973439362819271794470658904562860362470215133491491305622841328989108583065554731667738937158958161399293136952726957825424616696098290625805073806865420810062253320746566043770582998650738545122821954094593047815197564256009823257422725379706679933315631514838786135447434356419391187561619401952168548631044553632502869921434523792993783307013326156305798890689568359302672301544894715282222433613932715358768884516049207059704442128612279932500000000000000000000000000000000000000000", + "next_bit_lower": "374050380000830479912607937870818083834173718615907103079616878943322706260497332605534066060136407627149268792108716494485294881071/374050380000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + } + }, + "comparison": { + "additional_precision_gain": "2116843/200000000000000000", + "difference": "1238116843/200000000000000000", + "difference_pr65": "59693903/12500000000000000", + "kappa": "10206752116843/200000000000000000", + "pr63_kappa": "5102757/100000000000", + "pr65_kappa": "2041159402879/40000000000000000", + "structural_gain_on_original_grid": "309/50000000000" + }, + "grid_denominator": 1000000000000000000, + "next_bit_saving": "5103636516201/100000000000000000", + "preferred": { + "assembly": { + "absorption_gap": "12957517239351787231794417587/100005103636516190692726967598200000000000000000", + "constraints": { + "K_dominates_log": "25518182705927945452132037536365162009/500025518182580953463634837991000000000000", + "K_geometry": "375025518182705953463634837991/500025518182580953463634837991000000000000", + "a_below_b": "20663634837991/1000000000000000000", + "a_positive": "51036365162009/1000000000000000000", + "alpha_below_one": "999999999999500025518182580953463634837991/1000051036365161906927269675982000000000000", + "alpha_below_one_fourth": "249961722725628595322730323966963634837991/1000051036365161906927269675982000000000000", + "alpha_positive": "51036365661881409087095028536365162009/1000051036365161906927269675982000000000000", + "artificial_boundary": "28001633163690681098227177374284390904513973/4000204145460647627709078703928000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "499974481817294046536365162009/500000000000000000000000000000", + "c_positive": "25518182705953463634837991/500000000000000000000000000000", + "cell_above_band": "999999999998499974481817419046536365162009/2000102072730323813854539351964000000000000", + "compact_leaf": "8539317419046536365162009/500000000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "25518183080953463634837991/500025518182580953463634837991", + "epsilon_positive": "499999999999500000000000000000/500025518182580953463634837991", + "g1_above_kappa": "100005116594033430044514199392617587/100005103636516190692726967598200000000000000000", + "g2_above_kappa": "1302288897/500000000000000000", + "g3_above_kappa": "12957517239351787231794417587/100005103636516190692726967598200000000000000000", + "g4_above_kappa": "1302288897/500000000000000000", + "g5_above_kappa": "37501926821210810861559844643742587/100005103636516190692726967598200000000000000000", + "g6_above_kappa": "87504478639468906207923328442842587/100005103636516190692726967598200000000000000000", + "g7_above_kappa": "99994896363383814423867065831844514199392617587/100005103636516190692726967598200000000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "25518183080953463634837991/500025518182580953463634837991", + "lambda_above_internal": "51036365162009/1000000000000000000000000000000", + "lambda_above_sigma": "20663634838042036365162009/1000000000000000000000000000000", + "lambda_above_tau": "51036365162009/1000000000000000000000000000000", + "lambda_prime_above_lambda": "51036365162009/1000000000000000000000000000000", + "lambda_prime_below_one": "25518182580953463634837991/500000000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "40829092429500023633159832136365162009/800040829092129525541815740785600000000000", + "phase_leaf_above_bit": "17078634837991/1000000000000000000", + "phase_local": "204145464147602190896122974536365162009/4000204145460647627709078703928000000000000", + "prime_interval_packing": "25518183080953463634837991/500025518182580953463634837991", + "q_below_internal": "51036365162009/500000000000000000000000000000", + "q_below_leaf": "8539317419046536365162009/500000000000000000000000000000", + "q_below_reservations": "1/4000000000000", + "q_positive": "25518182580953463634837991/500000000000000000000000000000", + "record_suffix": "25518183080953463634837991/500025518182580953463634837991", + "row_product_gap": "6548/25", + "short_record_fallback": "499974480514563711027641740160491885440816916081/500025518182580953463634837991000000000000000000", + "small_field_exposure": "1/1000000000000" + }, + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "margins": { + "g1": "25518183080953463634837991/500025518182580953463634837991", + "g2": "51036365162009/1000000000000000000", + "g3": "25518182580927945452257037536365162009/500025518182580953463634837991000000000000", + "g4": "51036365162009/1000000000000000000", + "g5": "40829092429500023633159832136365162009/800040829092129525541815740785600000000000", + "g6": "204145464147602190896122974536365162009/4000204145460647627709078703928000000000000", + "g7": "499999999999500000000000000000/500025518182580953463634837991" + }, + "minimum_margin": "25518182580927945452257037536365162009/500025518182580953463634837991000000000000", + "parameters": { + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": "1", + "a_bit": "51036365162009/1000000000000000000", + "a_complex": "717/10000000", + "alpha_squared_power": "51036365661881409087095028536365162009/1000051036365161906927269675982000000000000", + "beta": "1/20", + "c": "25518182705953463634837991/500000000000000000000000000000", + "delta": "1/8000000000000", + "epsilon": "499999999999500000000000000000/500025518182580953463634837991", + "h": "1/1000000000000", + "kappa": "10206752116843/200000000000000000", + "lambda_": "999948963634838042036365162009/1000000000000000000000000000000", + "lambda_prime": "499974481817419046536365162009/500000000000000000000000000000", + "q": "25518182580953463634837991/500000000000000000000000000000", + "sigma": "9999283/10000000", + "tau": "999948963634837991/1000000000000000000" + }, + "recurrence": { + "internal": "999948963634837991/1000000000000000000", + "leaf": "199986377/200000000", + "reservations": "499974481817294046536365162009/500000000000000000000000000000" + }, + "scoped_limit": "51036365162009/1000051036365162009" + }, + "eventual_bounds": { + "additional_eventual_conditions": [ + "BHP prime threshold and distinct-prime packing", + "Fixed rational basis, eligible common prime and native table setup", + "Catalogue/descriptor domination, logarithm absorption, exact recovery" + ], + "all_interval_argument": "For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). Successive intervals double LHS; the positive affine RHS grows at most linearly, so 2^j >= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956143, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + "exponent": 5333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5715743812, + "rhs": 1792000000313576, + "rhs_bits": 51 + }, + "rows": { + "exponent": 5715743812, + "rhs": 896000000156824000, + "rhs_bits": 60 + } + } + }, + { + "log2_input": 224000000000000, + "powers": { + "alpha": { + "exponent": 11431487624, + "rhs": 1792000000156824, + "rhs_bits": 51 + }, + "compact": { + "exponent": 11431487624, + "rhs": 7168000000627232, + "rhs_bits": 53 + }, + "leaf": { + "exponent": 10666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11431487624, + "rhs": 3584000000313576, + "rhs_bits": 52 + }, + "rows": { + "exponent": 11431487624, + "rhs": 1792000000156824000, + "rhs_bits": 61 + } + } + }, + { + "log2_input": 448000000000000, + "powers": { + "alpha": { + "exponent": 22862975248, + "rhs": 3584000000156824, + "rhs_bits": 52 + }, + "compact": { + "exponent": 22862975248, + "rhs": 14336000000627232, + "rhs_bits": 54 + }, + "leaf": { + "exponent": 21333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 22862975248, + "rhs": 7168000000313576, + "rhs_bits": 53 + }, + "rows": { + "exponent": 22862975248, + "rhs": 3584000000156824000, + "rhs_bits": 62 + } + } + } + ], + "practical_runtime_claim": false + }, + "kappa": "10206752116843/200000000000000000", + "next_kappa": "6379220073027/125000000000000000", + "next_kappa_rejection": "{'g3_above_kappa': '-54404741498227752163082843757/62503189772822619182954354748875000000000000000'}" + }, + "profile_path": "research/slot-cost-rank-pair/paired-candidate.json", + "profile_sha256": "be0322ad60f73923953f242eaffaf114ff12438e8617dae38888b77fa03184cc", + "proof_limits": [ + "The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.", + 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a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) ++ slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();pending={};stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): +@@ -149,7 +151,8 @@ + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 +- return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) ++ endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 ++ return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} +@@ -161,6 +164,9 @@ + old,e=bb[p];row^=old;expr^=e + return expr + for s in anchors:ins(s) ++ for s,target in pending.items(): ++ if contains(blocks[frames[s]]['frame'],blocks[g]['frame']) and contains(blocks[g]['frame'],blocks[target]['frame']): ++ ins(s);stats['live_anchor_candidates']+=1 + best=None + # Inspect every eligible dependent candidate across all retired ranks. + # Rank the actual fixed-basis growth/cleanup profiles by an integer entropy score. +@@ -176,7 +182,9 @@ + if best is None or key= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and kappa > previous_kappa + bridge = json.loads((OLD/'certificate.json').read_text())['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/split-pair/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr67_commit='b3745601e947a94316bf25c2c6263d93c06e3364', + pr67_kappa=previous_kappa, ratio_pr67=kappa/previous_kappa, + absolute_gain_pr67=kappa-previous_kappa, + pr67_complete_profile_exclusion_lower=prior65_lower, + full_pr67_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected split-pair partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'split-pair-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py new file mode 100644 index 0000000000..1290ef2eb8 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py @@ -0,0 +1,275 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py new file mode 100644 index 0000000000..7908c963a4 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py @@ -0,0 +1,78 @@ +#!/usr/bin/env python3 +"""Replay the aligned split-pair/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from split_pair_compose import compose, check_sources +from split_pair_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'split-pair-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='split-pair-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + 'c++', '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'split-pair-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'split-pair-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'split-pair-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'split-pair-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'split-pair-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair.py new file mode 100644 index 0000000000..5088cff133 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair.py @@ -0,0 +1,238 @@ +"""Physical and exact-arithmetic controls for the aligned split/pair witness.""" +from copy import deepcopy +from fractions import Fraction +from itertools import combinations +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile +import unittest +from unittest.mock import patch + +ROOT = Path(__file__).resolve().parents[1] +EXPERIMENTS = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXPERIMENTS)) +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from binary_frame_math import moment + + +class SplitPairControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.words = {h: json.loads(gzip.decompress((ROOT/f'certificates/split-pair-word-{h}.json.gz').read_bytes())) + for h in (23,25)} + + def reject_mutation(self, mutate, checker='both'): + for h, original in self.words.items(): + with self.subTest(h=h), tempfile.TemporaryDirectory() as directory: + changed = deepcopy(original) + mutate(changed) + path = Path(directory)/'word.json' + path.write_text(json.dumps(changed, separators=(',', ':'))+'\n') + with self.assertRaises((AssertionError, ValueError, IndexError, KeyError)): + if checker != 'transitions': + replay(path) + if checker != 'replay': + prepare(path, Path(directory)/'transitions.bin') + + def test_selected_words_pass_independent_replay(self): + recorded = json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + actual = replay(ROOT/f'certificates/split-pair-word-{h}.json.gz') + self.assertEqual(json.loads(json.dumps(actual)), recorded['axes'][str(h)]['replay']) + + def test_omitted_literal_xor_is_rejected(self): + self.reject_mutation(lambda word: word['ops'].pop(0)) + + def test_self_xor_is_rejected(self): + def mutate(word): + word['ops'][0][1] = word['ops'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_non_nested_operation_frame_is_rejected(self): + def mutate(word): + narrow = next(i for i,(core,cover) in enumerate(word['frames']) if core == cover) + operation = next(op for op in word['ops'] if word['frames'][op[2]][0] != word['frames'][op[2]][1]) + operation[2] = narrow + self.reject_mutation(mutate) + + def test_aliased_terminal_role_is_rejected(self): + def mutate(word): + word['outputs'][1][0] = word['outputs'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_missing_copied_center_is_rejected(self): + def mutate(word): + index = next(i for i,(_,_,_,target) in enumerate(word['outputs']) if len(target) == 1) + word['outputs'].pop(index) + self.reject_mutation(mutate) + + def test_omitted_transition_cannot_reduce_paid_profile(self): + self.reject_mutation(lambda word: word['events'].pop(0), 'transitions') + + def test_understated_physical_width_is_rejected(self): + def mutate(word): + word['R'] -= 1 + self.reject_mutation(mutate) + + def test_complete_pr67_profile_fails_new_bit_saving(self): + from split_pair_arithmetic import refine + previous = json.loads((ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/paired-candidate.json').read_text())['bit'] + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + result = refine.exact_moment(previous['m'], previous['W'], {int(t): n for t,n in previous['child_multiplicities'].items()}, Fraction(current['bit_saving'])) + self.assertGreater(result['lower'], 1) + self.assertGreater(Fraction(current['kappa']), Fraction(current['comparison']['pr67_kappa'])) + + def test_private_import_preserves_path_and_arithmetic_module(self): + import split_pair_graph as provider + import split_pair_arithmetic as arithmetic + sentinel = object() + existing = sys.modules.get('refine', sentinel) + previous_path = sys.path[:] + graph, schedule = provider._private_modules() + refine, audit = arithmetic.private_arithmetic() + self.assertIs(audit.refine, refine) + self.assertIs(sys.modules.get('refine', sentinel), existing) + self.assertEqual(sys.path, previous_path) + + def test_failed_graph_build_restores_original_providers(self): + import split_pair_graph as provider + previous_class, previous_points = provider._graph.circuit_class, provider._graph.alternating_points + with patch.object(provider._graph, 'graph', side_effect=RuntimeError('deliberate graph failure')): + with self.assertRaises(RuntimeError): + provider.graph(23) + self.assertIs(provider._graph.circuit_class, previous_class) + self.assertIs(provider._graph.alternating_points, previous_points) + + def test_failed_compilation_restores_engine_graph_and_schedule(self): + import split_pair_compiler as producer + previous_graph, previous_build = producer.compiler.graph, producer.compiler.build + missing = object() + runtime = {name:getattr(producer.compiler,name,missing) for name in ('PENDING_COST','ORACLE_EXE','ORACLE_INPUT','oracles')} + with patch.object(producer.compiler, 'compile_', side_effect=RuntimeError('deliberate compiler failure')): + with self.assertRaises(RuntimeError): + producer.compile_axis(23) + self.assertIs(producer.compiler.graph, previous_graph) + self.assertIs(producer.compiler.build, previous_build) + for name,value in runtime.items(): + self.assertIs(getattr(producer.compiler,name,missing),value) + + def test_uncertified_configurations_are_rejected(self): + import split_pair_graph as provider + wrong_anchor = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_anchor['anchor'] = False + boolean_group = deepcopy(provider.EXPECTED_CONFIGS[23]); boolean_group['groups'][0] = True + changed_schedule = deepcopy(provider.EXPECTED_CONFIGS[23]); changed_schedule['schedule'] = 'reverse-node' + for changed in (wrong_anchor, boolean_group, changed_schedule): + with self.subTest(configuration=changed), patch.object(provider.json, 'loads', return_value=changed): + with self.assertRaises(ValueError): + provider.configuration(23) + for dimension in (True, 22, 24, '23'): + with self.subTest(dimension=dimension), self.assertRaises(ValueError): + provider.configuration(dimension) + + def test_recursive_weighted_exclusions_and_contraction(self): + import split_pair_graph as provider + for h in (23,25): + block_sizes = [] + parent = provider._graph.circuit_class(h) + selected = provider.split_class(parent, provider.configuration(h)['groups']) + case = self + class Audited(selected): + def grouping(self, points): + groups = super().grouping(points) + case.assertEqual([x for group in groups for x in group], list(points)) + case.assertLess(len(groups), len(points)) + return groups + + def _block(self, points, edges, weights, level): + def expected(omitted): + values = [value for pair,value in edges.items() if not set(pair) & omitted] + values += [value for point,value in weights.items() if point not in omitted] + support = 0 + for value in values: + case.assertEqual(support & self.support[value], 0) + support |= self.support[value] + return support + total, single, pairs = super()._block(points, edges, weights, level) + case.assertEqual(self.support[total], expected(set())) + case.assertEqual(set(single), set(points)) + for a in points: + case.assertEqual(self.support[single[a]], expected({a})) + case.assertEqual(set(pairs), set(combinations(points,2))) + for a,b in combinations(points,2): + case.assertEqual(self.support[pairs[a,b]], expected({a,b})) + block_sizes.append(len(points)) + return total, single, pairs + local = Audited(h-1) + block_sizes.clear() + local.pair(list(range(h-1))) + self.assertEqual(sorted(block_sizes, reverse=True), [h-1, 12 if h==23 else 13, 7 if h==23 else 8, 5, 3, 2]) + + def test_next_fine_grid_points_and_old_assembly_controls_reject(self): + from split_pair_arithmetic import refine + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + bit = current['bit']; saving = Fraction(current['bit_saving']); kappa = Fraction(current['kappa']) + grid = Fraction(1,10**18) + rows = {int(t): n for t,n in bit['child_multiplicities'].items()} + self.assertLess(refine.exact_moment(bit['m'],bit['W'],rows,saving)['upper'], 1) + self.assertGreater(refine.exact_moment(bit['m'],bit['W'],rows,saving+grid)['lower'], 1) + for label, variant in ( + ('next_kappa', dict(kappa=kappa+grid)), + ('zero_backoff', dict(h=Fraction())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))): + call = dict(a_bit=saving, kappa=kappa, h=Fraction(1,10**12));call.update(variant) + with self.subTest(control=label), self.assertRaises(refine.balanced.InvalidAssembly): + refine.balanced.assembly(current['finite_bridge'], **call) + + def test_mass_preserving_profile_mutation_is_rejected(self): + from split_pair_compose import check_sources + profile_path = ROOT/'certificates/split-pair-profiles-23.json' + changed = json.loads(profile_path.read_text()) + before = sum(t*n for t,n in enumerate(changed['blocks'])) + changed['blocks'][2] += 3; changed['blocks'][3] -= 2 + self.assertTrue(all(n >= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'split-pair-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from split_pair_compose import check_sources + manifest_path = ROOT/'research/split-pair/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/split-pair-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import split_pair_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('split_pair_graph.py', 'split_pair_engine.py', 'split_pair_compiler.py', 'split_pair_arithmetic.py', 'split_pair_compose.py', 'verify_split_pair.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair_pending.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair_pending.py new file mode 100644 index 0000000000..e6d63f72a4 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/split_pair_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/research/balanced-split/PROOF.md b/references/frame-compiler/pr84/references/frame-compiler/pr79/research/balanced-split/PROOF.md new file mode 100644 index 0000000000..c34f8542cc --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/research/balanced-split/PROOF.md @@ -0,0 +1,251 @@ +# Finite certificate and inherited scope + +## 1. Exact change and provenance + +This construction preserves PR71's anchored `[1,1,2]` split recursion, +PR65 region schedules, PR67 profile-cost reclamation and PR68 pending live +controls with next-use scoring. It composes three finite choices: PR69's +balanced coarse parenthesization, future-compatible unit completion, and a +bounded adaptation of PR70 carry exchanges. The contributor originals, +licenses and notices are retained in hash-checked archives. The published +PR71 source, words and complete arithmetic certificate are preserved at +`1bef94fd40a746452548c84a4a8f8834670a3113` for the full-profile comparison. +The new namespace is `balanced-split`. Two portable engines differ from the +independently audited discovery engines only in the repository-relative ROOT +constant; their relocation patches and SHA256s are recorded. + +The h23 coarse cell uses columns when `i+jstep and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority):''' +check(s.count(completion)==1 and s.count(changed_start)==1,'Changed source not uniquely recognized') +check(s.replace(changed_start,old_start).replace(completion,' for i in range(len(ins)):')==old,'Compiler changed beyond the claimed unit-completion priority') +tree=ast.parse(s) +helpers=[n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name in ('basis','independent')] +namespace={};exec(compile(ast.Module(body=helpers,type_ignores=[]),str(SOURCE),'exec'),namespace) +basis=namespace['basis'];independent=namespace['independent'] +future=next(n for n in ast.walk(tree) if isinstance(n,ast.FunctionDef) and n.name=='future_priority') +contains=lambda a,b:not(b[0]&~a[0]) and not(a[1]&~b[1]) +# Actual-use fixtures distinguish future compatible uses from backward or nonnested uses. +ns=dict(position={0:0,1:1,2:2,3:3},step=1,b={'frame':(1,3),'inputs':[10,11,12,13]},blocks=[{'frame':(1,3)},{'frame':(1,3)},{'frame':(1,7)},{'frame':(1,5)}],uses=[(10,2,None),(10,2,('terminal',)),(11,2,None),(11,0,None),(12,3,None),(13,3,None)],value_uses={10:[0,1],11:[2,3],12:[4],13:[5]},contains=contains,slots=[7,1,3,3],ins=[0,1,2,3]) +exec(compile(ast.Module(body=[future],type_ignores=[]),str(SOURCE),'exec'),ns) +check([ns['future_priority'](i) for i in range(4)]==[(-2,3,0),(-1,1,1),(0,2,2),(0,2,3)],'Priority does not use compatible actual future uses, symbolic support, index') +check(sorted(range(4),key=ns['future_priority'])==[0,1,2,3],'Priority is not deterministic') +# General span argument is below; these adversarial numerical fixtures check the actual helpers and literal synthesis. +rng=Random(20261008);cases=0;operations=0 +for n in range(1,10): + for trial in range(250): + rows=[] + for _ in range(rng.randrange(n+1)*3): + candidate=rng.randrange(1,1<>i&1) + if j!=i: + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];ops.append((a,z)) + for j in range(n): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];ops.append((j,i)) + check(rr==[1< 1 and kappa > previous_kappa + bridge = finite_bridge(p['W']) + validate_bridge(bridge, p['W']) + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/balanced-split/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113', + pr71_kappa=previous_kappa, ratio_pr71=kappa/previous_kappa, + absolute_gain_pr71=kappa-previous_kappa, + pr71_complete_profile_exclusion_lower=prior71_lower, + full_pr71_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected balanced-split partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring, PR69 balanced coarse sums, future unit completion and bounded PR70 carry exchanges; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'balanced-split-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/balanced_split_engine.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/balanced_split_engine.py new file mode 100644 index 0000000000..e1a9883726 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/balanced_split_engine.py @@ -0,0 +1,278 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + _graph = _graphs[h] + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_math.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_math.py new file mode 100644 index 0000000000..b87855e808 --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_math.py @@ -0,0 +1,87 @@ +"""Exact rational helpers extracted without body changes from pinned PR48 verify.py. +Credits: icekylinx PR32/36, Dominik Scholz PR35, Zhihao Chen PR29/23, +Paureel/Aurel Prosz, Swapnil Jain, Rohan Arun PR25/31, RaD/hipotures, +Chafik Boukhalfa and inherited notices in references/frame-compiler/pr48. +Prepared with OpenAI Codex assistance; no formal theorem claim. +""" +from fractions import Fraction as Q +from functools import lru_cache +from math import comb, factorial, isqrt, prod + +def js(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):js(v)for k,v in x.items()} + if isinstance(x,(list,tuple)):return [js(v)for v in x] + return x + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def mersenne(exponent): + require(exponent >= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'balanced-split-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from balanced_split_compose import check_sources + manifest_path = ROOT/'research/balanced-split/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/balanced-split-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import balanced_split_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_all_threshold_dependent_bridge_fields_are_checked(self): + from balanced_split_compose import finite_bridge, validate_bridge + expected = finite_bridge(134126064) + self.assertTrue(validate_bridge(expected, 134126064)) + for section,key in (('bit','wire_bits'),('rows','coefficient'),('rows','degree'),('rows','degree_gap'),('rows','suffix_slope')): + changed = deepcopy(expected) + changed[section][key] = Fraction(changed[section][key])+1 + with self.subTest(field=section+'.'+key), self.assertRaisesRegex(AssertionError, 'Stale finite bridge'): + validate_bridge(changed, 134126064) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('balanced_split_graph.py', 'balanced_split_engine.py', 'balanced_split_compiler.py', 'split_pair_arithmetic.py', 'balanced_split_exchange_engine.py', 'balanced_split_compose.py', 'verify_balanced_split.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr84/references/frame-compiler/pr79/tests/test_balanced_split_pending.py b/references/frame-compiler/pr84/references/frame-compiler/pr79/tests/test_balanced_split_pending.py new file mode 100644 index 0000000000..cce267112e --- /dev/null +++ b/references/frame-compiler/pr84/references/frame-compiler/pr79/tests/test_balanced_split_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/balanced_split_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/balanced-split-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main() diff --git a/references/frame-compiler/pr84/research/indexed-cycle/PROOF.md b/references/frame-compiler/pr84/research/indexed-cycle/PROOF.md new file mode 100644 index 0000000000..61621dd74e --- /dev/null +++ b/references/frame-compiler/pr84/research/indexed-cycle/PROOF.md @@ -0,0 +1,63 @@ +# Finite indexed-cycle certificate and inherited scope + +## 1. Frozen construction and general weighted recursion + +At level d, start with the inherited ordered groups of size one or two. The chosen vector requests first/middle pair splits: h23 `[4,1,1]`, h25 `[1,4,1]`, where 1 requests the first group and 4 requests first then middle. Requested indices are deduplicated, valid, and must contain two points. Before admitting the kth split require `number_of_groups + admitted_splits + 1 < number_of_points`. Apply admitted splits in decreasing index order so earlier indices keep their meaning. Each split replaces one pair by its two ordered singletons; the point partition and ordering are unchanged. + +The admission guard proves that the final number of groups is strictly less than the number of points, even for multiple requested splits and overlapping first/middle indices. Splits are disabled for n≤3; n=3 has two coarse groups and n≤2 uses the direct base case. Thus every recursive call strictly contracts, for every input size allowed by the grouping interface. + +Coarse vertex weights contain the original vertex weights in that group and its internal edges. Each coarse edge contains exactly the Cartesian-product edges between its two groups. These sets partition the original weighted total. Recursive total and single/pair exclusions therefore have the required support by induction on size. Row and column coarse parenthesizations partition the same Cartesian product into disjoint sets, so changing between them preserves every identity. The half-plane rule uses fixed indices only. The generic singleton/pair assembly and interval-strip identities are inherited; tests independently check weighted exclusions at each recursive call. + +At common coordinate c, choose the smallest intact fixed global pair disjoint from c and move it to the front of the inherited alternating order, preserving all other relative positions. This is a permutation of precisely the other coordinates and preserves scalar exclusions. Dense graph verification checks the full triple-input map and all disjoint additions in both selected dimensions. + +## 2. PR74 node order, synthesis, and completion + +Group active computed nodes by exact `(core,cover)` frame and sort groups by `(rank,-core,cover,min_node)`, where rank is cover size minus core size. Keep input IDs fixed and retain original node order inside each group. Remap every dependency, active ID, output ID and provenance entry, and clear support caches. This is a bijective graph renaming; the preserved within-frame order and rank order retain scalar dependencies. The graph verifier recomputes the dense supports, and the compiler recomputes fixed linear signals before accepting the natural region order `(rank,min_node)`. Candidate carriers target strictly later regions with containing frames. No PR65 schedule wrapper is applied. + +The output rows and selected carriers form an independent prefix. Scan every standard input unit vector in future-use priority order and retain it only if independent. Every rejected unit is already in the current span and remains there; after the scan every standard unit is in the span. The final rows therefore form a full basis and keep the chosen prefix. Gaussian elimination and its reversed literal XOR synthesis implement an invertible transformation on arbitrary inputs and dirty roles. Future-use priority depends only on fixed graph incidence, symbolic signal supports and indices. It never examines runtime input data. + +Retired roles are reclaimed only by a valid literal clearing expression in an eligible signal span. Pending live controls have current frame F and assigned future frame G. They may clear a retired role in frame E only when F⊆E⊆G. A control's value does not change; its literal frame raise is charged, and the future inclusion remains valid. Candidate comparison makes no physical mutation until a chosen expression is emitted. Exact integer profile scores only order legal candidates; they do not certify the final recurrence. + +## 3. Exact retired and pending indexes + +For frames `(core,cover)`, containment F⊆E means `core(E)⊆core(F)` and `cover(F)⊆cover(E)`. The retired index intersects active-role core bitmaps for each coordinate in core(E), and removes roles whose cover includes any coordinate outside cover(E). This selects exactly the eligible roles. Rank bitmaps partition that set; descending rank and ascending set-bit order exactly reproduce the original `(-rank,slot)` enumeration. + +The pending index first enforces F⊆E using the same lower-frame index. It then removes target cores containing coordinates outside core(E) and intersects target-cover bitmaps for coordinates in cover(E). The result is precisely F⊆E⊆G. Each insertion receives a serial; removal deletes it; frame moves keep it. Sorting eligible roles by serial reproduces pending dictionary insertion order, including removal/reinsertion of reused slots. + +Insertion, reclamation and incoming-use removal update both representations. Every frame raise updates a retired role's old/new rank/frame index, or a pending control's lower frame without changing serial order. Retired and pending lifecycles remain disjoint. Actual-source exhaustive and randomized audits compare ordered queries with the direct predicates and exercise actual frame-raise functions, not copies of those functions. These indexes preserve compiler semantics; no measured speedup is claimed. + +## 4. Carry exchanges, two-cycles, and output routing + +Candidate edges remain subject to inherited temporal/frame eligibility. A single exchange removes the selected owner of an occupied future use, or drops a carrier from the receiving region for an unoccupied future use. The full output/carrier basis of the receiving region is checked after the removal. A distinct donor region only loses a row, preserving independence. Thus cardinality, linear independence and unique future-use ownership remain valid. Each accepted exchange decreases a fixed integer score; at most three deterministic passes execute. + +A two-cycle swaps carriers between distinct regions and distinct already-owned future uses. For new edge e and its complementary edge other, `carry_can(e,z)` checks the receiving region after removing z and `carry_can(other,f)` checks the other region after removing f. Because the regions differ, these tests describe exactly the final two bases. Remove both old edges before inserting either new edge; the two freed future uses are distinct, so unique ownership and global cardinality are preserved. Both regions lose and gain one carrier. The `(region,use)` lookup is checked for uniqueness. Accept only a strictly positive decrease of the sum of the two fixed integer scores; execute at most three passes. The source audit instruments every accepted exchange in 1,204 cases, including adverse linear dependence, equal-price, missing-complement and duplicate-key cases. This is a bounded legal heuristic, not an optimality proof. + +For h25, outgoing non-carrier uses are visited by descending fixed future-region deadline, with original use ID as tie-breaker. Terminal uses keep the explicit terminal deadline. This permutes a fixed list of uses; each is still assigned exactly once to a physical role. It may affect later reclamation choices, but changes no scalar target or candidate legality. h23 retains baseline output order. Both final physical words are independently regenerated and checked, including every charged allocation, XOR, raise and copy. + +## 5. Coordinate bijection and physical evidence + +For a permutation π of h coordinates, map every triple input to its sorted π-image, every frame's core/cover bitmask by π, each source's triple index, scatter input row, output common coordinate and output triple. Physical role IDs, operation order, operation frame IDs and transition event IDs are unchanged. Coordinate permutation is a bijection on triples, preserves set inclusion, and conjugates the scalar linear map. The scatter mapping changes only designated data-bank target rows and leaves auxiliary control rows fixed. Therefore arbitrary-dirty reversibility and the scalar target identities transport to the new word. + +The fixed I+J geometry is preserved by coordinate permutations, but the ordered fixed-coordinate child profile need not be invariant. Consequently profiles are freshly computed from the relabeled word's actual transitions; parent profiles are not reused. Full-basis replay checks both orientations on every ordinary and dirty column. The transition checker reconstructs every raise from literal XORs, splits side growth into paid singletons and requires exact equality with the event list. The original bounded-minor/CRT profiler verifies sufficient modulus product and agreement. Missing XORs, frames, centers, transitions, aliased terminals and understated width fail adverse tests. + +## 6. Complete recursive multiset and exact inequalities + +Let a=23, b=25, m=575, and N=binom(23,3)binom(25,3)=4,073,300. With R23=26,834 and R25=35,348, + + W = 2N + (N/binom(23,3))R23 + (N/binom(25,3))R25 = 132,466,108. + +Include all 18N rank-one data children and 2N at each data rank 21,17,481; N endpoint-copy singletons; every axis profile block replicated N/binom(h,3) times; (N/binom(h,3))Rh exterior children at each rank h and m−2h; and 2N growth children at each rank 1 and h−2. Each axis has rank sum hRh+h(h−1). Thus total rank is 76,166,165,200, deficit from mW is 1,846,900, and every child lies between 1 and 5291. The exponential tail bound is `(v^9/9!)/(1-v/10)` for upper argument v<1. An independent atanh log expansion at base 3/2 with 60 terms and a degree-12 exponential bound confirms both signs. Complete pinned PR79 and reported PR74 child lists separately have lower moment greater than one at s. These are complete-profile historical comparisons; the foreign PR74 claim is an accepted working input, not an independent audit of its entire construction. + +The reconstructed bridge has bit wire bits 27, row coefficient 843, row degree 2000, gap `2000-(51/25)*843=7007/25`, and suffix slope 8000. Tests reject stale values. The complex saving stays 717/10^7 and the backoff stays 10^-12. All 47 strict assembly constraints and seven margins hold for κ=261356445457/5000000000000000. The next 10^-18 κ point violates a controlling strict margin; coarser-grid reassembly and original-prefix/old-guard/old-exposure negative controls also execute. Eventual arithmetic cutoffs are recomputed by the unchanged inherited routine. + +## 7. Provenance and proof boundary + +This proves the stated finite scalar, arbitrary-dirty physical, actual-frame/profile, complete-child and exact-inequality claims. The ordered affine residual compiler, all-size construction and recursion, finite scalar alphabet/overhead, routing, prime selection, exact recovery, fixed-tape simulation and analytic transfer remain inherited assumptions. Arithmetic cutoffs cover the recorded inequalities and do not establish every operational threshold. Existing Lean packages remain inherited checks, not a formalization of the complete multiplication theorem. + +The engine is byte-identical to the preserved R5 compiler; the graph wrapper implements its selected split/coarse branch; PR74 order/relabel functions are byte-identical extracts. PR79's complete published construction archive and PR74/78 original input archives are immutable. The full source closure binds the selected configs, wrapper, engine, tests, proof, words, transition profiles and integration files. Derived arithmetic and validation receipts are excluded to avoid circular pins. + +Source credits: @eumemic [#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57) and [#69](https://github.com/CrocSwap/integer-mult-bounds/pull/69), reversible compilation and balanced coarse sums; @rohangar1 [#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59), split recursion; @ikeboy [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62), interval strips and core-aware assembly; @DominikScholz [#63](https://github.com/CrocSwap/integer-mult-bounds/pull/63) and [#68](https://github.com/CrocSwap/integer-mult-bounds/pull/68), ranked composition and pending live controls; @rohanarun [#65](https://github.com/CrocSwap/integer-mult-bounds/pull/65), [#67](https://github.com/CrocSwap/integer-mult-bounds/pull/67) and [#78](https://github.com/CrocSwap/integer-mult-bounds/pull/78), exact refined assembly, profile-cost reclamation and coordinate-flag search; @alejandrozu [#70](https://github.com/CrocSwap/integer-mult-bounds/pull/70), carry exchanges; Thomas DiFiore (@tomdif) [#74](https://github.com/CrocSwap/integer-mult-bounds/pull/74), exact node order, coordinate relabeling and the selected h25 permutation; @chafreaky [#60](https://github.com/CrocSwap/integer-mult-bounds/pull/60), [#71](https://github.com/CrocSwap/integer-mult-bounds/pull/71), [#79](https://github.com/CrocSwap/integer-mult-bounds/pull/79) and this composition, ranked reclamation, anchored splits, future completion, integer scoring, exact indexes, two-cycles, output routing, search and certification. + +Chafik Boukhalfa prepared this package with OpenAI Codex assistance. Original contributor, OpenAI/manuscript, Apache-2.0, and AI-assistance notices remain attached. In particular Avi Eisenberg's Claude assistance and the original contributors' OpenAI disclosures are retained verbatim in the archives. PR78 inspires the coordinate search; its published selected permutations are not claimed as the selected permutations here. diff --git a/references/frame-compiler/pr84/research/indexed-cycle/README.md b/references/frame-compiler/pr84/research/indexed-cycle/README.md new file mode 100644 index 0000000000..c6c59c54b6 --- /dev/null +++ b/references/frame-compiler/pr84/research/indexed-cycle/README.md @@ -0,0 +1,32 @@ +# Indexed two-cycles with balanced multi-splits and coordinate flags + +The frozen finite conditional witness has **κ = 261356445457/5000000000000000 = 5.22712890914e-5**, with bit saving **408390793141/7812500000000000**. This is about **0.8494742%** above the reported PR74 value at `3f78d8967c009153f2df5c6a6577b6ab1d37e2ca`, observed 2026-10-08. This is a historical pinned comparison, not a claim about the current community frontier. The complete pinned PR74 and PR79 recursive profiles are strictly excluded at the new accepted bit saving. + +| Quantity | This witness | +|---|---:| +| h23 auxiliary roles | 26,834 | +| h25 auxiliary roles | 35,348 | +| Physical width W | 132,466,108 | +| Total recursive rank | 76,166,165,200 | +| Rank deficit | 1,846,900 | +| Largest child / parent dimension | 529 / 575 | +| Bit wire bits / row coefficient | 27 / 843 | + +Additional reported comparisons observed on 2026-10-08: PR81 at `acae4964aef41c69f3c57e72a45e76afc4d4934d` reports κ=5.1915547765237e-5; PR82 at `3410b940aa26e5876202152dfa7c4f66451ee22c` reports κ=5.203279888519e-5. This frozen witness is about 0.4583459% above the reported PR82 value. These are metadata comparisons only; their foreign producers were not replayed. Exact rational ratios and authors are recorded in `reported-comparisons.json`. + +Both axes use balanced coarse columns when `i+j>i&1) + if j!=i: + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];ops.append((a,z)) + for j in range(n): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];ops.append((j,i)) + check(rr==[1<0 and current==previous-gain,'Fixed integer price does not strictly improve') + previous=current;observed.append([e,other,f,z]) + invariant() + env=dict(blocks=blocks,edges=edges,chosen=chosen,right=right,prices=prices,priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])),basis=basis,independent=independent,stats=Counter(),sys=types.SimpleNamespace(stderr=io.StringIO()),audit_cycle=audit_cycle) + exec(code,env);invariant();check(env['stats']['carry_two_cycles']==len(observed),'Cycle count differs') + if expected is not None:check(len(observed)==expected,'Targeted cycle outcome differs') + cycles+=len(observed);cases+=1 + return observed + +# Each group is full (one outbasis row + one carrier). Neither cross-group +# single addition is independent, but simultaneous replacement is legal. +blocks=[{'outbasis':[3]},{'outbasis':[3]}] +edges=[(1,0,0),(0,1,0),(0,0,1),(1,1,1)] +run(blocks,edges,{0,1},[10,10,9,9],1) +run(blocks,edges,{0,1},[10,10,10,10],0) +# With the receiving group's unit vector already in its output span, reject. +run([{'outbasis':[2]},{'outbasis':[3]}],edges,{0,1},[10,10,9,9],0) +# Missing the complementary future-use edge also rejects. +run(blocks,edges[:3],{0,1},[10,10,9],0) +# Duplicate group/use lookup keys are explicitly rejected before iteration. +try:run(blocks,edges+[(0,0,0)],{0,1},[10,10,9,9,1]) +except AssertionError:duplicate_rejected=True +else:raise ValueError('Ambiguous group/use candidate key accepted') +rng=Random(231025) +for trial in range(1200): + ng=rng.randrange(2,6);nuses=rng.randrange(2,14);blocks=[];edges=[] + for g in range(ng): + width=rng.randrange(2,6);rows=[] + for _ in range(rng.randrange(width)*2): + v=rng.randrange(1,1<150 or choice<.34): + s=rng.choice(list(records));f,g=records.pop(s);idx.remove(s,f,g) + elif records and choice<.66: + s=rng.choice(list(records));f,g=records[s];new=between(f,g);check(contains(f,new) and contains(new,g),'Invalid random promotion') + before_order=dict(idx.order);idx.move(s,f,new);records[s]=(new,g);check(idx.order==before_order,'Frame move changes insertion order') + else: + s=rng.randrange(1200) + if s in records:continue + f=envelope();g=extend(f);idx.insert(s,f,g);records[s]=(f,g) + mutations+=1 + if iteration%4==0: + for target in (envelope(),(1,mask)): + check(idx.eligible(target)==query(records,target),'Random ordered pending query differs');queries+=1 + if iteration%100==0: + check(idx.lower.all==sum(1<>k&1),'Target core bitmap stale') + check(idx.cover[k]==sum(1<>k&1),'Target cover bitmap stale') +idx=Pending(4);idx.insert(1,(1,3),(1,5)) +check(idx.lower.eligible_mask((1,7))==2 and idx.eligible((1,7))==[],'Fixture does not reject missing future containment') +# Audit the actual integrated raise_ function on passive live controls. +compile_node=next(n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name=='compile_');raise_node=next(n for n in compile_node.body if isinstance(n,ast.FunctionDef) and n.name=='raise_') +blocks=[dict(frame=(3,3),rank=1),dict(frame=(1,7),rank=2),dict(frame=(1,15),rank=3)] +idx=Pending(4);idx.insert(0,blocks[0]['frame'],blocks[2]['frame']);idx.insert(1,blocks[0]['frame'],blocks[2]['frame']) +env=dict(frames=[0,0],blocks=blocks,contains=contains,retired=set(),retired_index=Retired(4),pending={0:2,1:2},pending_index=idx,hist=Counter(),events=[]) +exec(compile(ast.Module(body=[raise_node],type_ignores=[]),str(NEW),'exec'),env);env['raise_'](0,1) +check(idx.eligible(blocks[0]['frame'])==[1] and idx.eligible(blocks[1]['frame'])==[0,1],'Actual raise changes pending selection incorrectly') +check(idx.order=={0:0,1:1},'Actual raise changes pending order') +receipt=dict(status='PASS actual ordered two-envelope pending index and frame lifecycle',source_sha256=sha256(SOURCE.read_bytes()).hexdigest(),mutations=mutations,ordered_queries=queries,actual_raise_fixture=True,future_containment_negative_fixture=True) +(ROOT/'certificates/indexed-cycle-pending-index-validation.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt)) diff --git a/references/frame-compiler/pr84/scripts/experiments/audit_indexed_cycle_retired.py b/references/frame-compiler/pr84/scripts/experiments/audit_indexed_cycle_retired.py new file mode 100644 index 0000000000..10fc7fe4b2 --- /dev/null +++ b/references/frame-compiler/pr84/scripts/experiments/audit_indexed_cycle_retired.py @@ -0,0 +1,67 @@ +"""Focused actual-source audit. Chafik Boukhalfa with OpenAI Codex assistance; Apache-2.0.""" +from pathlib import Path +from hashlib import sha256 +from datetime import datetime,timezone +from random import Random +from collections import Counter +from copy import deepcopy +import ast,gzip,json,io,types,sys +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1] +SOURCE=HERE/'indexed_cycle_engine.py';NEW=SOURCE +source=SOURCE.read_text();tree=ast.parse(source) +def check(ok,why): + if not ok:raise ValueError(why) +klass=next(n for n in tree.body if isinstance(n,ast.ClassDef) and n.name=='RetiredIndex') +space={};exec(compile(ast.Module(body=[n for n in tree.body if isinstance(n,ast.ClassDef)],type_ignores=[]),str(SOURCE),'exec'),space);Index=space['RetiredIndex'] +contains=lambda f,g:not(g[0]&~f[0]) and not(f[1]&~g[1]) +def valid_frames(h): + return [(c,d) for d in range(1,1<150 or rng.random()<0.48): + s=rng.choice(list(records));f,r=records.pop(s);idx.remove(s,f,r) + else: + s=rng.randrange(1200) + if s in records:continue + f=frame();r=rng.randrange(h+1);idx.insert(s,f,r);records[s]=(f,r) + mutations+=1 + if iteration%4==0: + for target in (frame(),(1,full)): + check(list(idx.eligible(target))==order(records,target),'Random exact frame/order query differs');queries+=1 + if iteration%100==0: + check(idx.all==sum(1<>k&1),'Core bitmap stale') + check(idx.cover[k]==sum(1<>k&1),'Cover bitmap stale') +# The actual integrated raise function keeps already-retired controls indexed at their new frame. +compile_node=next(n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name=='compile_') +raise_node=next(n for n in compile_node.body if isinstance(n,ast.FunctionDef) and n.name=='raise_') +blocks=[dict(frame=(3,3),rank=1),dict(frame=(1,7),rank=2),dict(frame=(1,15),rank=3)] +idx=Index(4);idx.insert(0,blocks[0]['frame'],1) +env=dict(frames=[0,0],blocks=blocks,contains=contains,retired={0},retired_index=idx,pending={},pending_index=space['PendingIndex'](4),hist=Counter(),events=[]) +exec(compile(ast.Module(body=[raise_node],type_ignores=[]),str(NEW),'exec'),env) +env['raise_'](0,1) +check(list(idx.eligible(blocks[0]['frame']))==[] and list(idx.eligible(blocks[1]['frame']))==[0],'Actual retired control frame promotion not reflected') +env['raise_'](1,1) +check(idx.all==1 and env['frames']==[1,1],'Nonretired raise inserted an indexed role') +env['raise_'](0,2);idx.remove(0,blocks[2]['frame'],3) +check(idx.all==0 and not any(idx.ranks) and not any(idx.core) and not any(idx.cover),'Actual promoted role removal leaves stale bits') +receipt=dict(status='PASS actual ordered retired index and frame lifecycle',source_sha256=sha256(SOURCE.read_bytes()).hexdigest(),mutations=mutations,ordered_queries=queries,actual_raise_fixture=True) +(ROOT/'certificates/indexed-cycle-retired-index-validation.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt)) diff --git a/references/frame-compiler/pr84/scripts/experiments/binary_frame_math.py b/references/frame-compiler/pr84/scripts/experiments/binary_frame_math.py new file mode 100644 index 0000000000..b87855e808 --- /dev/null +++ b/references/frame-compiler/pr84/scripts/experiments/binary_frame_math.py @@ -0,0 +1,87 @@ +"""Exact rational helpers extracted without body changes from pinned PR48 verify.py. +Credits: icekylinx PR32/36, Dominik Scholz PR35, Zhihao Chen PR29/23, +Paureel/Aurel Prosz, Swapnil Jain, Rohan Arun PR25/31, RaD/hipotures, +Chafik Boukhalfa and inherited notices in references/frame-compiler/pr48. +Prepared with OpenAI Codex assistance; no formal theorem claim. +""" +from fractions import Fraction as Q +from functools import lru_cache +from math import comb, factorial, isqrt, prod + +def js(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):js(v)for k,v in x.items()} + if isinstance(x,(list,tuple)):return [js(v)for v in x] + return x + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def mersenne(exponent): + require(exponent >= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr84/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr84/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr84/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr84/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr84/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr84/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"< 1 and kappa > previous_kappa + prior74 = json.loads((ROOT/'references/frame-compiler/pr74/research/balanced-split-frames/certificate.json').read_text()) + rows74 = {int(t):n for t,n in prior74['child_multiplicities'].items()} + prior74_lower = refine.exact_moment(575, prior74['W'], rows74, bit_saving)['lower'] + reported74 = Q('10366199626713/200000000000000000') + assert prior74_lower > 1 and kappa > reported74 + bridge = finite_bridge(p['W']) + validate_bridge(bridge, p['W']) + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/indexed-cycle/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr79_commit='9a58e62cf9e8954a4dde3c9b1372d733c276a6d1', + pr74_commit='3f78d8967c009153f2df5c6a6577b6ab1d37e2ca', reported_pr74_kappa=reported74, + ratio_reported_pr74=kappa/reported74, pr74_complete_profile_exclusion_lower=prior74_lower, + pr79_kappa=previous_kappa, ratio_pr79=kappa/previous_kappa, + absolute_gain_pr79=kappa-previous_kappa, + pr79_complete_profile_exclusion_lower=prior71_lower, + full_pr79_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected indexed-cycle partition and point permutation, PR74 node order, natural execution, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring, PR69 balanced coarse sums, future unit completion and bounded PR70-derived single exchanges and two-cycles, exact frame indices, late-output routing and PR74/78-inspired coordinate relabeling; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'indexed-cycle-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr84/scripts/experiments/indexed_cycle_engine.py b/references/frame-compiler/pr84/scripts/experiments/indexed_cycle_engine.py new file mode 100644 index 0000000000..beb64af862 --- /dev/null +++ b/references/frame-compiler/pr84/scripts/experiments/indexed_cycle_engine.py @@ -0,0 +1,407 @@ +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + first,mid,last = 0,(len(groups)-1)//2,len(groups)-1 + requested = {1:[first],2:[mid],3:[last],4:[first,mid],5:[first,last],6:[mid,last],7:[first,mid,last],8:[first,first+1],9:[last-1,last]}[choice] + chosen=[] + for k in requested: + if k not in chosen and 0<=k>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + diff --git a/references/frame-compiler/pr84/scripts/experiments/joint_dual_reclaim_compiler.py b/references/frame-compiler/pr84/scripts/experiments/joint_dual_reclaim_compiler.py new file mode 100644 index 0000000000..1eb8dea9fa --- /dev/null +++ b/references/frame-compiler/pr84/scripts/experiments/joint_dual_reclaim_compiler.py @@ -0,0 +1,240 @@ +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'indexed-cycle-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from indexed_cycle_compose import check_sources + manifest_path = ROOT/'research/indexed-cycle/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/indexed-cycle-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_all_threshold_dependent_bridge_fields_are_checked(self): + from indexed_cycle_compose import finite_bridge, validate_bridge + expected = finite_bridge(132466108) + self.assertTrue(validate_bridge(expected, 132466108)) + for section,key in (('bit','wire_bits'),('rows','coefficient'),('rows','degree'),('rows','degree_gap'),('rows','suffix_slope')): + changed = deepcopy(expected) + changed[section][key] = Fraction(changed[section][key])+1 + with self.subTest(field=section+'.'+key), self.assertRaisesRegex(AssertionError, 'Stale finite bridge'): + validate_bridge(changed, 132466108) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('indexed_cycle_graph.py', 'indexed_cycle_engine.py', 'indexed_cycle_compiler.py', 'split_pair_arithmetic.py', 'indexed_cycle_compose.py', 'verify_indexed_cycle.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr84/tests/test_indexed_cycle_coordinates.py b/references/frame-compiler/pr84/tests/test_indexed_cycle_coordinates.py new file mode 100644 index 0000000000..12fedd3b90 --- /dev/null +++ b/references/frame-compiler/pr84/tests/test_indexed_cycle_coordinates.py @@ -0,0 +1,49 @@ +"""Bijection and adverse-coordinate controls for the actual PR74 relabel functions.""" +from pathlib import Path +from itertools import combinations +from copy import deepcopy +from hashlib import sha256 +import gzip,json,sys,unittest +ROOT=Path(__file__).resolve().parents[1];sys.path.insert(0,str(ROOT/'scripts/experiments')) +from indexed_cycle_nodeops import relabel +from indexed_cycle_graph import configuration + +class CoordinateControls(unittest.TestCase): + def test_selected_permutations_are_exact_integer_bijections(self): + for h in (23,25): + perm=configuration(h)['coordinate_permutation'] + self.assertEqual(sorted(perm),list(range(h))) + self.assertTrue(all(type(x) is int for x in perm)) + self.assertEqual(configuration(23)['coordinate_permutation'],list(range(1,23))+[0]) + + def test_every_selected_word_roundtrips_full_coordinate_inverse(self): + for h in (23,25): + word=json.loads(gzip.decompress((ROOT/f'certificates/indexed-cycle-word-{h}.json.gz').read_bytes())) + perm=configuration(h)['coordinate_permutation'];inverse=[perm.index(i) for i in range(h)] + parent=relabel(deepcopy(word),inverse) + # Dict iteration and scatter order are deliberately retained by the actual function. + raw=(json.dumps(parent,separators=(',',':'))+'\n').encode() + selection=json.loads((ROOT/'research/indexed-cycle/discovery-selection.json').read_text())['axes'][str(h)] + self.assertEqual(sha256(raw).hexdigest(),selection['parent_word_sha256']) + self.assertEqual(relabel(parent,perm),word) + + def test_relabel_preserves_physical_operations_and_frame_inclusions(self): + h=5;triples=list(combinations(range(h),3));v=len(triples);perm=[4,0,2,1,3] + word=dict(h=h,v=v,frames=[[3,7],[1,31]],sources={str(i):i for i in range(v)}, + scatter=[[v+i,2*v+i] for i in reversed(range(v))],outputs=[[2*v+i,0,0,list(t)] for i,t in enumerate(triples)], + ops=[[2*v,2*v+1,0]],events=[[2*v,0,1]]) + changed=relabel(deepcopy(word),perm) + self.assertEqual(changed['ops'],word['ops']);self.assertEqual(changed['events'],word['events']) + self.assertEqual(set(map(int,changed['sources'])),set(range(v))) + self.assertEqual([b for a,b in changed['scatter']],[b for a,b in word['scatter']]) + self.assertEqual(set(a for a,b in changed['scatter']),set(range(v,2*v))) + (a,b),(c,d)=changed['frames'];self.assertEqual(c&~a,0);self.assertEqual(b&~d,0) + + def test_invalid_permutation_and_scatter_source_are_rejected(self): + word=dict(h=3,v=1,frames=[[1,7]],sources={'0':0},scatter=[[1,2]],outputs=[[2,0,0,[0,1,2]]]) + for permutation in ([0,1,1],[0,1],[0,1,3]): + with self.subTest(permutation=permutation),self.assertRaises(AssertionError):relabel(deepcopy(word),permutation) + word['scatter'][0][0]=0 + with self.assertRaises(AssertionError):relabel(word,[0,1,2]) + +if __name__=='__main__':unittest.main() diff --git a/references/frame-compiler/pr88/.gitattributes b/references/frame-compiler/pr88/.gitattributes new file mode 100644 index 0000000000..90018fc83a --- /dev/null +++ b/references/frame-compiler/pr88/.gitattributes @@ -0,0 +1,28 @@ +* text=auto eol=lf +*.pdf binary +# Unified diffs require a leading space on blank context lines. +*.patch -whitespace +# Preserve the exact upstream bytes, including original whitespace. +upstream/** -whitespace +# Preserve the exact pinned third-party proof snapshots and notices. +references/copied-centers/pr29/** -whitespace +references/copied-centers/pr33/** -whitespace +references/semantic-bulk/** -whitespace + +# Immutable contributor archives retain original CRLF and whitespace bytes. +references/frame-compiler/pr69/** -text -whitespace +references/frame-compiler/pr70/** -text -whitespace +references/frame-compiler/pr71/** -text -whitespace + +# Preserve original contributor and frozen discovery bytes. +references/frame-compiler/pr74/** -text -whitespace +references/frame-compiler/pr78/** -text -whitespace +references/frame-compiler/pr79/** -text -whitespace +references/frame-compiler/indexed-r5/** -text -whitespace +# Byte-identical credited PR74 extracts retain original trailing blank lines. +scripts/experiments/indexed_cycle_nodeops.py -whitespace + +# Final construction archives retain exact Git bytes, CRLF and notices. +references/frame-compiler/pr82/** -text -whitespace +references/frame-compiler/pr84/** -text -whitespace +references/frame-compiler/final-r10/** -text -whitespace diff --git a/references/frame-compiler/pr88/.github/workflows/verify.yml b/references/frame-compiler/pr88/.github/workflows/verify.yml new file mode 100644 index 0000000000..87d09ed6c0 --- /dev/null +++ b/references/frame-compiler/pr88/.github/workflows/verify.yml @@ -0,0 +1,63 @@ +name: Verify research artifacts + +on: + push: + pull_request: + workflow_dispatch: + +permissions: + contents: read + +jobs: + verify: + runs-on: ubuntu-24.04 + timeout-minutes: 20 + strategy: + fail-fast: false + matrix: + python-version: ['3.11', '3.13', '3.14'] + group: [community, producers, certificates, ternary, research, tests, strips, clones, positive, joint, pair, balanced, indexed, final] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: ${{ matrix.python-version }} + - name: Install headers for the exact enlarged-frame profiler + if: matrix.group == 'positive' + run: | + if ! test -f /usr/include/boost/multiprecision/cpp_int.hpp; then + sudo apt-get update + sudo apt-get install -y libboost-dev + fi + - name: Check arithmetic, source hashes, finite identities, and patches + run: make verify-${{ matrix.group }} + - name: Require reproducible certificates and patches + run: git diff --exit-code + + formal: + runs-on: ubuntu-24.04 + timeout-minutes: 30 + strategy: + fail-fast: false + matrix: + package: [historical, gaussian, matrix] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: '3.13' + - name: Install elan; each project pins its Lean toolchain + run: | + curl --proto '=https' --tlsv1.2 -sSf https://raw.githubusercontent.com/leanprover/elan/0e36a07b9bbcc5381fa6250df109f9a4f94d7bac/elan-init.sh -o /tmp/elan-init.sh + sh /tmp/elan-init.sh -y --default-toolchain none + echo "$HOME/.elan/bin" >> "$GITHUB_PATH" + - name: Fetch pinned Mathlib build cache + if: matrix.package == 'historical' + working-directory: formal/lean + run: lake exe cache get + - name: Check formal package and theorem axiom dependencies + run: make formal-${{ matrix.package }}-verify diff --git a/references/frame-compiler/pr88/LICENSE b/references/frame-compiler/pr88/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/pr88/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Keep local verification sequential: +# different groups regenerate certificates that another group may read. +verify: + $(MAKE) verify-community + $(MAKE) verify-producers + $(MAKE) verify-certificates + $(MAKE) verify-ternary + $(MAKE) verify-research + $(MAKE) verify-strips + $(MAKE) verify-clones + $(MAKE) verify-positive + $(MAKE) verify-joint + $(MAKE) verify-pair + $(MAKE) verify-balanced + $(MAKE) verify-indexed + $(MAKE) verify-final + $(MAKE) verify-tests + +verify-community: community-audit-check community-followup-check copied-reversed-producer copied-reversed-check copied-fixed-reversed-producer copied-fixed-reversed-check + $(MAKE) copied-fixed-verify + $(MAKE) climbed-48-verify + +verify-producers: + $(MAKE) copied-centers-verify + $(MAKE) structured-bulk-verify + $(MAKE) endpoint-gauge-producer endpoint-gauge-certificate + $(MAKE) partial-swap-producer partial-swap-certificate + +verify-certificates: + python3 scripts/prime_field_network.py + python3 scripts/complex_network.py + python3 scripts/fast_gaussian.py + $(MAKE) batched-certificate batched-patch + python3 scripts/certify.py + python3 scripts/search_network.py + python3 scripts/make_patch.py + python3 scripts/nonadjacent.py + python3 scripts/make_nonadjacent_patch.py + python3 scripts/tune_routing.py + python3 scripts/research_networks.py + python3 scripts/search_network_variants.py + python3 scripts/block_label_targets.py + python3 scripts/audit_block_labels.py + python3 scripts/audit_additive_labels.py + python3 scripts/small_block_witness.py + python3 scripts/incidence_network.py + python3 scripts/make_incidence_patch.py + python3 scripts/search_incidence_partitions.py + python3 scripts/dag_network.py + python3 scripts/make_dag_patch.py + python3 scripts/shared_point_network.py + python3 scripts/make_shared_point_patch.py + python3 scripts/paired_network.py + python3 scripts/make_paired_patch.py + python3 scripts/prepare_layers.py + python3 scripts/audit_sparse_fusion.py + python3 scripts/audit_fused_block.py + python3 scripts/audit_short_guards.py + python3 scripts/audit_gather_schedules.py + python3 scripts/audit_coded_carries.py + python3 scripts/audit_cancellation.py + python3 scripts/audit_joint_frames.py + python3 scripts/audit_compact_controls.py + python3 scripts/compact_control_layer.py + python3 scripts/make_compact_control_patch.py + python3 scripts/audit_scratch_pooling.py + python3 scripts/reuse_network.py + python3 scripts/make_reuse_patch.py + +verify-ternary: + python3 scripts/complex_compression.py + python3 scripts/make_complex_compression_patch.py + python3 scripts/audit_ternary_side.py + python3 scripts/make_ternary_patch.py + +verify-tests: + python3 scripts/run_isolated_tests.py + git apply --check --directory=upstream patches/frozen-154.patch + git apply --check --directory=upstream patches/balanced-153.patch + git apply --check --directory=upstream patches/same-network-129.patch + git apply --check --directory=upstream patches/h46-111.patch + git apply --check --directory=upstream patches/h46-109.patch + git apply --check --directory=upstream patches/h46-108.patch + git apply --check --directory=upstream patches/h46-rational.patch + git apply --check --directory=upstream patches/nonadjacent-layout.patch + git apply --check --directory=upstream patches/frozen-nonadjacent-107.patch + git apply --check --directory=upstream patches/h46-nonadjacent-78.patch + git apply --check --directory=upstream patches/h46-nonadjacent-76.patch + git apply --check --directory=upstream patches/h46-shared-side-75.patch + git apply --check --directory=upstream patches/h46-incidence-67.patch + git apply --check --directory=upstream patches/h46-dag-63.patch + git apply --check --directory=upstream patches/h46-shared-point.patch + git apply --check --directory=upstream patches/h50-paired-59.patch + git apply --check --directory=upstream patches/compact-control-34.patch + git apply --check --directory=upstream patches/complex-compression-31.patch + git apply --check --directory=upstream patches/ternary-30.patch + git apply --check --directory=upstream patches/batched-23.patch + +note: + mkdir -p artifacts + tectonic --outdir artifacts notes/parameter-note.tex + +audit-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/nonadjacent-axis-note.tex + +tuned-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/routing-tuned-note.tex + +reuse-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/stage-reuse-note.tex + +incidence-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/incidence-note.tex + +dag-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/dag-note.tex + +shared-point-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/shared-point-note.tex + +paired-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/paired-note.tex + +compact-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/compact-control-note.tex + +complex-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/complex-compression-note.tex + +ternary-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/ternary-note.tex + +fetch: + python3 scripts/fetch_upstream.py + +.PHONY: batched-certificate batched-patch batched-note +PDFLATEX ?= pdflatex +TEX_ENGINE ?= pdflatex +TECTONIC ?= tectonic + +batched-certificate: + python3 scripts/controlled_bit_rank_moment.py --output certificates/controlled-bit-rank-moment.json > /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify + +.PHONY: balanced-split-verify verify-balanced +balanced-split-verify: + python3 scripts/experiments/verify_balanced_split.py + python3 scripts/experiments/audit_balanced_split_completion.py + python3 scripts/experiments/audit_balanced_split_exchange.py + python3 -m unittest discover -s tests -p 'test_balanced_split*.py' -v + +verify-balanced: balanced-split-verify + +.PHONY: indexed-cycle-verify verify-indexed +indexed-cycle-verify: + python3 scripts/experiments/verify_indexed_cycle.py + python3 scripts/experiments/audit_indexed_cycle_completion.py + python3 scripts/experiments/audit_indexed_cycle_exchange.py + python3 scripts/experiments/audit_indexed_cycle_cycles.py + python3 scripts/experiments/audit_indexed_cycle_retired.py + python3 scripts/experiments/audit_indexed_cycle_pending.py + python3 -m unittest discover -s tests -p 'test_indexed_cycle*.py' -v + +verify-indexed: indexed-cycle-verify + +.PHONY: final-frame-verify verify-final +final-frame-verify: + python3 scripts/experiments/verify_final_frame.py + python3 scripts/experiments/audit_final_frame_completion.py + python3 scripts/experiments/audit_final_frame_exchange.py + python3 scripts/experiments/audit_final_frame_cycles.py + python3 scripts/experiments/audit_final_frame_retired.py + python3 scripts/experiments/audit_final_frame_pending.py + python3 scripts/experiments/audit_final_frame_three_cycles.py + python3 scripts/experiments/audit_final_frame_pricing.py + python3 -m unittest discover -s tests -p 'test_final_frame*.py' -v + +verify-final: final-frame-verify diff --git a/references/frame-compiler/pr88/NOTICE b/references/frame-compiler/pr88/NOTICE new file mode 100644 index 0000000000..d27b657ee7 --- /dev/null +++ b/references/frame-compiler/pr88/NOTICE @@ -0,0 +1,341 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Balanced coarse split composition (2026-10-08) +--------------------------------------------- +Eumemic / @eumemic supplied PR69's balanced coarse sums, with OpenAI Codex +assistance. Alejandro Zarzuelo Urdiales / @alejandrozu supplied PR70's bounded +carry-exchange strategy with the AI disclosures retained in the source archive. +Chafik Boukhalfa / @chafreaky, with OpenAI Codex assistance, selected the row/ +half-plane coarse rules, future-compatible unit completion, exact integer-price +carry adaptation, composition and this certificate package. The PR71 anchored +split vector, schedules, arithmetic, pending controls and their contributor +chain are retained as credited above. Original PR69/70 sources, licenses and +notices and the complete published PR71 baseline are preserved under +references/frame-compiler. All earlier notices remain applicable. + +Indexed two-cycle composition (2026-10-08): Chafik Boukhalfa with OpenAI Codex assistance. Thomas DiFiore (@tomdif, PR74) supplied exact node ordering and coordinate relabeling, including the selected h25 permutation. Rohan Arun (@rohanarun, PR78) supplied the coordinate-flag search idea. Balanced multi-splits, exact retired/pending indices, bounded two-cycles, late-output routing and selected-coordinate certification compose inherited PR57/59/60/62/63/65/67/68/69/70/71/79 work. All original authorship, Apache-2.0 and AI disclosures remain in unchanged contributor archives. + +Final frame composition: Chafik Boukhalfa with OpenAI Codex assistance. Rank-preserving tie orders extend Thomas DiFiore PR74; coordinate-aware oracle pricing is adapted from Rohan Arun PR82. Three-donor cycles extend the credited bounded carrier exchange strategy. All earlier authors, OpenAI/manuscript, Apache-2.0 and AI-assistance notices remain attached in preserved archives. diff --git a/references/frame-compiler/pr88/README.md b/references/frame-compiler/pr88/README.md new file mode 100644 index 0000000000..2a2338d794 --- /dev/null +++ b/references/frame-compiler/pr88/README.md @@ -0,0 +1,192 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: balanced coarse split frames + +The [balanced-split proof and reproduction guide](research/balanced-split/README.md) +gives **κ=25872812736433/500000000000000000=5.1745625472866e-5**, approximately +**0.6437453019850683%** above the complete published PR71 witness. It composes +PR69 balanced coarse sums and a bounded PR70 carry exchange with PR71's +anchored split graph, future unit completion and profile-cost pending controls. +All actual words, dirty inputs, paid profiles and 47 strict assembly constraints +are checked by `make balanced-split-verify`. This finite conditional construction +retains the inherited all-size hypotheses and contributor notices. Chafik +Boukhalfa prepared the selected composition with OpenAI Codex assistance. + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. + +### Indexed two-cycle finite witness + +[Indexed-cycle proof and evidence](research/indexed-cycle/README.md) gives κ = 261356445457/5000000000000000 with W=132466108. It combines attributed balanced multi-splits, exact frame indexes, bounded carry two-cycles, PR74 node ordering and coordinate flags; all-size transfer remains inherited. Verify with `make indexed-cycle-verify`. The comparison is to pinned historical PR74/PR79 witnesses observed 2026-10-08. + +### Final frame composition + +The [final finite composition](research/final-frame/README.md) gives conditional κ=5.2514124198891e-5 using rank-preserving envelope ties, coordinate-aware prices and bounded three-donor exchanges. Run `make final-frame-verify`; all inherited gates remain included in `make verify`. 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bounded composition before the next publication freeze. Independently compare original74 versus best-tested rank-preserving order; exact original versus coordinate-aware heuristic pricing fromPR82; zero versus three passes of improving three-donor cycles. Selected R9 grouping/output policy and R6 map fixed peraxis. First reproduce R9 winning words/profiles as canaries. Full independent dense scalar/support check, dirty physical replay both orientations, exact CRT profiles and complete47+7 assembly on everycase. No source edits during a run. diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/FROZEN.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/FROZEN.json new file mode 100644 index 0000000000..74d58ee763 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/FROZEN.json @@ -0,0 +1,178 @@ +{ + "PR74_commit": "3f78d8967c009153f2df5c6a6577b6ab1d37e2ca", + "PR78_commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf", + "R5_SOURCE_sha256": "57d9a8742b3870e8899f46b43f62654b2fbd1daab62d6c7f4fff4496e64af900", + "W": 132466108, + "axes": { + "23": { + "coarse": "half", + "coordinate_permutation": [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 22, + 0 + ], + "groups": "411", + "node_order": "PR74 rank,-core,cover,minnode; natural execution", + "output_mode": "baseline", + "paid_profile": { + "R": 26834, + "blocks": [ + 0, + 360947, + 18308, + 10287, + 5376, + 3976, + 3779, + 2686, + 2296, + 1754, + 1371, + 1322, + 902, + 790, + 495, + 433, + 233, + 96, + 102, + 0, + 90, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 5567, + "distinct_matrices": 38555, + "field_prime": 2305843009213693951, + "frames": 65728, + "h": 23, + "loss": 506, + "rank_sum": 617688, + "v": 1771 + }, + "parent": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/spark-results/spark/envelope-r5/results/23-411-envelope-half", + "parent_word_sha256": "18cf81638085c4851d0346d8398fc8ea50a5be84b40aa85a5478b51a5264e25d", + "profiles_sha256": "263c516190c53723bf103dd603309efbbceac1e30193ed1781f92df19e0e08bc", + "roles": 26834, + "selected": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/coordinate-r5-search/h23-shift1", + "word_sha256": "c67fb6efa490db56814c743a48044c99397f3067f0038ce80673930c2f0ed829" + }, + "25": { + "coarse": "half", + "coordinate_permutation": [ + 2, + 1, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "groups": "141", + "node_order": "PR74 rank,-core,cover,minnode; natural execution", + "output_mode": "route-late", + "paid_profile": { + "R": 35348, + "blocks": [ + 0, + 492700, + 23012, + 12086, + 6121, + 4924, + 5649, + 4980, + 3550, + 2660, + 2408, + 2123, + 1685, + 1370, + 958, + 775, + 544, + 438, + 260, + 97, + 130, + 0, + 126, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 7465, + "distinct_matrices": 48221, + "field_prime": 2305843009213693951, + "frames": 86507, + "h": 25, + "loss": 600, + "rank_sum": 884300, + "v": 2300 + }, + "parent": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/spark-results/spark2/envelope-r5/results/25-141-envelope-half", + "parent_word_sha256": "7a5b52058bcc4b3923914e8633764f75f0b9214909c8f72f6e153121cc7e9070", + "profiles_sha256": "a74d3c0bccfbfb96b8e416536d3c52a2e9c0d99faa5f1c35b90d4d5647153ddb", + "roles": 35348, + "selected": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/coordinate-r5-search/h25-pr74", + "word_sha256": "ec153b2cd0ef6edeb626dbb2831abc5ce7a59c99870ec6a5e08afb5a1530c845" + } + }, + "bit_saving": "408390793141/7812500000000000", + "coordinate_driver_sha256": "acd52c55a9c4e43833d0d81ff952d2882336ed188f5857bc1dbb2866fdbfb082", + "equivalent_best_pairs": [ + [ + "coordinate-r5-search:shift1", + "coordinate-r5-search:pr74" + ] + ], + "kappa": "261356445457/5000000000000000", + "portfolio": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/spark-results/final-portfolio.json", + "portfolio_pairs": 7569, + "portfolio_sha256": "1631e97c3a58dd28f7a0b8aee732c739a7be82566159070bf460ee9f83775166", + "rank_mass": 76166165200, + "relabel_source_sha256": "9476e799b86aca3f6941acdd4d57779ba5bb5f4f29ed89247569daa9e88c1600", + "reported_pr74_kappa": "10366199626713/200000000000000000", + "status": "FROZEN pending independent physical/arithmetic final clearance" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/LICENSE b/references/frame-compiler/pr88/references/frame-compiler/final-r10/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. 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a/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h23/profiles.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h23/profiles.json new file mode 100644 index 0000000000..7baddf40c6 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h23/profiles.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27285,"loss":506,"rank_sum":628061,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38513,"crt_matrices":5538,"crt_disagreements":0,"blocks":[0,356669,20912,7996,5407,4043,3702,3146,2579,1990,1706,1444,980,839,542,483,239,205,49,97,0,23,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h23/replay.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h23/replay.json new file mode 100644 index 0000000000..d37ffd1add --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h23/replay.json @@ -0,0 +1,34 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27285, + "output_roles": 5336, + "elementary_xors": 160435, + "word_length": 666534, + "full_basis_vectors": 30827, + "rank_mass": 628061, + "histogram": { + "1": 58281, + "0": 171307, + "2": 80793, + "4": 14511, + "3": 10007, + "5": 6429, + "6": 2036, + "8": 1110, + "10": 535, + "9": 471, + "12": 661, + "14": 1868, + "13": 193, + "16": 431, + "11": 120, + "17": 574, + "18": 3412, + "15": 334, + "19": 6482, + "22": 23, + "21": 393, + "7": 627 + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h23/result.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h23/result.json new file mode 100644 index 0000000000..349e949822 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h23/result.json @@ -0,0 +1,19 @@ +{ + "h": 23, + "roles": 27285, + "stats": { + "augmentations": 13, + "regions": 59801, + "matched": 41730, + "multi_node_regions": 8694, + "carry_exchanges": 644, + "carry_two_cycles": 52, + "live_anchor_candidates": 72361, + "reclaimed": 2125, + "clearing_xors": 3916, + "live_anchor_xors": 76 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "word_sha256": "3f58db33edc2059ad6ca01cf8c36dd8cd8ae12149e1072e1f42757ca4ef17b82" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h25/profiles.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h25/profiles.json new file mode 100644 index 0000000000..2be4368700 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h25/profiles.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35684,"loss":600,"rank_sum":892700,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":51168,"crt_matrices":7278,"crt_disagreements":0,"blocks":[0,491871,27309,10127,7839,5460,4947,4006,3802,2943,2456,2025,1787,1423,1124,867,560,478,221,170,46,59,0,25,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h25/replay.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h25/replay.json new file mode 100644 index 0000000000..3ec3c54dc6 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h25/replay.json @@ -0,0 +1,36 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 35684, + "output_roles": 6925, + "elementary_xors": 224161, + "word_length": 928844, + "full_basis_vectors": 40284, + "rank_mass": 892700, + "histogram": { + "1": 77041, + "0": 238437, + "2": 118217, + "3": 13314, + "4": 18459, + "6": 3215, + "5": 8388, + "7": 948, + "8": 1195, + "9": 721, + "10": 828, + "12": 708, + "13": 182, + "14": 653, + "16": 2171, + "18": 506, + "19": 981, + "17": 633, + "15": 187, + "11": 15, + "20": 4464, + "21": 8405, + "24": 25, + "23": 463 + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h25/result.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h25/result.json new file mode 100644 index 0000000000..50b259fcd7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/baseline/h25/result.json @@ -0,0 +1,19 @@ +{ + "h": 25, + "roles": 35684, + "stats": { + "augmentations": 16, + "regions": 84843, + "matched": 60971, + "multi_node_regions": 11575, + "carry_exchanges": 1000, + "carry_two_cycles": 62, + "live_anchor_candidates": 98464, + "reclaimed": 3263, + "clearing_xors": 6027, + "live_anchor_xors": 132 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "word_sha256": "7c60369042197c356dfac3516ae396d68dc92edbc5824b6078dce0e6676f7f79" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/batch.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/batch.py new file mode 100644 index 0000000000..eb46375f78 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/batch.py @@ -0,0 +1,32 @@ +"""Final bounded factorial composition with exact parent canaries.""" +from pathlib import Path +from hashlib import sha256 +from fractions import Fraction as Q +from concurrent.futures import ProcessPoolExecutor,as_completed +import argparse,json,subprocess,sys,time +ROOT=Path(__file__).resolve().parent +sys.path.insert(0,str(ROOT)) +from graph_batch import generate,load + +def run(job): + h,node_order,pricing,passes,label=job + parent=json.loads((ROOT/'CANDIDATE_PARENT.json').read_text())[str(h)] + return generate(h,parent['groups'],mode='envelope-half',output_mode=parent['output_mode'],coordinate=parent['coordinate_permutation'],label=label,pricing=pricing,three_cycle_passes=passes,node_order=node_order) + +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--h',type=int,choices=(23,25),required=True);ap.add_argument('--workers',type=int,default=8);args=ap.parse_args();assert 1<=args.workers<=8 + manifest=json.loads((ROOT/'SOURCE.json').read_text()) + for path,digest in manifest['files'].items():assert sha256((ROOT/path).read_bytes()).hexdigest()==digest,path + print('SOURCE PASS',len(manifest['files']),sha256((ROOT/'SOURCE.json').read_bytes()).hexdigest(),flush=True) + subprocess.run([sys.executable,str(ROOT/'test_order.py')],check=True) + subprocess.run([sys.executable,str(ROOT/'test_three_cycles.py')],check=True) + parent=json.loads((ROOT/'CANDIDATE_PARENT.json').read_text())[str(args.h)];rows=[];started=time.monotonic();h=args.h + row=run((h,'pr74',False,0,'canary'));assert row['word_sha256']==parent['word_sha256'];assert row['kappa']==parent['kappa'];assert json.loads((ROOT/row['path']/'profiles.json').read_text())==json.loads((ROOT/f'candidate-parent/h{h}/profiles.json').read_text());rows.append(row);print('CANARY',json.dumps(row),flush=True) + jobs=[(h,key,pricing,passes,f'{key}-pricing{int(pricing)}-cycles{passes}') for key in ('pr74','cover-minus-core-minus') for pricing in (False,True) for passes in (0,3) if (key,pricing,passes)!=('pr74',False,0)] + with ProcessPoolExecutor(max_workers=args.workers) as pool: + for future in as_completed([pool.submit(run,job) for job in jobs]): + row=future.result();rows.append(row);receipt={'h':h,'complete':False,'validated_cases':len(rows),'expected_cases':8,'rows':rows,'wall_seconds':time.monotonic()-started} + temp=ROOT/'progress.tmp';temp.write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');temp.replace(ROOT/'progress.json');print('RESULT',json.dumps(row),flush=True) + best=max(rows,key=lambda row:Q(row['kappa']));receipt.update(complete=True,best_axis=best,wall_seconds=time.monotonic()-started) + (ROOT/'progress.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print('COMPLETE',json.dumps({k:v for k,v in receipt.items() if k not in ('rows','best_axis')}),flush=True) +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/build.sh b/references/frame-compiler/pr88/references/frame-compiler/final-r10/build.sh new file mode 100644 index 0000000000..44cbeea56b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/build.sh @@ -0,0 +1,5 @@ +#!/bin/sh +set -eu +mkdir -p bin +c++ -O3 -std=c++17 -I references/frame-compiler/pr48/scripts/partial_swap scripts/experiments/profile_oracle.cpp -o bin/profile-oracle +c++ -O3 -std=c++17 -I references/frame-compiler/pr48/scripts/partial_swap scripts/experiments/binary_frame_profiles.cpp -o bin/profiles diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h23/profiles.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h23/profiles.json new file mode 100644 index 0000000000..d881b695c2 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h23/profiles.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":26620,"loss":506,"rank_sum":612766,"field_prime":2305843009213693951,"frames":67863,"distinct_matrices":37844,"crt_matrices":5571,"crt_disagreements":0,"blocks":[0,362191,17808,9346,4092,3667,3946,3336,2453,1663,1220,1339,814,768,525,441,247,102,108,0,92,23,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h23/replay.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h23/replay.json new file mode 100644 index 0000000000..174e857f58 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h23/replay.json @@ -0,0 +1,34 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 26620, + "output_roles": 5336, + "elementary_xors": 181432, + "word_length": 750522, + "full_basis_vectors": 30162, + "rank_mass": 612766, + "histogram": { + "1": 79271, + "0": 196941, + "2": 77528, + "4": 14036, + "3": 9524, + "6": 1494, + "5": 5451, + "8": 2029, + "7": 785, + "9": 1807, + "10": 711, + "11": 580, + "12": 707, + "13": 267, + "14": 1131, + "16": 243, + "15": 404, + "17": 629, + "18": 2574, + "19": 5438, + "22": 23, + "21": 354 + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h23/result.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h23/result.json new file mode 100644 index 0000000000..669c2d7c98 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h23/result.json @@ -0,0 +1,24 @@ +{ + "h": 23, + "groups": "444", + "mode": "envelope-half", + "roles": 26620, + "word_sha256": "a2fc7194e9190f0fa4ddeac38aa76605f1b08243a7b51642a2433a52325b98c7", + "stats": { + "augmentations": 134, + "regions": 67861, + "matched": 50244, + "multi_node_regions": 8625, + "carry_exchanges": 1774, + "carry_two_cycles": 140, + "live_anchor_candidates": 74199, + "live_anchor_xors": 576, + "reclaimed": 2658, + "clearing_xors": 5682 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "compile_seconds": 41.97542989999056, + "replay_seconds": 1.7665091671515256, + "profile_seconds": 1.6327140040230006 +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h23/word.json.gz b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h23/word.json.gz new file mode 100644 index 0000000000..72140140b2 Binary files /dev/null and b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h23/word.json.gz differ diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h25/profiles.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h25/profiles.json new file mode 100644 index 0000000000..67f4cf0c33 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h25/profiles.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35138,"loss":600,"rank_sum":879050,"field_prime":2305843009213693951,"frames":93830,"distinct_matrices":53695,"crt_matrices":7335,"crt_disagreements":0,"blocks":[0,504362,27018,10748,5926,4937,5498,3818,3229,2589,2366,1865,1416,1370,1008,737,503,423,251,98,124,0,107,25,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h25/replay.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h25/replay.json new file mode 100644 index 0000000000..0b2dbfd701 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h25/replay.json @@ -0,0 +1,36 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 35138, + "output_roles": 6925, + "elementary_xors": 247252, + "word_length": 1021208, + "full_basis_vectors": 39738, + "rank_mass": 879050, + "histogram": { + "1": 101941, + "0": 266827, + "2": 108937, + "4": 22808, + "3": 12153, + "5": 7685, + "6": 1999, + "8": 2775, + "7": 826, + "9": 1016, + "10": 888, + "11": 552, + "12": 965, + "14": 478, + "13": 459, + "15": 454, + "16": 1970, + "18": 268, + "17": 661, + "19": 916, + "20": 3478, + "21": 7250, + "24": 25, + "23": 461 + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h25/result.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h25/result.json new file mode 100644 index 0000000000..373a2a5a79 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h25/result.json @@ -0,0 +1,24 @@ +{ + "h": 25, + "groups": "441", + "mode": "envelope-half", + "roles": 35138, + "word_sha256": "a378551e7c6511576d2ed7d0d035bf0403c4a1e5fa14b458c1de8d7b988e23fb", + "stats": { + "augmentations": 166, + "regions": 93828, + "matched": 70124, + "multi_node_regions": 11375, + "carry_exchanges": 2090, + "carry_two_cycles": 266, + "live_anchor_candidates": 97315, + "live_anchor_xors": 868, + "reclaimed": 3491, + "clearing_xors": 7148 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "compile_seconds": 68.12840775190853, + "replay_seconds": 2.661699212156236, + "profile_seconds": 2.3878593081608415 +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h25/word.json.gz b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h25/word.json.gz new file mode 100644 index 0000000000..04e196397b Binary files /dev/null and b/references/frame-compiler/pr88/references/frame-compiler/final-r10/candidate-parent/h25/word.json.gz differ diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/configs.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/configs.json new file mode 100644 index 0000000000..56e87fd388 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/configs.json @@ -0,0 +1,8 @@ +[ + "111", + "112", + "411", + "171", + "141", + "181" +] diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/evaluate.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/evaluate.py new file mode 100644 index 0000000000..ad3369d6c0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/evaluate.py @@ -0,0 +1,65 @@ +"""Exact high-precision comparisons, compounding verified PR65 arithmetic.""" +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +from copy import deepcopy +import importlib.util,json,sys,itertools +HERE=Path(__file__).resolve().parent +BASE=HERE +AR=BASE/'research/reordered-rank-pair/arithmetic' +sys.path.insert(0,str(AR)) +import refine +N=4073300;m=575 + +def load(path): + f=json.loads((path/'profiles.json').read_text());r=json.loads((path/'replay.json').read_text());s=json.loads((path/'result.json').read_text()) + assert f['crt_disagreements']==0 and f['R']==r['roles']==s['roles'] + return f + +def counts(profiles): + W=2*N;L=0;hist=Counter({1:19*N,21:2*N,17:2*N,481:2*N}) + for h,f in profiles.items(): + rep=N//f['v'];bank=rep*f['R'];W+=bank;L+=rep*f['loss'] + assert sum(t*n for t,n in enumerate(f['blocks']))==h*f['R']+f['loss']==f['rank_sum'] + hist.update({t:n*rep for t,n in enumerate(f['blocks']) if t and n});hist.update({h:bank,m-2*h:bank});hist.update({1:2*N,h-2:2*N}) + mass=sum(t*n for t,n in hist.items());assert mass==m*W-N+L + return dict(m=m,N=N,W=W,L=L,total_rank=mass,deficit=m*W-mass,maxchild=max(hist),child_multiplicities=dict(sorted(hist.items()))) + +def fine(profiles): + p=counts(profiles);rows=p['child_multiplicities'];den=10**18;lo=1;hi=6*10**13 + assert refine.exact_moment(m,p['W'],rows,Q(lo,den))['upper']<11:hi=mid + else:raise ArithmeticError('Enclosure inconclusive') + a=Q(lo,den);bridge=deepcopy(baseline['finite_bridge']);bridge['bit']['W']=p['W'] + bridge['bit']['wire_bits']=p['W'].bit_length() + bridge['rows']['coefficient']=sum(bridge[name]['halving_degree']*bridge[name]['wire_bits'] for name in ('bit','complex')) + bridge['rows']['degree_gap']=Q(bridge['rows']['degree'])-Q(51,25)*bridge['rows']['coefficient'] + bridge['rows']['suffix_slope']=4*bridge['rows']['degree'] + accepted=refine.exact_moment(m,p['W'],rows,a);rejected=refine.exact_moment(m,p['W'],rows,Q(hi,den));assert accepted['upper']<1prior and best['prior65_moment']['lower']>1 + for r in rows: + r['moment_at_best_bit']=refine.exact_moment(m,r['bit']['W'],r['bit']['child_multiplicities'],best['bit_saving']) + output={'verified_baseline':{'pr':65,'commit':'49e84f939d15b618b50714eb039cabf97c74256a','kappa':prior},'best':best,'rows':rows,'cases':len(rows)} + (HERE/'fine-pair-comparison.json').write_text(json.dumps(refine.arithmetic.js(output),indent=2,sort_keys=True)+'\n') + (HERE/'selected-exact-result.json').write_text(json.dumps(refine.arithmetic.js(best),indent=2,sort_keys=True)+'\n') + print('BEST',json.dumps({'pair':best['pair'],'kappa':str(best['kappa']),'bit_saving':str(best['bit_saving']),'W':best['bit']['W'],'gain_percent_vs_verified65':float(100*(best['kappa']/prior-1))},sort_keys=True),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h23/profiles.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h23/profiles.json new file mode 100644 index 0000000000..51adafc2f2 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h23/profiles.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":26834,"loss":506,"rank_sum":617688,"field_prime":2305843009213693951,"frames":65728,"distinct_matrices":38555,"crt_matrices":5567,"crt_disagreements":0,"blocks":[0,360947,18308,10287,5376,3976,3779,2686,2296,1754,1371,1322,902,790,495,433,233,96,102,0,90,23,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h23/replay.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h23/replay.json new file mode 100644 index 0000000000..22be4b8d75 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h23/replay.json @@ -0,0 +1,34 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 26834, + "output_roles": 5336, + "elementary_xors": 176951, + "word_length": 732598, + "full_basis_vectors": 30376, + "rank_mass": 617688, + "histogram": { + "1": 73048, + "0": 192243, + "2": 78597, + "4": 14768, + "3": 9345, + "6": 2630, + "5": 5655, + "7": 906, + "8": 1692, + "9": 1014, + "10": 793, + "11": 207, + "12": 370, + "13": 104, + "14": 1219, + "15": 400, + "16": 493, + "17": 1036, + "18": 2643, + "19": 5609, + "22": 23, + "21": 384 + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h23/result.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h23/result.json new file mode 100644 index 0000000000..ab84bad553 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h23/result.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "label": "shift1", + "permutation": [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 22, + 0 + ], + "parent_word_sha256": "18cf81638085c4851d0346d8398fc8ea50a5be84b40aa85a5478b51a5264e25d", + "word_sha256": "c67fb6efa490db56814c743a48044c99397f3067f0038ce80673930c2f0ed829", + "roles": 26834, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "seconds": 7.054715915990528 +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h23/word.json.gz b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h23/word.json.gz new file mode 100644 index 0000000000..3260f9aef6 Binary files /dev/null and b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h23/word.json.gz differ diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h25/profiles.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h25/profiles.json new file mode 100644 index 0000000000..1b7e20ff3a --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h25/profiles.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35348,"loss":600,"rank_sum":884300,"field_prime":2305843009213693951,"frames":86507,"distinct_matrices":48221,"crt_matrices":7465,"crt_disagreements":0,"blocks":[0,492700,23012,12086,6121,4924,5649,4980,3550,2660,2408,2123,1685,1370,958,775,544,438,260,97,130,0,126,25,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h25/replay.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h25/replay.json new file mode 100644 index 0000000000..2aed6f7d02 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h25/replay.json @@ -0,0 +1,36 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 35348, + "output_roles": 6925, + "elementary_xors": 234549, + "word_length": 970396, + "full_basis_vectors": 39948, + "rank_mass": 884300, + "histogram": { + "1": 78977, + "0": 255645, + "2": 122604, + "4": 15384, + "3": 13298, + "5": 8687, + "6": 1876, + "8": 2952, + "10": 987, + "9": 849, + "12": 1101, + "11": 156, + "13": 318, + "14": 575, + "15": 208, + "16": 1351, + "18": 673, + "17": 472, + "19": 779, + "20": 4243, + "21": 8332, + "24": 25, + "7": 609, + "23": 495 + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h25/result.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h25/result.json new file mode 100644 index 0000000000..e4e4ef2705 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h25/result.json @@ -0,0 +1,37 @@ +{ + "h": 25, + "label": "pr74", + "permutation": [ + 2, + 1, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "parent_word_sha256": "7a5b52058bcc4b3923914e8633764f75f0b9214909c8f72f6e153121cc7e9070", + "word_sha256": "ec153b2cd0ef6edeb626dbb2831abc5ce7a59c99870ec6a5e08afb5a1530c845", + "roles": 35348, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "seconds": 9.73521841596812 +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h25/word.json.gz b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h25/word.json.gz new file mode 100644 index 0000000000..074ec5c508 Binary files /dev/null and b/references/frame-compiler/pr88/references/frame-compiler/final-r10/frozen/h25/word.json.gz differ diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/graph_batch.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/graph_batch.py new file mode 100644 index 0000000000..12192418a9 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/graph_batch.py @@ -0,0 +1,92 @@ +"""Durable independent CPU search over pinned current two-cycle construction. +Each accepted case regenerates and independently replays the literal word, +reconstructs paid frames, computes CPU CRT profiles and exact inequalities. +""" +from pathlib import Path +from hashlib import sha256 +from concurrent.futures import ProcessPoolExecutor,as_completed +import argparse,ast,cProfile,gzip,importlib.util,json,os,pstats,subprocess,sys,time,types +ROOT=Path(__file__).resolve().parent +sys.path.insert(0,str(ROOT/'scripts/experiments')) + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m + +def generate(h,groups,profile=False,mode="baseline",output_mode=None,coordinate=None,label="search",pricing=False,three_cycle_passes=0,node_order="pr74"): + started=time.monotonic();out=ROOT/'results'/f'{h}-{groups}-{mode}-{output_mode}-{label}';out.mkdir(parents=True,exist_ok=True) + compiler=load('search_compiler',ROOT/'scripts/experiments/compiler.py') + source=(ROOT/'research/pair-assembly/pair_graph.py').read_text() + donor=ROOT/'references/pr69/balanced_coarse_compiler.py' + constants={n.targets[0].id:ast.literal_eval(n.value) for n in ast.parse(donor.read_text()).body if isinstance(n,ast.Assign) and isinstance(n.targets[0],ast.Name) and n.targets[0].id in ('BEFORE','AFTER')} + replacement=constants['AFTER'];needle='columns = [self.total([e(a,b) for a in groups[i]]) for b in groups[j]]' + orientation=mode.removeprefix('envelope-') if mode.startswith('envelope-') else ('half' if h==23 else 'row') + if orientation=='half': + replacement=replacement.replace(needle,'columns = ([self.total([e(a,b) for a in groups[i]]) for b in groups[j]] if i+j < ng-1 else [self.total([e(a,b) for b in groups[j]]) for a in groups[i]])') + elif orientation=='row':replacement=replacement.replace(needle,'columns = [self.total([e(a,b) for b in groups[j]]) for a in groups[i]]') + assert source.count(constants['BEFORE'])==1 + graph=types.ModuleType('balanced_graph');graph.__file__=str(ROOT/'research/pair-assembly/pair_graph.py');exec(compile(source.replace(constants['BEFORE'],replacement),graph.__file__,'exec'),graph.__dict__) + original=graph.circuit_class + def subclass(dim): + parent=original(dim) + class Split(parent): + def grouping(self,points): + result=super().grouping(points);choices=[int(x) for x in groups];choice=choices[self._level] if self._level3 and choice: + first,mid,last=0,(len(result)-1)//2,len(result)-1 + requested={1:[first],2:[mid],3:[last],4:[first,mid],5:[first,last],6:[mid,last],7:[first,mid,last],8:[first,first+1],9:[last-1,last]}[choice] + chosen=[] + for k in requested: + if k not in chosen and 0<=k>common&1 and not(mask&forbidden)) + assert support[x]==expected + return {'status':'PASS all global supports, exact envelopes, disjoint additions and target outputs','nodes':len(c.active),'outputs':len(c.outputs),'sha256':digest.hexdigest()} + +# Coordinate action preserves the literal physical word under a global input relabel. +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/original/carry_cycle_compiler.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/original/carry_cycle_compiler.py new file mode 100644 index 0000000000..d883cbc71d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/original/carry_cycle_compiler.py @@ -0,0 +1,338 @@ +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path('/Users/chafreaky/Documents/personal/integer-mult-research-20261008/joint-reclaim/references/frame-compiler/pr48') +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/original/output_basis_compiler.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/original/output_basis_compiler.py new file mode 100644 index 0000000000..517e4cd5e8 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/original/output_basis_compiler.py @@ -0,0 +1,407 @@ +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path('/Users/chafreaky/Documents/personal/integer-mult-research-20261008/joint-reclaim/references/frame-compiler/pr48') +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": "41187950749917624099/1000000000000000000000000", + "cell_above_band": "666666666665666652937349833360791967/1333388250600666556832132000000000000", + "compact_leaf": "26927049500082375901/1000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "13729317166639208033/333347062650166639208033", + "epsilon_positive": "333333333333000000000000/333347062650166639208033", + "g1_above_kappa": "3408408254232349301008147/3333470626501666392080330000000000000", + "g2_above_kappa": "4241/2500000000000", + "g3_above_kappa": "74937627730682908927817/3333470626501666392080330000000000000", + "g4_above_kappa": "4241/2500000000000", + "g5_above_kappa": "5299956450675231223831763/13333882506006665568321320000000000000", + "g6_above_kappa": "11966897703678564007992423/13333882506006665568321320000000000000", + "g7_above_kappa": "3333196040161742016173902349301008147/3333470626501666392080330000000000000", + "gamma_sublinear": 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OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": 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"scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1", + "scripts/partial_swap/graph.py": "fd8c567759e26a10d2bad05508fd0355eb70fb116664d4e06e1858d0d8cb2ef9", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + } + }, + "status": "Conditional exact arithmetic witness; general transfer proofs are dependencies" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000000000, + "cutoff_log2_input": { + "alpha": 5956134977, + "compact": 23824539905, + "geometry": 3999930893196446780, + "guard": 4283152, + "log_p": 25, + "normalization": 14000000000000000000, + "period": 47649079809, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000000000, + "powers": { + "alpha": { + "exponent": 725614180574271, + "rhs": 112000000000000154416, + "rhs_bits": 67 + }, + "compact": { + "exponent": 725614180574271, + "rhs": 448000000000000617600, + "rhs_bits": 69 + }, + "leaf": { + "exponent": 666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 725614180574271, + "rhs": 224000000000000308760, + "rhs_bits": 68 + }, + "rows": { + "exponent": 725614180574271, + "rhs": 112000000000000154416000, + "rhs_bits": 77 + } + } + }, + { + "log2_input": 28000000000000000000, + "powers": { + "alpha": { + "exponent": 1451228361148543, + "rhs": 224000000000000154416, + "rhs_bits": 68 + }, + "compact": { + "exponent": 1451228361148543, + "rhs": 896000000000000617600, + "rhs_bits": 70 + }, + "leaf": { + "exponent": 1333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1451228361148543, + "rhs": 448000000000000308760, + "rhs_bits": 69 + }, + "rows": { + "exponent": 1451228361148543, + "rhs": 224000000000000154416000, + "rhs_bits": 78 + } + } + }, + { + "log2_input": 56000000000000000000, + "powers": { + "alpha": { + "exponent": 2902456722297087, + "rhs": 448000000000000154416, + "rhs_bits": 69 + }, + "compact": { + "exponent": 2902456722297087, + "rhs": 1792000000000000617600, + "rhs_bits": 71 + }, + "leaf": { + "exponent": 2666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2902456722297087, + "rhs": 896000000000000308760, + "rhs_bits": 70 + }, + "rows": { + "exponent": 2902456722297087, + "rhs": 448000000000000154416000, + "rhs_bits": 79 + } + } + }, + { + "log2_input": 112000000000000000000, + "powers": { + "alpha": { + "exponent": 5804913444594174, + "rhs": 896000000000000154416, + "rhs_bits": 70 + }, + "compact": { + "exponent": 5804913444594174, + "rhs": 3584000000000000617600, + "rhs_bits": 72 + }, + "leaf": { + "exponent": 5333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5804913444594174, + "rhs": 1792000000000000308760, + "rhs_bits": 71 + }, + "rows": { + "exponent": 5804913444594174, + "rhs": 896000000000000154416000, + "rhs_bits": 80 + } + } + }, + { + "log2_input": 224000000000000000000, + "powers": { + "alpha": { + "exponent": 11609826889188348, + "rhs": 1792000000000000154416, + "rhs_bits": 71 + }, + "compact": { + "exponent": 11609826889188348, + "rhs": 7168000000000000617600, + "rhs_bits": 73 + }, + "leaf": { + "exponent": 10666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11609826889188348, + "rhs": 3584000000000000308760, + "rhs_bits": 72 + }, + "rows": { + "exponent": 11609826889188348, + "rhs": 1792000000000000154416000, + "rhs_bits": 81 + } + } + }, + { + "log2_input": 448000000000000000000, + "powers": { + "alpha": { + "exponent": 23219653778376697, + "rhs": 3584000000000000154416, + "rhs_bits": 72 + }, + "compact": { + "exponent": 23219653778376697, + "rhs": 14336000000000000617600, + "rhs_bits": 74 + }, + "leaf": { + "exponent": 21333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 23219653778376697, + "rhs": 7168000000000000308760, + "rhs_bits": 73 + }, + "rows": { + "exponent": 23219653778376697, + "rhs": 3584000000000000154416000, + "rhs_bits": 82 + } + } + } + ], + "practical_runtime_claim": false + }, + "finite_bridge": { + "bit": { + "W": 133862024, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 27 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 843, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "7007/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "10366199626713/200000000000000000", + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "endpoint_copy": { + "1": 4073300 + }, + "exterior_23": { + "23": 62412800, + "529": 62412800 + }, + "exterior_25": { + "25": 63302624, + "525": 63302624 + }, + "growth_23": { + "1": 8146600, + "21": 8146600 + }, + "growth_25": { + "1": 8146600, + "23": 8146600 + }, + "internal_23": { + "1": 818158300, + "10": 4816200, + 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witness; inherited all-size transfer remains assumed" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/check.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/check.py new file mode 100644 index 0000000000..0630cfc19a --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/check.py @@ -0,0 +1,104 @@ +#!/usr/bin/env python3 +"""Screen complete paid profiles from independently replayed axis constructions.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions required') +from pathlib import Path +from collections import Counter +from fractions import Fraction as Q +import importlib.util,argparse,json,subprocess,tempfile,hashlib,os,shlex +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +from producer import check_sources +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m +exact=load('candidate_exact',ROOT/'research/rank-pair-refinement/refine.py') +balanced=load('candidate_assembly',DEP/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') + +def profile(path): + v=json.loads(Path(path).read_text()) + return v['profile'] if 'profile' in v else v + +def calculate(first,second): + profiles=[profile(first),profile(second)] + N=4073300;m=575 + assert [p['h'] for p in profiles]==[23,25] + W=2*N+sum(N//p['v']*p['R'] for p in profiles) + parts={'data':Counter({1:18*N,21:2*N,17:2*N,481:2*N}),'endpoint_copy':Counter({1:N})} + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 + assert p['rank_sum']==h*p['R']+p['loss']==sum(t*n for t,n in enumerate(p['blocks'])) + assert p['loss']==h*(h-1) + parts[f'internal_{h}']=Counter({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + parts[f'exterior_{h}']=Counter({h:bank,m-2*h:bank}) + parts[f'growth_{h}']=Counter({1:2*N,h-2:2*N}) + rows=sum(parts.values(),Counter());assert sum(t*n for t,n in rows.items())==m*W-1846900 + lo,hi,grid=1,71700000000000,10**18 + while lo+11 + result.update(status='Verified finite conditional witness; inherited all-size transfer remains assumed', + source_manifest_sha256=hashlib.sha256((HERE/'SOURCE.json').read_bytes()).hexdigest(), + axes=axes,eventual_bounds=balanced.cutoffs(result['finite_bridge'],result['assembly']), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113',pr71_kappa=Q(previous['kappa']), + relative_gain_pr71=result['kappa']/Q(previous['kappa'])-1, + pr71_complete_profile_exclusion_lower=old_lower)) + result=arithmetic.js(result) + path=HERE/'certificate.json' + if record:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:assert result==json.loads(path.read_text()) + print('PASS exact moment, next-grid exclusions, 47 inequalities and seven margins',flush=True) + return result + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--record',action='store_true');args=parser.parse_args();generate(args.record) diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/producer.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/producer.py new file mode 100644 index 0000000000..8d68303a3b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/producer.py @@ -0,0 +1,132 @@ +#!/usr/bin/env python3 +"""Balanced coarse sums + anchored split/live frames + core ordering and coordinates. + +Composition for Thomas DiFiore with OpenAI Codex assistance. Apache-2.0. +PR69 coarse sums: eumemic. PR71 split/live composition: Chafik Boukhalfa. +Graph: Avi Eisenberg PR62; split operation: Rohan Garg PR59; reclamation: +Rohan Arun PR65/67, Dominik Scholz PR63/68, eumemic PR57. Original notices +and exact sources are retained under references/frame-compiler/pr69 and pr71. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +from hashlib import sha256 +import argparse,ast,gzip,importlib.util,json,types +from concurrent.futures import ProcessPoolExecutor +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +import split_pair_graph as provider +import split_pair_compiler as ancestor +from binary_frame_replay import replay + + +def check_sources(): + for folder in (DEP,ROOT/'references/frame-compiler/pr69'): + manifest=json.loads((folder/'SOURCE.json').read_text()) + for name,digest in manifest['files'].items(): + assert sha256((folder/name).read_bytes()).hexdigest()==digest,name + manifest=json.loads((HERE/'SOURCE.json').read_text()) + required={str((HERE/name).relative_to(ROOT)) for name in ('producer.py','check.py','graph_audit.py','independent_check.py','selection.json')} + assert required <= set(manifest['files']), 'Incomplete selected source closure' + for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + + +def reorder(c): + groups={} + for x in sorted(c.active): + if c.args[x]: groups.setdefault((c.core[x],c.union[x]),[]).append(x) + def key(item): + (core,cover),nodes=item + return cover.bit_count()-core.bit_count(),-core,cover,min(nodes) + ids=list(range(len(c.inputs)+1))+[x for _,nodes in sorted(groups.items(),key=key) for x in nodes] + mapping={x:i for i,x in enumerate(ids)} + args,core,cover,provenance=c.args,c.core,c.union,c.provenance + c.args=[tuple(mapping[y] for y in args[x]) if args[x] else None for x in ids] + c.core=[core[x] for x in ids];c.union=[cover[x] for x in ids] + c.provenance=[provenance[x] for x in ids] + c.active={mapping[x] for x in c.active};c.outputs={k:mapping[v] for k,v in c.outputs.items()} + c.support_in.cache_clear() + c.verify() + return c + + +def graph(h,ordered=True): + source=Path(provider._graph.__file__).read_text() + original=ROOT/'references/frame-compiler/pr69/scripts/experiments/balanced_coarse_compiler.py' + replacements={} + for node in ast.parse(original.read_text()).body: + if isinstance(node,ast.Assign): + for target in node.targets: + if isinstance(target,ast.Name) and target.id in ('BEFORE','AFTER'): + replacements[target.id]=ast.literal_eval(node.value) + assert source.count(replacements['BEFORE'])==1 + module=types.ModuleType('balanced_split_private_graph');module.__file__=provider._graph.__file__ + exec(compile(source.replace(replacements['BEFORE'],replacements['AFTER']),module.__file__+':balanced-coarse','exec'),module.__dict__) + previous=provider._graph + try: + provider._graph=module + c=provider.graph(h) + finally: + provider._graph=previous + return reorder(c) if ordered else c + + +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + +def compile_axis(h): + check_sources() + config=json.loads((HERE/'selection.json').read_text())['axes'][str(h)] + previous_graph,previous_order=provider.graph,provider.ordered_build + # graph() calls the original provider; keep that callable private while + # the inherited driver resolves the selected composed graph dynamically. + original_graph=previous_graph + def selected_graph(dimension): + provider.graph=original_graph + try:return graph(dimension) + finally:provider.graph=selected_graph + try: + provider.graph=selected_graph + provider.ordered_build=lambda original,dimension:original + compiled,word=ancestor.compile_axis(h) + finally: + provider.graph,provider.ordered_build=previous_graph,previous_order + compiled['graph_configuration']=config + word=relabel(word,config['coordinate_permutation']) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + path=HERE/f'word-{h}.json.gz' + with path.open('wb') as stream: + with gzip.GzipFile(filename='',fileobj=stream,mode='wb',mtime=0) as archive:archive.write(raw) + receipt=replay(path) + assert sha256(raw).hexdigest()==config['expected_word_sha256'] + axis=dict(configuration=config,compiled=compiled,replay=receipt, + word_sha256=sha256(raw).hexdigest(),gzip_sha256=sha256(path.read_bytes()).hexdigest()) + (HERE/f'axis-{h}.json').write_text(json.dumps(axis,indent=2)+'\n') + print(f'PASS fresh balanced/split/core word h={h}, roles={receipt["roles"]}',flush=True) + + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--h',type=int,choices=(23,25));args=parser.parse_args() + if args.h:compile_axis(args.h) + else: + with ProcessPoolExecutor(max_workers=2) as pool:list(pool.map(compile_axis,(23,25))) diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/profile-23.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/profile-23.json new file mode 100644 index 0000000000..013f4e59c7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/profile-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27136,"loss":506,"rank_sum":624634,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38292,"crt_matrices":5488,"crt_disagreements":0,"blocks":[0,355721,21666,6948,6524,3093,4314,2400,3266,1501,2094,1008,1374,586,732,353,307,139,62,16,0,23,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/profile-25.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/profile-25.json new file mode 100644 index 0000000000..1e3b6b89aa --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/profile-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35744,"loss":600,"rank_sum":894200,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52202,"crt_matrices":7623,"crt_disagreements":0,"blocks":[0,490052,26188,13531,7191,4637,5355,4229,3705,2610,2620,2080,1814,1357,1070,868,612,463,233,56,141,0,71,25,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/selection.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/selection.json new file mode 100644 index 0000000000..57cf3b6b65 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr74/research/balanced-split-frames/selection.json @@ -0,0 +1,86 @@ +{ + "source_pr71": "1bef94fd40a746452548c84a4a8f8834670a3113", + "source_pr69": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "axes": { + "23": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 22, + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 20, + 19, + 21 + ], + "expected_word_sha256": "8dc6696a274e70ca0af3fc49c4bdede362adaedc8dc322f335e3dab499f1ed48" + }, + "25": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 2, + 1, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "expected_word_sha256": "2c923afe366219ee3fffc9db063c91e44cdf7cbbdb62246b8e6a297dc440b577" + } + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr82/FETCH.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr82/FETCH.json new file mode 100644 index 0000000000..0dccc67c62 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr82/FETCH.json @@ -0,0 +1,43 @@ +{ + "commit": "3410b940aa26e5876202152dfa7c4f66451ee22c", + "files": { + "LICENSE": { + "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64", + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4" + }, + "NOTICE": { + "git_blob": "8a6bef1613ee24ca140ea612af48fb51d8cd9000", + "sha256": "ef6c74f5103d624f1a9910668d4124b213775e9b7e24edde089d9f4d1377abbb" + }, + "research/envelope-balanced/README.md": { + "git_blob": "77486a38c26058fa5690952254a056c1035b6e30", + "sha256": 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"47632a745319452f4237754ccb1793e7d0ae455654b68c6a31eb2a79a0f98b9f" + }, + "research/envelope-balanced/verify.py": { + "git_blob": "e74b03c41417c914bcf0e4e8fd0150a27e61aaef", + "sha256": "bd767d460a85414ca320a449705860a376bee42cb8ce0734233a8e9706ad4fc5" + } + }, + "repo": "rohanarun/integer-mult-bounds", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/82" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr82/LICENSE b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr82/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr82/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Balanced coarse split composition (2026-10-08) +--------------------------------------------- +Eumemic / @eumemic supplied PR69's balanced coarse sums, with OpenAI Codex +assistance. Alejandro Zarzuelo Urdiales / @alejandrozu supplied PR70's bounded +carry-exchange strategy with the AI disclosures retained in the source archive. +Chafik Boukhalfa / @chafreaky, with OpenAI Codex assistance, selected the row/ +half-plane coarse rules, future-compatible unit completion, exact integer-price +carry adaptation, composition and this certificate package. The PR71 anchored +split vector, schedules, arithmetic, pending controls and their contributor +chain are retained as credited above. Original PR69/70 sources, licenses and +notices and the complete published PR71 baseline are preserved under +references/frame-compiler. All earlier notices remain applicable. diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/README.md b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/README.md new file mode 100644 index 0000000000..77486a38c2 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/README.md @@ -0,0 +1,127 @@ +# Envelope ordering inside balanced split compilation + +The finite conditional witness gives **kappa = 5203279888519/100000000000000000 = 5.2032798885190e-05**, +0.49049670% above PR80. Bit saving is 13008876609597/250000000000000000. +This is a draft pending the full expanded repository verification. + +PR80 selected already-compiled axes from PR76 and PR79. Here we compose +their construction methods before compilation on both axes: PR79's balanced +coarse graph and future-compatible unit completion; PR76/PR74's envelope +node ordering; three passes of PR79/PR70's bounded carry exchanges; and +PR78's geometric coordinate flags. h23 uses the half-plane coarse choice +and cover-core schedule; h25 uses row coarse sums and reverse-node schedule. +Both retain the anchored [1,1,2] split vector and exact next-use profile costs. +All archived sources are unchanged. `compiler.py` is the portable composition. +At h25 the discovery oracle receives coordinate-permuted frame masks, so its +costs refer to the final flag rather than the original coordinate order. +`flag_engine.py` differs from PR79's engine only in that oracle frame writer +and an attribution comment; operations, eligibility, independence and dirty +checks are unchanged. This changes only heuristic selection among legal +choices. Its final word is still independently replayed and exactly priced. +At h23 oracle pricing retains the original coordinate order. + +| Quantity | PR80 | This witness | +|---|---:|---:| +| h23 auxiliary roles | 27256 | 27075 | +| h25 auxiliary roles | 35684 | 35500 | +| Physical width | 134031764 | 133289600 | +| Total recursive rank | 77066417400 | 76639673100 | +| Deficit | 1846900 | 1846900 | + +## General compatibility argument + +Balanced coarse parenthesization changes only how the same Cartesian-product +edge sums are evaluated. The weighted scalar identities and recursively +contracting anchored partition are inherited from PR79's proof. Envelope +ordering then applies a bijection to non-source scalar node IDs, grouping +nodes by (core, cover), preserving the order inside each group and every +argument, output and provenance reference. It changes no scalar linear form +or frame. The graph verifier is rerun after this relabeling. Dependency and +carrier-eligibility checks in the compiler remain enabled. + +Future-compatible completion chooses independent unit rows after the desired +outputs and retained carriers. Any accepted independent completion is a full +invertible basis; the unchanged synthesis emits its literal XOR operations. +Bounded carrier exchanges preserve matching cardinality, unique uses and +independence of the output-plus-retained-input rows. These choices can change +each other's costs, so the words are recompiled and every profile recomputed; +we do not add reported savings or assume independent numerical gains. + +All clearing targets and controls remain charged. Both frame-containment +checks for pending controls remain enabled. The compiler and independent +replay verify the full arbitrary-dirty-role wrapper in both orientations. +Independent axis implementations expose the same source triple lines, fixed +I+J basis, terminal frames and scatter identity. Hence the complete tensor/data +construction is unchanged. Every endpoint/copy/data-growth/complex term is +retained exactly once. The fixed-width bridge is derived from the actual W. + +## General relabeling argument + +Let P be a permutation matrix on the h coordinates. It commutes with J, +so P commutes with the fixed basis L = I+J and preserves the form I-J/9. +For a core/cover frame F(C,U), the relabeled projector is +P F(C,U) P^-1 = F(P C,P U). Consequently, every frame inclusion, rank, +nondegeneracy condition, projector denominator bound and elementary role +operation is preserved. The existing exact CRT bounds apply unchanged. + +Relabel each input triple T to P T, each output (c,T) to (P c,P T), +each frame mask by P, and each scatter row by the induced triple permutation. +The role slots and literal XOR operations do not change. This conjugates +the complete linear word by the input/output permutation and therefore +preserves its identity on every ordinary input and arbitrary dirty role. +The verifier independently replays that identity in both orientations. + +The data component sums over every pair of source triples. Independent +coordinate permutations on the two axes induce a bijection on that complete +Cartesian product. Hence its existing complete histogram, copied-center +costs and endpoint corrections are unchanged. This argument uses the full +case set; it would not justify retaining a selected subset's histogram. + +North-east corner rank profiles depend on the fixed coordinate order. +Conjugating by P can change which adjacent pivots form a recursive block, +even though total rank is unchanged. We regenerate these profiles from the +actual relabeled words rather than assuming their costs are invariant. +Both dimensions use the selected orders in order-23.json and order-25.json. + +## Reproduction and validation + +From the repository root with assert-enabled Python 3.11+ and C++17: + +```sh +python3 research/envelope-balanced/verify.py --regenerate +(cd research/envelope-balanced && python3 -m unittest test_controls -v) +make verify +``` + +The regeneration option launches two isolated compiler processes and requires +both original words to reproduce byte-for-byte. The verifier then regenerates +the coordinate-permuted words, performs independent full input/dirty replay, +reconstructs all transitions, and regenerates exact bounded-minor/CRT profiles. +The complete paid child list is reconstructed; independent rational moment +bounds, 47 strict inequalities, seven margins and both next-grid exclusions +are checked. The complete PR76, PR79 and PR80 child lists are each excluded at +the new bit saving using their own width. Six physical/coordinate failure +controls and three stale bridge controls run separately. A dedicated +three-version CI workflow retains every inherited workflow. + +The bounded searches are not proofs of global optimality. All inherited +all-size residual compiler, routing, recovery, prime selection, finite +alphabet/tape, precision and analytic transfer interfaces remain hypotheses. +No unconditional multiplication theorem or practical speedup is claimed. + +## Attribution + +Thomas DiFiore (PR74) introduced the envelope ordering; Dominik Scholz +(PR76) composed it with carried exchanges; Chafik Boukhalfa (PR79/71) +provided balanced/future/exchange and anchored split compilation; eumemic +(PR69/57) provided balanced coarse sums and reversible compilation; +Alejandro Zarzuelo Urdiales (PR70) supplied the carry-exchange strategy; +Rohan Arun (PR78/80/65/67) supplied coordinate flags, axis selection, +schedules and profile-cost reclamation. This new pre-compilation composition +and finite selection were prepared by Rohan Arun with OpenAI Codex assistance. + +Credit also Rohan Garg, Avi Eisenberg, icekylinx, James Chang, Zhihao Chen, +Aurel Prosz/Paureel, Swapnil Jain, RaD/hipotures, Douglas Colkitt, OpenAI, +Harvey–van der Hoeven and all inherited contributors. Original licenses, +author and AI-assistance notices remain preserved. Tested PR75 zero-circuit +variants were not selected for this witness and are not claimed as its method. diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/SOURCE.json new file mode 100644 index 0000000000..6b7fbca6d0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/SOURCE.json @@ -0,0 +1,304 @@ +{ + "parent_pr80": "a9ed157ff106fd35557b5896197f66a1272f7f13", + "files": { + ".gitattributes": "5f257f4e9e574ad5767f902242f519dad19cc455d6858f49234d0ccc345cabf1", + ".github/workflows/combined-flags.yml": "53d0f33c83356b2764f3cb332892690ff74ffa0e68b9ae1203fe837979c15396", + ".github/workflows/envelope-balanced.yml": "d658c2f91e1377eac5288cff7725ae1e573efdff70dac5472e6a4060085ab7fc", + ".github/workflows/verify.yml": 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Composition by Rohan Arun +with OpenAI Codex assistance. Apache-2.0; finite conditional witness only. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2] +sys.path.insert(0,str(ROOT/'scripts/experiments')) +import balanced_split_graph as graph +import balanced_split_exchange_engine as baseline_engine +import flag_engine +sys.path.insert(0,str(ROOT/'references/frame-compiler/pr76/research/round7-scheduling')) +from schedule_variant import reorder +import argparse,gzip,json,subprocess,os,shlex + +def check_flag_engine(): + original=(ROOT/'scripts/experiments/balanced_split_exchange_engine.py').read_text() + before="for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank']))" + after="for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank']))" + assert original.count(before)==1 + expected='# Coordinate-conjugated oracle pricing by Rohan Arun with OpenAI Codex.\n'+original.replace(before,after) + assert (Path(__file__).parent/'flag_engine.py').read_text()==expected,'Flag engine contains changes beyond oracle coordinate pricing' + +def compile_axis(h,work): + check_flag_engine() + engine=flag_engine if h==25 else baseline_engine + if h==25: + cfg=json.loads((ROOT/f'research/envelope-balanced/order-{h}.json').read_text()) + assert sorted(cfg['order'])==list(range(h)) + engine.COORD_MAP={int(k):v for k,v in cfg['mapping'].items()} + assert engine.COORD_MAP=={old:new for new,old in enumerate(cfg['order'])} + work.mkdir(parents=True,exist_ok=True) + oracle=work/'oracle' + subprocess.run([*shlex.split(os.environ.get('CXX','c++')),'-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/profile_oracle.cpp'),'-o',str(oracle)],check=True) + engine.graph=lambda dimension:reorder(graph.graph(dimension)) + engine.build=graph.ordered_build(engine.build,h) + engine.ORACLE_EXE=str(oracle);engine.ORACLE_INPUT=str(work/'oracle.bin');engine.PENDING_COST=True;engine.oracles=[] + try:result,word=engine.compile_(h,matching=True,reclaim=True,dirty=True) + finally: + for process in engine.oracles: + process.stdin.close();assert process.wait(timeout=10)==0 + result.pop('seconds',None);result['scalar']=engine.graph(h).verify() + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + (work/'word.json.gz').write_bytes(gzip.compress(raw,mtime=0)) + (work/'compiler.json').write_text(json.dumps(result,indent=2)+'\n') + print('PASS compiled envelope-balanced axis',h,result['roles'],flush=True) + +if __name__=='__main__': + p=argparse.ArgumentParser();p.add_argument('--h',type=int,choices=(23,25),required=True);p.add_argument('--work',type=Path,required=True);args=p.parse_args();compile_axis(args.h,args.work) diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/flag_engine.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/flag_engine.py new file mode 100644 index 0000000000..d210d9336b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/references/pr82/research/envelope-balanced/flag_engine.py @@ -0,0 +1,312 @@ +# Coordinate-conjugated oracle pricing by Rohan Arun with OpenAI Codex. +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(index[int(i)]):s for i,s in word['sources'].items()} + v=word['v'];word['scatter']=[[v+index[a-v],b] for a,b in word['scatter']] + word['outputs']=[[s,g,perm[c],sorted(perm[x] for x in triple)] for s,g,c,triple in word['outputs']] + return word + +def exact(profiles): + cert=json.loads((HERE/'certificate.json').read_text()) + N=comb(23,3)*comb(25,3);m=575;W=2*N+sum(N//p['v']*p['R'] for p in profiles) + L=sum(N//p['v']*p['loss'] for p in profiles) + rows=Counter({1:19*N,21:2*N,17:2*N,481:2*N}) + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 and p['v']==comb(h,3) + assert sum(t*n for t,n in enumerate(p['blocks']))==h*p['R']+h*(h-1)==p['rank_sum'] + rows.update({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + rows[h]+=bank;rows[m-2*h]+=bank;rows[1]+=2*N;rows[h-2]+=2*N + bit=dict(m=m,N=N,W=W,L=L,total_rank=sum(t*n for t,n in rows.items()),child_multiplicities=dict(sorted(rows.items()))) + assert bit['total_rank']==m*W-N+L + assert arithmetic.js(bit)==cert['bit'] + saving=Q(cert['bit_saving']);moment=refine.exact_moment(m,W,rows,saving) + rejected=refine.exact_moment(m,W,rows,saving+Q(1,10**18)) + assert moment['upper']<11 + assert Q(cert['kappa'])>Q(old['kappa']) + print('PASS exact conditional kappa',result['kappa'],'47 constraints, seven margins, independent bounds and next-grid controls') + +def verify(regenerate=False): + sources();profiles=[] + with tempfile.TemporaryDirectory(prefix='coordinate-flags-') as directory: + work=Path(directory);exe=work/'profiles' + subprocess.run(['c++','-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'scripts/experiments/binary_frame_profiles.cpp'),'-o',str(exe)],check=True) + if regenerate: + jobs=[] + for h in (23,25): + axis=work/str(h);axis.mkdir() + jobs.append(subprocess.Popen([sys.executable,str(HERE/'compiler.py'),'--h',str(h),'--work',str(axis)])) + for job in jobs:assert job.wait()==0,'Portable compiler regeneration failed' + for h in (23,25): + assert gzip.decompress((work/str(h)/'word.json.gz').read_bytes())==gzip.decompress(original_path(h).read_bytes()),'Regenerated physical word changed' + print('PASS portable deterministic regeneration of both unpermuted words',flush=True) + for h in (23,25): + original=json.loads(gzip.decompress((original_path(h)).read_bytes())) + config=json.loads((HERE/f'order-{h}.json').read_text());word=relabel(original,config) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + assert raw==gzip.decompress((HERE/f'word-{h}.json.gz').read_bytes()) + path=work/f'word-{h}.json';path.write_bytes(raw);checked=replay(path) + stored=json.loads((HERE/f'replay-{h}.json').read_text());assert arithmetic.js(checked)==stored['replay'] + trans=work/f'transitions-{h}.bin';receipt=prepare(path,trans);assert arithmetic.js(receipt)==stored['transitions'] + subprocess.run([str(exe),str(trans)],check=True) + profile=json.loads(Path(str(trans)+'.profiles.json').read_text());assert profile==json.loads((HERE/f'profiles-{h}.json').read_text()) + profiles.append(profile);print('PASS complete relabelled physical word and profile',h,flush=True) + exact(profiles) +if __name__=='__main__': + import argparse + parser=argparse.ArgumentParser();parser.add_argument('--regenerate',action='store_true');args=parser.parse_args();verify(args.regenerate) diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/research/reordered-rank-pair/arithmetic/refine.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr88/references/frame-compiler/final-r10/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/final-r10/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/final-r10/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/final-r10/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/final-r10/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<0 and carry_can(x,f) and carry_can(other,y): + options.append((-gain,z,x,y,other)) + if not options:continue + _,z,x,y,other=min(options) + old=(f,z,y);new=(e,x,other) + assert len(set(old))==len(set(new))==3 and not set(old)&set(new) + assert {edges[t][1] for t in old}=={edges[t][1] for t in new} + assert len({edges[t][0] for t in old})==len({edges[t][0] for t in new})==3 + for t in old: + tg,tu,ti=edges[t];chosen.remove(t);blocks[tg]['selected'].remove(t);del right[tu] + for t in new: + tg,tu,ti=edges[t];assert tu not in right;chosen.add(t);blocks[tg]['selected'].add(t);right[tu]=t + changes+=1 + return changes + + +def compile_(h,matching=True,reclaim=False,dirty=True): + t0=time.time();c,blocks,uses,value_uses,owner,signal,order,contains=build(h);v=len(c.inputs);position={g:i for i,g in enumerate(order)} + print('built',h,len(blocks),'regions',flush=True,file=sys.stderr) + mode=globals().get('OUTPUT_MODE','baseline') + edges,chosen,right,stats=match(blocks,uses,matching) + print('matched',len(chosen),'seconds',time.time()-t0,flush=True,file=sys.stderr) + slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();retired_index=RetiredIndex(h);pending={};pending_index=PendingIndex(h);stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + oracle_map=globals().get('ORACLE_COORDINATES',list(range(h))) + assert sorted(oracle_map)==list(range(h)), 'Invalid oracle coordinate permutation' + for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + for phase in range(globals().get('THREE_CYCLE_PASSES',0)): + changes=improve_three_cycles(blocks,edges,chosen,right,prices,priority,carry_can) + stats['carry_three_cycles']+=changes + print('carry three-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=3 or result[0]==0 +assert accepted>0 +print(json.dumps({'status':'PASS','actual_source':str(ROOT/'scripts/experiments/compiler.py'),'fixtures':1604,'accepted_three_cycles':accepted,'checks':['strict-cycle-only fixture','equal and worsening cost rejected','dependent replacement rejected','cardinality','one use per choice','local vector independence','exact integer descent','determinism','distinct block requirement']})) diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/EXPERIMENT.txt b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/EXPERIMENT.txt new file mode 100644 index 0000000000..ad69d585b0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/EXPERIMENT.txt @@ -0,0 +1 @@ +Compose Thomas DiFiore PR74 exact node-envelope renumbering with independently audited two-cycle matching, future completion, exact indexed reclamation, and selected h25 late output-use routing. Test six grouping structures and three coarse-sum orientations per dimension. Canary retains unchanged earlier cycles112 graph/schedule and hashes. Every new scalar graph and dirty physical word is independently checked and CPU CRT profiles/certificates are rebuilt. Imported PR74 functions and source/credits are preserved exactly. No imported claim is re-verified as a gate. diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/LICENSE b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/NOTICE b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/NOTICE new file mode 100644 index 0000000000..e75caef6fe --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/NOTICE @@ -0,0 +1,241 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/SOURCE.json new file mode 100644 index 0000000000..1f208b3942 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/SOURCE.json @@ -0,0 +1,61 @@ +{ + "experiment": "envelope-r5", + "files": { + "EXPERIMENT.txt": "7547e7255fc629a6887398c6b68d5432fdf8f6c8325db1b73e0616a02ee54eaa", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "62d9c3390f8c61fcc5efcdbeb4cd60ceb7b31aaf75c4ac214288fd72c86a5890", + "baseline/exact-results.json": "3e7e34ff9a3b61540de9c834bc393e6430972f5adfb549c9fafa15bd52ad3bbd", + "baseline/h23/profiles.json": "1764c61542871447ed5604d8b4a93f8d9bf542d5a3ffee8ee30cf4b2ed5a1feb", + 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a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h23/profiles.json b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h23/profiles.json new file mode 100644 index 0000000000..7baddf40c6 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h23/profiles.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27285,"loss":506,"rank_sum":628061,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38513,"crt_matrices":5538,"crt_disagreements":0,"blocks":[0,356669,20912,7996,5407,4043,3702,3146,2579,1990,1706,1444,980,839,542,483,239,205,49,97,0,23,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h23/replay.json b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h23/replay.json new file mode 100644 index 0000000000..d37ffd1add --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h23/replay.json @@ -0,0 +1,34 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27285, + "output_roles": 5336, + "elementary_xors": 160435, + "word_length": 666534, + "full_basis_vectors": 30827, + "rank_mass": 628061, + "histogram": { + "1": 58281, + "0": 171307, + "2": 80793, + "4": 14511, + "3": 10007, + "5": 6429, + "6": 2036, + "8": 1110, + "10": 535, + "9": 471, + "12": 661, + "14": 1868, + "13": 193, + "16": 431, + "11": 120, + "17": 574, + "18": 3412, + "15": 334, + "19": 6482, + "22": 23, + "21": 393, + "7": 627 + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h23/result.json b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h23/result.json new file mode 100644 index 0000000000..349e949822 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h23/result.json @@ -0,0 +1,19 @@ +{ + "h": 23, + "roles": 27285, + "stats": { + "augmentations": 13, + "regions": 59801, + "matched": 41730, + "multi_node_regions": 8694, + "carry_exchanges": 644, + "carry_two_cycles": 52, + "live_anchor_candidates": 72361, + "reclaimed": 2125, + "clearing_xors": 3916, + "live_anchor_xors": 76 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "word_sha256": "3f58db33edc2059ad6ca01cf8c36dd8cd8ae12149e1072e1f42757ca4ef17b82" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h25/profiles.json b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h25/profiles.json new file mode 100644 index 0000000000..2be4368700 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h25/profiles.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35684,"loss":600,"rank_sum":892700,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":51168,"crt_matrices":7278,"crt_disagreements":0,"blocks":[0,491871,27309,10127,7839,5460,4947,4006,3802,2943,2456,2025,1787,1423,1124,867,560,478,221,170,46,59,0,25,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h25/replay.json b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h25/replay.json new file mode 100644 index 0000000000..3ec3c54dc6 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h25/replay.json @@ -0,0 +1,36 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 35684, + "output_roles": 6925, + "elementary_xors": 224161, + "word_length": 928844, + "full_basis_vectors": 40284, + "rank_mass": 892700, + "histogram": { + "1": 77041, + "0": 238437, + "2": 118217, + "3": 13314, + "4": 18459, + "6": 3215, + "5": 8388, + "7": 948, + "8": 1195, + "9": 721, + "10": 828, + "12": 708, + "13": 182, + "14": 653, + "16": 2171, + "18": 506, + "19": 981, + "17": 633, + "15": 187, + "11": 15, + "20": 4464, + "21": 8405, + "24": 25, + "23": 463 + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h25/result.json b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h25/result.json new file mode 100644 index 0000000000..50b259fcd7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/baseline/h25/result.json @@ -0,0 +1,19 @@ +{ + "h": 25, + "roles": 35684, + "stats": { + "augmentations": 16, + "regions": 84843, + "matched": 60971, + "multi_node_regions": 11575, + "carry_exchanges": 1000, + "carry_two_cycles": 62, + "live_anchor_candidates": 98464, + "reclaimed": 3263, + "clearing_xors": 6027, + "live_anchor_xors": 132 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "word_sha256": "7c60369042197c356dfac3516ae396d68dc92edbc5824b6078dce0e6676f7f79" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/batch.py b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/batch.py new file mode 100644 index 0000000000..1f994fa396 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/batch.py @@ -0,0 +1,113 @@ +"""Durable independent CPU search over pinned current two-cycle construction. +Each accepted case regenerates and independently replays the literal word, +reconstructs paid frames, computes CPU CRT profiles and exact inequalities. +""" +from pathlib import Path +from hashlib import sha256 +from concurrent.futures import ProcessPoolExecutor,as_completed +import argparse,ast,cProfile,gzip,importlib.util,json,os,pstats,subprocess,sys,time,types +ROOT=Path(__file__).resolve().parent +sys.path.insert(0,str(ROOT/'scripts/experiments')) + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m + +def generate(h,groups,profile=False,mode="baseline"): + started=time.monotonic();out=ROOT/'results'/f'{h}-{groups}-{mode}';out.mkdir(parents=True,exist_ok=True) + compiler=load('search_compiler',ROOT/'scripts/experiments/compiler.py') + source=(ROOT/'research/pair-assembly/pair_graph.py').read_text() + donor=ROOT/'references/pr69/balanced_coarse_compiler.py' + constants={n.targets[0].id:ast.literal_eval(n.value) for n in ast.parse(donor.read_text()).body if isinstance(n,ast.Assign) and isinstance(n.targets[0],ast.Name) and n.targets[0].id in ('BEFORE','AFTER')} + replacement=constants['AFTER'];needle='columns = [self.total([e(a,b) for a in groups[i]]) for b in groups[j]]' + orientation=mode.removeprefix('envelope-') if mode.startswith('envelope-') else ('half' if h==23 else 'row') + if orientation=='half': + replacement=replacement.replace(needle,'columns = ([self.total([e(a,b) for a in groups[i]]) for b in groups[j]] if i+j < ng-1 else [self.total([e(a,b) for b in groups[j]]) for a in groups[i]])') + elif orientation=='row':replacement=replacement.replace(needle,'columns = [self.total([e(a,b) for b in groups[j]]) for a in groups[i]]') + assert source.count(constants['BEFORE'])==1 + graph=types.ModuleType('balanced_graph');graph.__file__=str(ROOT/'research/pair-assembly/pair_graph.py');exec(compile(source.replace(constants['BEFORE'],replacement),graph.__file__,'exec'),graph.__dict__) + original=graph.circuit_class + def subclass(dim): + parent=original(dim) + class Split(parent): + def grouping(self,points): + result=super().grouping(points);choices=[int(x) for x in groups];choice=choices[self._level] if self._level3 and choice: + first,mid,last=0,(len(result)-1)//2,len(result)-1 + requested={1:[first],2:[mid],3:[last],4:[first,mid],5:[first,last],6:[mid,last],7:[first,mid,last],8:[first,first+1],9:[last-1,last]}[choice] + chosen=[] + for k in requested: + if k not in chosen and 0<=k1:hi=mid + else:raise ArithmeticError('Enclosure inconclusive') + a=Q(lo,den);bridge=deepcopy(baseline['finite_bridge']);bridge['bit']['W']=p['W'] + bridge['bit']['wire_bits']=p['W'].bit_length() + bridge['rows']['coefficient']=sum(bridge[name]['halving_degree']*bridge[name]['wire_bits'] for name in ('bit','complex')) + bridge['rows']['degree_gap']=Q(bridge['rows']['degree'])-Q(51,25)*bridge['rows']['coefficient'] + bridge['rows']['suffix_slope']=4*bridge['rows']['degree'] + accepted=refine.exact_moment(m,p['W'],rows,a);rejected=refine.exact_moment(m,p['W'],rows,Q(hi,den));assert accepted['upper']<1prior and best['prior65_moment']['lower']>1 + for r in rows: + r['moment_at_best_bit']=refine.exact_moment(m,r['bit']['W'],r['bit']['child_multiplicities'],best['bit_saving']) + output={'verified_baseline':{'pr':65,'commit':'49e84f939d15b618b50714eb039cabf97c74256a','kappa':prior},'best':best,'rows':rows,'cases':len(rows)} + (HERE/'fine-pair-comparison.json').write_text(json.dumps(refine.arithmetic.js(output),indent=2,sort_keys=True)+'\n') + (HERE/'selected-exact-result.json').write_text(json.dumps(refine.arithmetic.js(best),indent=2,sort_keys=True)+'\n') + print('BEST',json.dumps({'pair':best['pair'],'kappa':str(best['kappa']),'bit_saving':str(best['bit_saving']),'W':best['bit']['W'],'gain_percent_vs_verified65':float(100*(best['kappa']/prior-1))},sort_keys=True),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/nodeops.py b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/nodeops.py new file mode 100644 index 0000000000..fa6164310d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/nodeops.py @@ -0,0 +1,40 @@ +# Exact function extracts from Thomas DiFiore PR74,3f78d8967c009153f2df5c6a6577b6ab1d37e2ca. Apache-2.0; original source and notices retained. + +def reorder(c): + groups={} + for x in sorted(c.active): + if c.args[x]: groups.setdefault((c.core[x],c.union[x]),[]).append(x) + def key(item): + (core,cover),nodes=item + return cover.bit_count()-core.bit_count(),-core,cover,min(nodes) + ids=list(range(len(c.inputs)+1))+[x for _,nodes in sorted(groups.items(),key=key) for x in nodes] + mapping={x:i for i,x in enumerate(ids)} + args,core,cover,provenance=c.args,c.core,c.union,c.provenance + c.args=[tuple(mapping[y] for y in args[x]) if args[x] else None for x in ids] + c.core=[core[x] for x in ids];c.union=[cover[x] for x in ids] + c.provenance=[provenance[x] for x in ids] + c.active={mapping[x] for x in c.active};c.outputs={k:mapping[v] for k,v in c.outputs.items()} + c.support_in.cache_clear() + c.verify() + return c + + +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/original/carry_cycle_compiler.py b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/original/carry_cycle_compiler.py new file mode 100644 index 0000000000..d883cbc71d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/original/carry_cycle_compiler.py @@ -0,0 +1,338 @@ +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path('/Users/chafreaky/Documents/personal/integer-mult-research-20261008/joint-reclaim/references/frame-compiler/pr48') +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": 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"scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1", + "scripts/partial_swap/graph.py": "fd8c567759e26a10d2bad05508fd0355eb70fb116664d4e06e1858d0d8cb2ef9", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + } + }, + "status": "Conditional exact arithmetic witness; general transfer proofs are dependencies" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000000000, + "cutoff_log2_input": { + "alpha": 5956134977, + "compact": 23824539905, + "geometry": 3999930893196446780, + "guard": 4283152, + "log_p": 25, + "normalization": 14000000000000000000, + "period": 47649079809, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000000000, + "powers": { + "alpha": { + "exponent": 725614180574271, + "rhs": 112000000000000154416, + "rhs_bits": 67 + }, + "compact": { + "exponent": 725614180574271, + "rhs": 448000000000000617600, + "rhs_bits": 69 + }, + "leaf": { + "exponent": 666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 725614180574271, + "rhs": 224000000000000308760, + "rhs_bits": 68 + }, + "rows": { + "exponent": 725614180574271, + "rhs": 112000000000000154416000, + "rhs_bits": 77 + } + } + }, + { + "log2_input": 28000000000000000000, + "powers": { + "alpha": { + "exponent": 1451228361148543, + "rhs": 224000000000000154416, + "rhs_bits": 68 + }, + "compact": { + "exponent": 1451228361148543, + "rhs": 896000000000000617600, + "rhs_bits": 70 + }, + "leaf": { + "exponent": 1333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1451228361148543, + "rhs": 448000000000000308760, + "rhs_bits": 69 + }, + "rows": { + "exponent": 1451228361148543, + "rhs": 224000000000000154416000, + "rhs_bits": 78 + } + } + }, + { + "log2_input": 56000000000000000000, + "powers": { + "alpha": { + "exponent": 2902456722297087, + "rhs": 448000000000000154416, + "rhs_bits": 69 + }, + "compact": { + "exponent": 2902456722297087, + "rhs": 1792000000000000617600, + "rhs_bits": 71 + }, + "leaf": { + "exponent": 2666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2902456722297087, + "rhs": 896000000000000308760, + "rhs_bits": 70 + }, + "rows": { + "exponent": 2902456722297087, + "rhs": 448000000000000154416000, + "rhs_bits": 79 + } + } + }, + { + "log2_input": 112000000000000000000, + "powers": { + "alpha": { + "exponent": 5804913444594174, + "rhs": 896000000000000154416, + "rhs_bits": 70 + }, + "compact": { + "exponent": 5804913444594174, + "rhs": 3584000000000000617600, + "rhs_bits": 72 + }, + "leaf": { + "exponent": 5333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5804913444594174, + "rhs": 1792000000000000308760, + "rhs_bits": 71 + }, + "rows": { + "exponent": 5804913444594174, + "rhs": 896000000000000154416000, + "rhs_bits": 80 + } + } + }, + { + "log2_input": 224000000000000000000, + "powers": { + "alpha": { + "exponent": 11609826889188348, + "rhs": 1792000000000000154416, + "rhs_bits": 71 + }, + "compact": { + "exponent": 11609826889188348, + "rhs": 7168000000000000617600, + "rhs_bits": 73 + }, + "leaf": { + "exponent": 10666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11609826889188348, + "rhs": 3584000000000000308760, + "rhs_bits": 72 + }, + "rows": { + "exponent": 11609826889188348, + "rhs": 1792000000000000154416000, + "rhs_bits": 81 + } + } + }, + { + "log2_input": 448000000000000000000, + "powers": { + "alpha": { + "exponent": 23219653778376697, + "rhs": 3584000000000000154416, + "rhs_bits": 72 + }, + "compact": { + "exponent": 23219653778376697, + "rhs": 14336000000000000617600, + "rhs_bits": 74 + }, + "leaf": { + "exponent": 21333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 23219653778376697, + "rhs": 7168000000000000308760, + "rhs_bits": 73 + }, + "rows": { + "exponent": 23219653778376697, + "rhs": 3584000000000000154416000, + "rhs_bits": 82 + } + } + } + ], + "practical_runtime_claim": false + }, + "finite_bridge": { + "bit": { + "W": 133862024, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 27 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 843, + "contract": 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witness; inherited all-size transfer remains assumed" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/check.py b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/check.py new file mode 100644 index 0000000000..0630cfc19a --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/check.py @@ -0,0 +1,104 @@ +#!/usr/bin/env python3 +"""Screen complete paid profiles from independently replayed axis constructions.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions required') +from pathlib import Path +from collections import Counter +from fractions import Fraction as Q +import importlib.util,argparse,json,subprocess,tempfile,hashlib,os,shlex +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +from producer import check_sources +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m +exact=load('candidate_exact',ROOT/'research/rank-pair-refinement/refine.py') +balanced=load('candidate_assembly',DEP/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') + +def profile(path): + v=json.loads(Path(path).read_text()) + return v['profile'] if 'profile' in v else v + +def calculate(first,second): + profiles=[profile(first),profile(second)] + N=4073300;m=575 + assert [p['h'] for p in profiles]==[23,25] + W=2*N+sum(N//p['v']*p['R'] for p in profiles) + parts={'data':Counter({1:18*N,21:2*N,17:2*N,481:2*N}),'endpoint_copy':Counter({1:N})} + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 + assert p['rank_sum']==h*p['R']+p['loss']==sum(t*n for t,n in enumerate(p['blocks'])) + assert p['loss']==h*(h-1) + parts[f'internal_{h}']=Counter({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + parts[f'exterior_{h}']=Counter({h:bank,m-2*h:bank}) + parts[f'growth_{h}']=Counter({1:2*N,h-2:2*N}) + rows=sum(parts.values(),Counter());assert sum(t*n for t,n in rows.items())==m*W-1846900 + lo,hi,grid=1,71700000000000,10**18 + while lo+11 + result.update(status='Verified finite conditional witness; inherited all-size transfer remains assumed', + source_manifest_sha256=hashlib.sha256((HERE/'SOURCE.json').read_bytes()).hexdigest(), + axes=axes,eventual_bounds=balanced.cutoffs(result['finite_bridge'],result['assembly']), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113',pr71_kappa=Q(previous['kappa']), + relative_gain_pr71=result['kappa']/Q(previous['kappa'])-1, + pr71_complete_profile_exclusion_lower=old_lower)) + result=arithmetic.js(result) + path=HERE/'certificate.json' + if record:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:assert result==json.loads(path.read_text()) + print('PASS exact moment, next-grid exclusions, 47 inequalities and seven margins',flush=True) + return result + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--record',action='store_true');args=parser.parse_args();generate(args.record) diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/producer.py b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/producer.py new file mode 100644 index 0000000000..8d68303a3b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/producer.py @@ -0,0 +1,132 @@ +#!/usr/bin/env python3 +"""Balanced coarse sums + anchored split/live frames + core ordering and coordinates. + +Composition for Thomas DiFiore with OpenAI Codex assistance. Apache-2.0. +PR69 coarse sums: eumemic. PR71 split/live composition: Chafik Boukhalfa. +Graph: Avi Eisenberg PR62; split operation: Rohan Garg PR59; reclamation: +Rohan Arun PR65/67, Dominik Scholz PR63/68, eumemic PR57. Original notices +and exact sources are retained under references/frame-compiler/pr69 and pr71. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +from hashlib import sha256 +import argparse,ast,gzip,importlib.util,json,types +from concurrent.futures import ProcessPoolExecutor +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +import split_pair_graph as provider +import split_pair_compiler as ancestor +from binary_frame_replay import replay + + +def check_sources(): + for folder in (DEP,ROOT/'references/frame-compiler/pr69'): + manifest=json.loads((folder/'SOURCE.json').read_text()) + for name,digest in manifest['files'].items(): + assert sha256((folder/name).read_bytes()).hexdigest()==digest,name + manifest=json.loads((HERE/'SOURCE.json').read_text()) + required={str((HERE/name).relative_to(ROOT)) for name in ('producer.py','check.py','graph_audit.py','independent_check.py','selection.json')} + assert required <= set(manifest['files']), 'Incomplete selected source closure' + for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + + +def reorder(c): + groups={} + for x in sorted(c.active): + if c.args[x]: groups.setdefault((c.core[x],c.union[x]),[]).append(x) + def key(item): + (core,cover),nodes=item + return cover.bit_count()-core.bit_count(),-core,cover,min(nodes) + ids=list(range(len(c.inputs)+1))+[x for _,nodes in sorted(groups.items(),key=key) for x in nodes] + mapping={x:i for i,x in enumerate(ids)} + args,core,cover,provenance=c.args,c.core,c.union,c.provenance + c.args=[tuple(mapping[y] for y in args[x]) if args[x] else None for x in ids] + c.core=[core[x] for x in ids];c.union=[cover[x] for x in ids] + c.provenance=[provenance[x] for x in ids] + c.active={mapping[x] for x in c.active};c.outputs={k:mapping[v] for k,v in c.outputs.items()} + c.support_in.cache_clear() + c.verify() + return c + + +def graph(h,ordered=True): + source=Path(provider._graph.__file__).read_text() + original=ROOT/'references/frame-compiler/pr69/scripts/experiments/balanced_coarse_compiler.py' + replacements={} + for node in ast.parse(original.read_text()).body: + if isinstance(node,ast.Assign): + for target in node.targets: + if isinstance(target,ast.Name) and target.id in ('BEFORE','AFTER'): + replacements[target.id]=ast.literal_eval(node.value) + assert source.count(replacements['BEFORE'])==1 + module=types.ModuleType('balanced_split_private_graph');module.__file__=provider._graph.__file__ + exec(compile(source.replace(replacements['BEFORE'],replacements['AFTER']),module.__file__+':balanced-coarse','exec'),module.__dict__) + previous=provider._graph + try: + provider._graph=module + c=provider.graph(h) + finally: + provider._graph=previous + return reorder(c) if ordered else c + + +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + +def compile_axis(h): + check_sources() + config=json.loads((HERE/'selection.json').read_text())['axes'][str(h)] + previous_graph,previous_order=provider.graph,provider.ordered_build + # graph() calls the original provider; keep that callable private while + # the inherited driver resolves the selected composed graph dynamically. + original_graph=previous_graph + def selected_graph(dimension): + provider.graph=original_graph + try:return graph(dimension) + finally:provider.graph=selected_graph + try: + provider.graph=selected_graph + provider.ordered_build=lambda original,dimension:original + compiled,word=ancestor.compile_axis(h) + finally: + provider.graph,provider.ordered_build=previous_graph,previous_order + compiled['graph_configuration']=config + word=relabel(word,config['coordinate_permutation']) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + path=HERE/f'word-{h}.json.gz' + with path.open('wb') as stream: + with gzip.GzipFile(filename='',fileobj=stream,mode='wb',mtime=0) as archive:archive.write(raw) + receipt=replay(path) + assert sha256(raw).hexdigest()==config['expected_word_sha256'] + axis=dict(configuration=config,compiled=compiled,replay=receipt, + word_sha256=sha256(raw).hexdigest(),gzip_sha256=sha256(path.read_bytes()).hexdigest()) + (HERE/f'axis-{h}.json').write_text(json.dumps(axis,indent=2)+'\n') + print(f'PASS fresh balanced/split/core word h={h}, roles={receipt["roles"]}',flush=True) + + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--h',type=int,choices=(23,25));args=parser.parse_args() + if args.h:compile_axis(args.h) + else: + with ProcessPoolExecutor(max_workers=2) as pool:list(pool.map(compile_axis,(23,25))) diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-23.json b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-23.json new file mode 100644 index 0000000000..013f4e59c7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27136,"loss":506,"rank_sum":624634,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38292,"crt_matrices":5488,"crt_disagreements":0,"blocks":[0,355721,21666,6948,6524,3093,4314,2400,3266,1501,2094,1008,1374,586,732,353,307,139,62,16,0,23,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-25.json b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-25.json new file mode 100644 index 0000000000..1e3b6b89aa --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35744,"loss":600,"rank_sum":894200,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52202,"crt_matrices":7623,"crt_disagreements":0,"blocks":[0,490052,26188,13531,7191,4637,5355,4229,3705,2610,2620,2080,1814,1357,1070,868,612,463,233,56,141,0,71,25,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/selection.json b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/selection.json new file mode 100644 index 0000000000..57cf3b6b65 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/selection.json @@ -0,0 +1,86 @@ +{ + "source_pr71": "1bef94fd40a746452548c84a4a8f8834670a3113", + "source_pr69": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "axes": { + "23": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 22, + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 20, + 19, + 21 + ], + "expected_word_sha256": "8dc6696a274e70ca0af3fc49c4bdede362adaedc8dc322f335e3dab499f1ed48" + }, + "25": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 2, + 1, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "expected_word_sha256": "2c923afe366219ee3fffc9db063c91e44cdf7cbbdb62246b8e6a297dc440b577" + } + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/research/reordered-rank-pair/arithmetic/refine.py b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": 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0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + 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"scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1", + "scripts/partial_swap/graph.py": "fd8c567759e26a10d2bad05508fd0355eb70fb116664d4e06e1858d0d8cb2ef9", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + } + }, + "status": "Conditional exact arithmetic witness; general transfer proofs are dependencies" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py b/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis 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"scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + }, + "integration_note": "Against main d55bcd62, binary_io.hpp adds only six standard-library includes. Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + } + }, + "gzip_sha256": "4629d45d5074f87706db46be3aa3cd369071cd215bc6560d641115aadcce54a0", + "word_sha256": "bd0cbf73756f2e4f8d3879ec6c7a194990eb9ec40aaf3580bdded6994798d920" + }, + "25": { + "compiled": { + "h": 25, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 36586, + "baseline_pr48_roles": 48329, + "histogram": { + "1": 55478, + "0": 416276, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + }, + "rank_mass": 915250, + "elementary_xors": 205650, + "stats": { + "augmentations": 286, + "regions": 73695, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json new file mode 100644 index 0000000000..346cf87ea3 --- /dev/null +++ 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mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": 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"field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 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}, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + "exponent": 5333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5715743812, + "rhs": 1792000000313576, + "rhs_bits": 51 + }, + "rows": { + "exponent": 5715743812, + "rhs": 896000000156824000, + "rhs_bits": 60 + } + } + }, + { + "log2_input": 224000000000000, + "powers": { + "alpha": { + "exponent": 11431487624, + "rhs": 1792000000156824, + "rhs_bits": 51 + }, + "compact": { + "exponent": 11431487624, + "rhs": 7168000000627232, + "rhs_bits": 53 + }, + "leaf": { + "exponent": 10666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11431487624, + "rhs": 3584000000313576, + "rhs_bits": 52 + }, + "rows": { + "exponent": 11431487624, + "rhs": 1792000000156824000, + "rhs_bits": 61 + } + } + }, + { + "log2_input": 448000000000000, + "powers": { + "alpha": { + "exponent": 22862975248, + "rhs": 3584000000156824, + "rhs_bits": 52 + }, + "compact": { + "exponent": 22862975248, + "rhs": 14336000000627232, + "rhs_bits": 54 + }, + "leaf": { + "exponent": 21333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 22862975248, + "rhs": 7168000000313576, + "rhs_bits": 53 + }, + "rows": { + "exponent": 22862975248, + "rhs": 3584000000156824000, + "rhs_bits": 62 + } + } + } + ], + "practical_runtime_claim": false + }, + "kappa": "40827/800000000", + "next_kappa": "318961/6250000000", + "next_kappa_rejection": "{'g1_above_kappa': '-25408022593116799041/7102635201420453820506250000000', 'g3_above_kappa': '-5201705247125960457841/1136421632227272611281000000000000', 'g5_above_kappa': '-7640875416065173165777/1818274611563636178049600000000000', 'g6_above_kappa': '-33658690551416775383761/9091373057818180890248000000000000'}", + "original_enclosure_control": { + "accepted_upper": 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a/references/frame-compiler/pr88/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr88/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 at the new bit saving, +and the new complete profile has exact upper moment <1. All47 strict assembly +conditions and seven margins pass. **53 Lean endpoints** pass:34 new universal, +15 concrete,4 reused rational-helper lemmas. No omitted proof, project axiom or +native decision shortcut. The math scope includes dirty-word/complement safety, +coordinate conjugacy, fresh-kernel clearing, actual finite rounding and old-profile +rejection. It does not formalize the Python/C++ compiler or the all-size theorem. + +## Reproduce the accepted words + +Use an external checkout of frozen PR62 commit +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No newer sources are consumed. +See `verification/README.md` to compile its exact C++17 profiler, then run: + +``` +python verification/verify_words.py --upstream UPSTREAM --profiler PROFILER --word23 words/word-23.json.gz --word25 words/word-25.json.gz --output work/recheck +python verification/check_guards.py words/word-23.json.gz +python verification/check_guards.py words/word-25.json.gz +cd math +lake build Frozen62Research +``` + +The verifier checks immutable sources and its own adapter hashes, full input/dirty +bases in both orientations, exact source/scatter inventory, every literal frame +transition and all fixed-I+J profiles with bounded-minor and CRT checks. It rejects +optimized Python assertion mode. Use the supplied words for authoritative replay; +floating discovery prices propose candidates and have no trusted-proof role. +Discovery source snapshots, exact oracle fixtures (gzip-compressed) and matching +seeds retain original byte hashes. `discovery/SEARCH.md` explains the algorithms, +heuristic boundary and experimental commands. Historical workspace paths in the +source-generation receipts identify the original run; the accepted-word replay +uses the explicit upstream argument and needs no private directory layout. +Portable discovery regeneration: + +``` +python discovery/regenerate_portable.py --upstream UPSTREAM --work work/regenerate +``` + +This rewrites workspace paths only and checks both raw words and deterministic +gzip against the accepted words. Floating discovery is outside the trusted +certificate; the independent word/profile verifier establishes acceptance. + +The one-hour session froze information through #62. The unchanged data geometry +and its rational recovery are inherited; selected physical words/profile checks +are fresh. All-size analytic, compiler/frame transfer, finite-alphabet tape, +routing, prime selection/recovery and eventual-threshold contracts remain +conditional. No practical runtime or global-optimality claim is made. + +Alejandro Zarzuelo Urdiales is the human author/developer, following earlier +Archivara and personal July/October matrix/parity work developed with multiple +AI tools. This synthesis involved substantial OpenAI Codex assistance. Known +linear algebra, matroid exchange, dirty uncomputation and concavity principles +retain prior-work status. The finite construction credits Avi Eisenberg/ikeboy +(#62 interval/core-aware graph), eumemic (#57 frame compiler), Chafik Boukhalfa +(#60 ranking and earlier exact profiling), Rohan Arun and other retained notices. +The prior matrix/parity source is in `../matrix-exponent-synthesis/` and prior +Gaussian work in PR45. Its product counts retain their separate arithmetic scope. +The paper is supplied as LaTeX source; no newly compiled PDF is claimed. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md b/references/frame-compiler/pr88/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md new file mode 100644 index 0000000000..b8dd669634 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md @@ -0,0 +1,136 @@ +# Local frame-compiler search, frozen through PR62 + +All experiments in this directory use the pinned PR62 pair graph at +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No later community source is consumed. +The original checkout is unchanged. Each emitted word and compiler copy has +a SHA256 recorded in its `compiled.json`; changed words are sent separately +to the independent literal replay and profile verifier. + +## New dependency-circuit choices + +The inherited compiler reduces retired fresh-signal rows against the current +live anchors and an echelon basis of compatible retired rows. Instead of +accepting the first dependent retired row, the new selectors collect the +available fundamental dependency circuits and choose a circuit by one of: + +- total charged target/provider rank growth (`all_growth`); +- number and rank growth of other retired providers (`all_collateral`); +- anchor-only dependence before general retired dependence (`anchor_first`); +- actual physical transition child-profile moment cost (`profile_cost*`). + +Every clearing XOR and every target/provider frame promotion is still emitted +and charged. A zero fresh-signal row can contain arbitrary physical dirty state; +its reuse is justified by the complete reversible word, not by claiming that +the physical register is initialized to zero. The compiler runs both complete +dirty-basis orientations, and the independent verifier repeats them. + +For the last selector let `C(A,B) = sum_t n_t(A,B) F_t`, where the `n_t` are +the exact inherited fixed-I+J pivot-run profile of the physical frame transition +and `F_t = t exp(a log(m/t))`. A candidate target `s` at old frame `A_s`, cleared +into frame `G` with providers `z`, is priced by + +``` +C(A_s,G) - C(A_s,I) + + sum_z [C(A_z,G) + C(G,I) - C(A_z,I)]. +``` + +This accounts for immediate promotions and the change in deferred cleanup, +assuming each other retired provider remains retired until cleanup. Future +reuse couples decisions, so this is a discovery heuristic, not an additive +global optimality certificate. Linear rank mass cancels between candidates; +`t*expm1(a*log(m/t))` avoids cancellation in floating discovery prices. +Missing transition profiles are recorded and collected for the next iteration. +Once a run has zero missing pairs, every local price uses an actual transition +profile. The final saving is accepted only through exact rational whole-profile +moment bounds and all assembly gates. + +`build_pair_oracle.py` is a local adaptation of the frozen C++ profiler that +additionally exports each transition histogram. It preserves the projector, +pivot, bounded-minor and three-prime CRT routines. Its synthetic transition-list +input is an oracle request, not a physical executable word. Each immutable +profile dump and the source/header hashes are recorded. + +## Moment-ordered carry selection + +The `--weighted` experiment orders the inherited linear/partition-matroid +candidate edges by their physical transition moment change before the original +greedy initialization and augmenting paths. For a value produced at `P`, +preserved through donor frame `G`, and carried to future target `T`, its +no-reclamation child-cost change is + +``` +C(G,T) - C(G,I) - C(0,P) - C(P,T). +``` + +At fixed cardinality, role and external-volume corrections are common to all +edge choices in the same axis. The inherited augmenting algorithm still seeks +maximum cardinality; it does not optimize the weights globally. Reclamation +adds coupling, so only the changed whole-word profile can establish an actual +improvement. This experiment makes no minimum-cost matroid claim. + +The `--exchange` variant starts from the frozen original maximum-cardinality +matching and tries bounded improving one-edge exchanges. A new edge may replace +the old donor of the same use when its donor block stays linearly independent; +or it may replace a selected edge in the same donor block and serve an unused +use. Both preserve cardinality and distinct-use constraints. The `--cycle` +variant additionally tests two-edge donor/use cycles, checking the independence +of both changed blocks. No improving two-edge cycle was found in the tested +native-price instance; this is not a proof that longer cycles cannot improve it. + +## Joint basis and schedule search + +`--basis shift1` profiles all candidate physical transitions after the point +permutation `i -> (i+1) mod h`, while preserving their original frame IDs. +Matching and reclamation are then priced in that basis. The emitted word is +renamed by `relabel_word.py`: all frame masks, canonical source/output triples, +common points and scatter port indices change together. Scratch slots and +literal XOR instructions are retained. The complete triple family and the +permutation-invariant `I+J` basis are inherited; every final renamed word still +gets fresh full-basis and actual physical-profile verification. + +This joint search differs from merely relabeling an already selected schedule: +the selected carries and clearing circuits are optimized under the new ordered +pivot-run prices. It remains a bounded discovery heuristic. + +## Regeneration + +The frozen graph/matching setup and a moment-cost exchange run are generated by: + +``` +python -S collect_matching_pairs.py --h 23 +python -S build_pair_oracle.py --h 23 --strategy matching_collect +python -S run_strategy.py --h 23 --strategy profile_cost --exchange +``` + +Repeat at `h=25`. For joint search, add `--basis shift1` to the oracle and +strategy commands. Reclamation may encounter transitions absent from the +initial carry-edge inventory. Run the oracle again on the emitted strategy +directory with `--incremental`, then run a new strategy label. The new label +must start with `profile_cost`; output directories are never overwritten. +`compiled.json` records the exact oracle dump hash, missing-pair count, word +hashes and source pin. Immutable earlier oracle dumps are retained by SHA256. +Use `--oracle path/to/the-immutable-dump.jsonl` to reproduce the prices of a +specific recorded run instead of consuming the subsequently enlarged cache. +The initial compiler matching cache is accepted only if its complete candidate +edge list matches the current frozen graph and every restored selected block +passes the same linear-independence check. + +The runner saves an immutable source copy and its hash for later runs. Floating +`expm1` prices at discovery saving `a=0.00005103` select proposals only. Neither +those prices nor their reported local gains are used as an arithmetic witness. + +## Acceptance boundary + +The independent verifier checks all input and dirty basis vectors in both +orientations, exact literal-scatter incidences, causal nested physical frames, +event equality reconstructed from the actual XOR word, rank mass, actual child +profiles and CRT agreement. It then computes the whole mixed-axis recurrence +and exact rational moment/assembly witnesses. Existing all-size geometry, +analytic envelopes, compiler/tape arguments and the surrounding reduction are +inherited from frozen PR62. A finite profile improvement does not by itself +formally prove those inherited hypotheses. + +Reduced XOR count alone is not accepted as an exponent improvement. In this +search `all_collateral` and `anchor_first` reduced clearing XORs but worsened +the certified characteristic. Actual child-size distributions decide the +saving, even when both physical-role counts and total rank mass are unchanged. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py b/references/frame-compiler/pr88/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py new file mode 100644 index 0000000000..7c154b1a29 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py @@ -0,0 +1,275 @@ +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +import sys;sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'matrix-synthesis/bridge/pr62/references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s,add=True): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>s&1;e^=1<=prices[f]-1e-14:continue + if not can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:-prices[z])if prices[e] /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/NOTICE b/references/frame-compiler/pr88/references/frame-compiler/pr71/NOTICE new file mode 100644 index 0000000000..8adab44ba3 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/NOTICE @@ -0,0 +1,324 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr71/README.md new file mode 100644 index 0000000000..4a9b481aa3 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/README.md @@ -0,0 +1,172 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/SOURCE.json new file mode 100644 index 0000000000..c8cc31f3d0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/SOURCE.json @@ -0,0 +1,120 @@ +{ + "commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "Makefile": "6e9e48a677b2f66643226840f574a6535e3564ffb0c72284b60302684a5dfbe4", + "NOTICE": "1e0702aa665673508fa91169163c5785d680637fff636fda01f36e3b127c3ee0", + "README.md": "24817241fcad7f0a294ec6ad9666ee552ed9057e8d89e3c1d27e8fa2c7fe4229", + "certificates/split-pair-compiler.json": 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Original upstream sources and notices are preserved byte-for-byte. Actual inherited dependencies are additionally checked through the shared PR48 manifest.", + "shared_dependency_manifest": "../pr48/SOURCE.json", + "shared_dependency_manifest_sha256": "6ccc673f88d3650d75ed600b082fe2fc2866dd88a172d182a38c1d0cd27d24b3" + }, + "pr67": { + "author": "Rohan Arun with OpenAI assistance", + "commit": "b3745601e947a94316bf25c2c6263d93c06e3364", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "5931cb7d43e09380594b113018cac70258fb66e0673b91f706b01ea482c1be1a", + "research/slot-cost-rank-pair/README.md": "e0fcd8e732c8b8becb3d860eb83dc979ed5e6b33ba16caf9dca1e44f7929c340", + "research/slot-cost-rank-pair/arithmetic/certificate.json": "e66f955f1b76ce3db7ecb84294993a072f42f972b8f3040015c12e6dc953d698", + "research/slot-cost-rank-pair/compiler.py": "29296211e0532aaf19101a6b2f2ceaebe374af95ae3acd63e63656db0afef7ae", + "research/slot-cost-rank-pair/frame-compiler.json": "eb5c0b401e677d3958ecfcd6d8de3bc825c4fb66d1cf79c3fcbcf23938ca6e69", + "research/slot-cost-rank-pair/paired-candidate.json": "be0322ad60f73923953f242eaffaf114ff12438e8617dae38888b77fa03184cc", + "research/slot-cost-rank-pair/profile_oracle.cpp": "d1f6b650de9fb5842b412595369271d9eeb6f54045c76c0fb5cad29854955c35", + "research/slot-cost-rank-pair/verify.py": "3c1d2eac9d3d2f13b60503deaa84e11ab2975aa84af71c8ad74584c5902b2d77" + }, + "repo": "rohanarun/integer-mult-bounds", + "scope": "Preserved immutable source and reported complete baseline profile/arithmetic for all-rank profile-cost reclamation. This package verifies its own composed words, actual paid profile and exact improvement.", + "shared_dependency_manifest": "../pr48/SOURCE.json", + "shared_dependency_manifest_sha256": "6ccc673f88d3650d75ed600b082fe2fc2866dd88a172d182a38c1d0cd27d24b3" + }, + "pr68": { + "author": "Dominik Scholz with OpenAI assistance", + "commit": "734c58e225e9d2254570c3b50296ed96943f62ea", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "d9db68e85db965bf7037d535ddc354b096b7c3b8f4cb0eb4887dc61eba5eae23", + "research/global-anchor-screen/PROOF.md": "3023c8c039acb3afc2a1e0c2ee55dcffaa4a1a2961076222ae20b03d0f3c6a38", + "research/global-anchor-screen/SOURCE.json": "f6249b8f91c7721a59ecc6d43a3f2ec65162578203bd430ef76732a3937399f3", + "research/global-anchor-screen/compiler-frozen.py": "12d646fa9ad69e4f3c532fe69080d8fe1509cde0968a6ab52a9d60273803adc0", + "research/global-anchor-screen/selected-manifest.json": "97bd86fc20fb3aee2d1adacd6a485b12e918b7340d2d3ca70e1318889e13e3a0", + "research/global-anchor-screen/selected_compile.py": "86bdfcf599c6b131e376773fe177bca57a9f63c9b60bad5de8aa00982d779b22" + }, + "repo": "DominikScholz/integer-mult-bounds", + "scope": "Preserved original pending live-carrier compiler, selected driver, proof and source provenance. This package composes the pending lifecycle and both containment checks with PR67 profile-cost selection and its own next-use scoring.", + "shared_dependency_manifest": "../pr48/SOURCE.json", + "shared_dependency_manifest_sha256": "6ccc673f88d3650d75ed600b082fe2fc2866dd88a172d182a38c1d0cd27d24b3" + }, + "split_operation": { + "author": "Rohan Garg / rohangar1 with OpenAI Codex assistance", + "commit": "641f22e52913db784f3b6ff1176b0c2945aae45b", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "f85437ee441f2a028660dd5e8dbdc0ec7b52bb55c04ea34fa4829c154bfd0ac1", + "research/split-skip/SOURCE.json": "7c2b4646a3ecfef6f881da5c43e4bd0fa9a4d1b00548b8ab458d897e16735134", + "research/split-skip/split_graph.py": "9b16ba907cbd58611fb64bfb9211be7809d54822d44c78fc6167cf4ba79eb905" + }, + "repo": "CrocSwap/integer-mult-bounds", + "scope": "Preserved original split-pair operation and attribution. These files document the adapted grouping operation; they are not imported by this producer. Actual imported source closure is PR65 plus shared PR48." + } + }, + "status": "Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-profiles-23.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-profiles-23.json new file mode 100644 index 0000000000..bf40dc76b4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-profiles-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27455,"loss":506,"rank_sum":631971,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38745,"crt_matrices":5750,"crt_disagreements":0,"blocks":[0,357148,21253,8022,5466,4156,3835,3250,2612,2109,1750,1529,1008,863,555,461,234,149,40,9,0,23,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-profiles-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-profiles-25.json new file mode 100644 index 0000000000..2f4bb6b9e9 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-profiles-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":36015,"loss":600,"rank_sum":900975,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52075,"crt_matrices":7444,"crt_disagreements":0,"blocks":[0,492698,27869,10467,7897,5674,5027,4110,3809,3047,2490,2047,1814,1443,1151,898,567,470,271,163,47,13,0,25,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-transitions-23.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-transitions-23.json new file mode 100644 index 0000000000..1a389c32fd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27455, + "frames": 59803, + "distinct_transitions": 152272, + "singles": 15939, + "rank_mass": 631971, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69190, + "2": 73632, + "3": 10224, + "4": 15382, + "5": 6461, + "6": 1593, + "7": 694, + "8": 1229, + "9": 411, + "10": 539, + "11": 98, + "12": 671, + "13": 254, + "14": 1927, + "15": 439, + "16": 440, + "17": 487, + "18": 3417, + "19": 6882, + "21": 171, + "22": 23 + }, + "word_sha256": "b0379d99fd6c10307da0d0fc526ed6171f19105a47bae61730fc3745ef60bd9e", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-transitions-25.json 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a/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-validation.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-validation.json new file mode 100644 index 0000000000..471a5bed88 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-validation.json @@ -0,0 +1,237 @@ +{ + "axes": { + "23": { + "profile": { + "R": 27455, + "blocks": [ + 0, + 357148, + 21253, + 8022, + 5466, + 4156, + 3835, + 3250, + 2612, + 2109, + 1750, + 1529, + 1008, + 863, + 555, + 461, + 234, + 149, + 40, + 9, + 0, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 5750, + "distinct_matrices": 38745, + "field_prime": 2305843009213693951, + "frames": 59803, + "h": 23, + "loss": 506, + "rank_sum": 631971, + "v": 1771 + }, + "replay": { + "elementary_xors": 162103, + "full_basis_vectors": 30997, + "h": 23, + "histogram": { + "0": 175253, + "1": 58564, + "2": 78945, + "3": 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4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "output_roles": 6925, + "rank_mass": 900975, + "roles": 36015, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 935228 + }, + "transitions": { + "R": 36015, + "copied_centers": 25, + "distinct_transitions": 212584, + "frames": 84845, + "h": 25, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 91026, + "2": 108047, + "3": 13560, + "4": 19874, + "5": 8387, + "6": 2967, + "7": 1127, + "8": 1443, + "9": 664, + "10": 791, + "11": 38, + "12": 758, + "13": 149, + "14": 681, + "15": 167, + "16": 2265, + "17": 680, + "18": 566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "rank_mass": 900975, + "singles": 20700, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 2300, + "word_sha256": "4c956749f0ec72c61875c51099afdf23e69ccea268a9b43b8d46da2ffdb24903" + } + } + }, + "bit_saving": 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and b/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-word-23.json.gz differ diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-word-25.json.gz b/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-word-25.json.gz new file mode 100644 index 0000000000..da9935d15a Binary files /dev/null and b/references/frame-compiler/pr88/references/frame-compiler/pr71/certificates/split-pair-word-25.json.gz differ diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/SOURCE.json new file mode 100644 index 0000000000..4e38e34dc8 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/SOURCE.json @@ -0,0 +1,16 @@ +{ + "files": { + "research/copied-fixed/balanced_assembly.py": "4d27575dcad2b45a281a34054d311409ecd954f373c0c3a62c29bcc843f06a86", + "research/copied-fixed/certificate.json": "33b3373c04e18a7f4cee33ba68da6ed71934acc3e0179cca6197696be4befa22", + "research/copied-fixed/changed_graph.py": "375a7ca6cac6d153c1880fd5ea5b4525e5dca9d4ee3018d24d679c219b59c5b3", + "research/copied-fixed/profiles.cpp": "b9fbd71c746609948b60c441ba4601e88436956fe636d1810f270ce4ce6a63a6", + "research/copied-fixed/verify.py": "44932182ce6c4d39776650311262ef0ac1ea9b5da7220bc0f728e2789881f84a", + "scripts/exclusion_circuit.py": "b253f9d7318becda1c1f3b24e2287ed44a9c27fcea00cf9d531afb950d0457a0", + "scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34" + }, + "head": "b7194b8586844956904b33e9fe18f0c75606c11b", + "scope": "Unmodified producer inputs for experimental frame compiler; attribution retained in each file", + "source_pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/48" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py new file mode 100644 index 0000000000..c7fd42867d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py @@ -0,0 +1,196 @@ +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit', 'complex'): + data = finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + 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"scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1", + "scripts/partial_swap/graph.py": "fd8c567759e26a10d2bad05508fd0355eb70fb116664d4e06e1858d0d8cb2ef9", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + } + }, + "status": "Conditional exact arithmetic witness; general transfer proofs are dependencies" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "PR48": { + "author": "Chafik Boukhalfa", + "commit": "b7194b8586844956904b33e9fe18f0c75606c11b", + 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Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + } + }, + "gzip_sha256": "4629d45d5074f87706db46be3aa3cd369071cd215bc6560d641115aadcce54a0", + "word_sha256": "bd0cbf73756f2e4f8d3879ec6c7a194990eb9ec40aaf3580bdded6994798d920" + }, + "25": { + "compiled": { + "h": 25, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 36586, + "baseline_pr48_roles": 48329, + "histogram": { + "1": 55478, + "0": 416276, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + }, + "rank_mass": 915250, + "elementary_xors": 205650, + "stats": { + "augmentations": 286, + "regions": 73695, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json new file mode 100644 index 0000000000..346cf87ea3 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json @@ -0,0 +1,1087 @@ +{ + "accepted_moment": { + "degree": 8, + "lower": "34287951499999999998997315662315085394575263036671/34287951500000000000000000000000000000000000000000", + "rounding_denominator": 10000000000000000000000000000000000000000, + "saving": "5103158916233/100000000000000000", + "strict_gap": "2278828040192983762647964739/77927162500000000000000000000000000000000000000", + "terms": { + "1": { + "exp_lower": "5001621630918375893019301295747281962987/5000000000000000000000000000000000000000", + "exp_upper": "10003243261836751786038602591494564437549/10000000000000000000000000000000000000000", + "log_lower": "3177185020398675220004135749131/500000000000000000000000000000", + "log_upper": "6354370040797350440008271498263/1000000000000000000000000000000", + "weight": "61988/2833715" + 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rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.", + "All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.", + "Neither global optimality nor measured practical speedup is claimed." + ], + "rejected_moment": { + "degree": 8, + "lower": "8571987875000000003683551653063012975552828889113/8571987875000000000000000000000000000000000000000", + "rounding_denominator": 10000000000000000000000000000000000000000, + "saving": "51031589162331/1000000000000000000", + "strict_gap": "-920887913265753353254538048853/2142996968750000000000000000000000000000000000000", + "terms": { + "1": { + "exp_lower": "2000648652367350369920582377063597092877/2000000000000000000000000000000000000000", + "exp_upper": "250081081545918796240072797132949649399/250000000000000000000000000000000000000", + "log_lower": "3177185020398675220004135749131/500000000000000000000000000000", + "log_upper": 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b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json new file mode 100644 index 0000000000..42958fc74b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json @@ -0,0 +1,195 @@ +{ + "artifact_sha256": { + "frame-profiles-23.json": "fec377bcf1512a427674983256b900229d4133026445b6e680c6e1e6dde5af7d", + "frame-profiles-25.json": 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orientations PASS", + "word_length": 621342 + }, + "schedule": "cover-core", + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4" + }, + "25": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 48329, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 41186, + "elementary_xors": 205977, + "h": 25, + "histogram": { + "0": 416741, + "1": 55478, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "2": 115781, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 915250, + "roles": 36586, + "stats": { + "augmentations": 286, + "clearing_xors": 2154, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "regions": 73695 + } + }, + "gzip_sha256": 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"3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "research/reordered-rank-pair/test_negative.py": "88832242e6f74e3fe08d109d4f21ff188a9ca0ae50c3e8f31da0243fe9501510", + "research/reordered-rank-pair/verify.py": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352", + "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3", + "scripts/experiments/binary_frame_profiles.cpp": "8e2e391d3ee57cbb1372c68e4aa031e1b861321536eabd642ada54e12e678669", + "scripts/experiments/binary_frame_replay.py": "392e78e62d7685c99a5888a7da743ea6c3dcad631af4a743c91e0c09348442bc", + "scripts/experiments/rank_pair_compiler.py": "9984aaccf880e4840402322d76678bfddb33ce7e494af78430a43429f51b85fd" + }, + "status": "Exact topological scheduling of unchanged PR63 graph/compiler; both physical orientations and fixed profiles checked" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json new file mode 100644 index 0000000000..3b648dbe21 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "loss": 506, + "rank_sum": 642620, + "field_prime": 2305843009213693951, + "frames": 52475, + "distinct_matrices": 36399, + "crt_matrices": 6049, + "crt_disagreements": 0, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json new file mode 100644 index 0000000000..19cc34b4ca --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json @@ -0,0 +1,40 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "loss": 600, + "rank_sum": 915250, + "field_prime": 2305843009213693951, + "frames": 73697, + "distinct_matrices": 50394, + "crt_matrices": 8127, + "crt_disagreements": 0, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json new file mode 100644 index 0000000000..2883a5f7c9 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "frames": 52475, + "distinct_transitions": 138016, + "singles": 15939, + "rank_mass": 642620, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 53320, + "2": 77409, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "21": 165, + "22": 23 + }, + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json new file mode 100644 index 0000000000..3b4bc33ff6 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json @@ -0,0 +1,35 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "frames": 73697, + "distinct_transitions": 190838, + "singles": 20700, + "rank_mass": 915250, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69278, + "2": 108881, + "3": 14362, + "4": 16908, + 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a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz new file mode 100644 index 0000000000..6a239a3e9f Binary files /dev/null and b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz differ diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + 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a/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) ++ slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();pending={};stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): +@@ -149,7 +151,8 @@ + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 +- return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) ++ endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 ++ return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} +@@ -161,6 +164,9 @@ + old,e=bb[p];row^=old;expr^=e + return expr + for s in anchors:ins(s) ++ for s,target in pending.items(): ++ if contains(blocks[frames[s]]['frame'],blocks[g]['frame']) and contains(blocks[g]['frame'],blocks[target]['frame']): ++ ins(s);stats['live_anchor_candidates']+=1 + best=None + # Inspect every eligible dependent candidate across all retired ranks. + # Rank the actual fixed-basis growth/cleanup profiles by an integer entropy score. +@@ -176,7 +182,9 @@ + if best is None or key= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and kappa > previous_kappa + bridge = json.loads((OLD/'certificate.json').read_text())['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/split-pair/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr67_commit='b3745601e947a94316bf25c2c6263d93c06e3364', + pr67_kappa=previous_kappa, ratio_pr67=kappa/previous_kappa, + absolute_gain_pr67=kappa-previous_kappa, + pr67_complete_profile_exclusion_lower=prior65_lower, + full_pr67_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected split-pair partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'split-pair-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py new file mode 100644 index 0000000000..1290ef2eb8 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py @@ -0,0 +1,275 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py new file mode 100644 index 0000000000..7908c963a4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py @@ -0,0 +1,78 @@ +#!/usr/bin/env python3 +"""Replay the aligned split-pair/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from split_pair_compose import compose, check_sources +from split_pair_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'split-pair-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='split-pair-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + 'c++', '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'split-pair-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'split-pair-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'split-pair-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'split-pair-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'split-pair-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/tests/test_split_pair.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/tests/test_split_pair.py new file mode 100644 index 0000000000..5088cff133 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/tests/test_split_pair.py @@ -0,0 +1,238 @@ +"""Physical and exact-arithmetic controls for the aligned split/pair witness.""" +from copy import deepcopy +from fractions import Fraction +from itertools import combinations +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile +import unittest +from unittest.mock import patch + +ROOT = Path(__file__).resolve().parents[1] +EXPERIMENTS = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXPERIMENTS)) +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from binary_frame_math import moment + + +class SplitPairControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.words = {h: json.loads(gzip.decompress((ROOT/f'certificates/split-pair-word-{h}.json.gz').read_bytes())) + for h in (23,25)} + + def reject_mutation(self, mutate, checker='both'): + for h, original in self.words.items(): + with self.subTest(h=h), tempfile.TemporaryDirectory() as directory: + changed = deepcopy(original) + mutate(changed) + path = Path(directory)/'word.json' + path.write_text(json.dumps(changed, separators=(',', ':'))+'\n') + with self.assertRaises((AssertionError, ValueError, IndexError, KeyError)): + if checker != 'transitions': + replay(path) + if checker != 'replay': + prepare(path, Path(directory)/'transitions.bin') + + def test_selected_words_pass_independent_replay(self): + recorded = json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + actual = replay(ROOT/f'certificates/split-pair-word-{h}.json.gz') + self.assertEqual(json.loads(json.dumps(actual)), recorded['axes'][str(h)]['replay']) + + def test_omitted_literal_xor_is_rejected(self): + self.reject_mutation(lambda word: word['ops'].pop(0)) + + def test_self_xor_is_rejected(self): + def mutate(word): + word['ops'][0][1] = word['ops'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_non_nested_operation_frame_is_rejected(self): + def mutate(word): + narrow = next(i for i,(core,cover) in enumerate(word['frames']) if core == cover) + operation = next(op for op in word['ops'] if word['frames'][op[2]][0] != word['frames'][op[2]][1]) + operation[2] = narrow + self.reject_mutation(mutate) + + def test_aliased_terminal_role_is_rejected(self): + def mutate(word): + word['outputs'][1][0] = word['outputs'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_missing_copied_center_is_rejected(self): + def mutate(word): + index = next(i for i,(_,_,_,target) in enumerate(word['outputs']) if len(target) == 1) + word['outputs'].pop(index) + self.reject_mutation(mutate) + + def test_omitted_transition_cannot_reduce_paid_profile(self): + self.reject_mutation(lambda word: word['events'].pop(0), 'transitions') + + def test_understated_physical_width_is_rejected(self): + def mutate(word): + word['R'] -= 1 + self.reject_mutation(mutate) + + def test_complete_pr67_profile_fails_new_bit_saving(self): + from split_pair_arithmetic import refine + previous = json.loads((ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/paired-candidate.json').read_text())['bit'] + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + result = refine.exact_moment(previous['m'], previous['W'], {int(t): n for t,n in previous['child_multiplicities'].items()}, Fraction(current['bit_saving'])) + self.assertGreater(result['lower'], 1) + self.assertGreater(Fraction(current['kappa']), Fraction(current['comparison']['pr67_kappa'])) + + def test_private_import_preserves_path_and_arithmetic_module(self): + import split_pair_graph as provider + import split_pair_arithmetic as arithmetic + sentinel = object() + existing = sys.modules.get('refine', sentinel) + previous_path = sys.path[:] + graph, schedule = provider._private_modules() + refine, audit = arithmetic.private_arithmetic() + self.assertIs(audit.refine, refine) + self.assertIs(sys.modules.get('refine', sentinel), existing) + self.assertEqual(sys.path, previous_path) + + def test_failed_graph_build_restores_original_providers(self): + import split_pair_graph as provider + previous_class, previous_points = provider._graph.circuit_class, provider._graph.alternating_points + with patch.object(provider._graph, 'graph', side_effect=RuntimeError('deliberate graph failure')): + with self.assertRaises(RuntimeError): + provider.graph(23) + self.assertIs(provider._graph.circuit_class, previous_class) + self.assertIs(provider._graph.alternating_points, previous_points) + + def test_failed_compilation_restores_engine_graph_and_schedule(self): + import split_pair_compiler as producer + previous_graph, previous_build = producer.compiler.graph, producer.compiler.build + missing = object() + runtime = {name:getattr(producer.compiler,name,missing) for name in ('PENDING_COST','ORACLE_EXE','ORACLE_INPUT','oracles')} + with patch.object(producer.compiler, 'compile_', side_effect=RuntimeError('deliberate compiler failure')): + with self.assertRaises(RuntimeError): + producer.compile_axis(23) + self.assertIs(producer.compiler.graph, previous_graph) + self.assertIs(producer.compiler.build, previous_build) + for name,value in runtime.items(): + self.assertIs(getattr(producer.compiler,name,missing),value) + + def test_uncertified_configurations_are_rejected(self): + import split_pair_graph as provider + wrong_anchor = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_anchor['anchor'] = False + boolean_group = deepcopy(provider.EXPECTED_CONFIGS[23]); boolean_group['groups'][0] = True + changed_schedule = deepcopy(provider.EXPECTED_CONFIGS[23]); changed_schedule['schedule'] = 'reverse-node' + for changed in (wrong_anchor, boolean_group, changed_schedule): + with self.subTest(configuration=changed), patch.object(provider.json, 'loads', return_value=changed): + with self.assertRaises(ValueError): + provider.configuration(23) + for dimension in (True, 22, 24, '23'): + with self.subTest(dimension=dimension), self.assertRaises(ValueError): + provider.configuration(dimension) + + def test_recursive_weighted_exclusions_and_contraction(self): + import split_pair_graph as provider + for h in (23,25): + block_sizes = [] + parent = provider._graph.circuit_class(h) + selected = provider.split_class(parent, provider.configuration(h)['groups']) + case = self + class Audited(selected): + def grouping(self, points): + groups = super().grouping(points) + case.assertEqual([x for group in groups for x in group], list(points)) + case.assertLess(len(groups), len(points)) + return groups + + def _block(self, points, edges, weights, level): + def expected(omitted): + values = [value for pair,value in edges.items() if not set(pair) & omitted] + values += [value for point,value in weights.items() if point not in omitted] + support = 0 + for value in values: + case.assertEqual(support & self.support[value], 0) + support |= self.support[value] + return support + total, single, pairs = super()._block(points, edges, weights, level) + case.assertEqual(self.support[total], expected(set())) + case.assertEqual(set(single), set(points)) + for a in points: + case.assertEqual(self.support[single[a]], expected({a})) + case.assertEqual(set(pairs), set(combinations(points,2))) + for a,b in combinations(points,2): + case.assertEqual(self.support[pairs[a,b]], expected({a,b})) + block_sizes.append(len(points)) + return total, single, pairs + local = Audited(h-1) + block_sizes.clear() + local.pair(list(range(h-1))) + self.assertEqual(sorted(block_sizes, reverse=True), [h-1, 12 if h==23 else 13, 7 if h==23 else 8, 5, 3, 2]) + + def test_next_fine_grid_points_and_old_assembly_controls_reject(self): + from split_pair_arithmetic import refine + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + bit = current['bit']; saving = Fraction(current['bit_saving']); kappa = Fraction(current['kappa']) + grid = Fraction(1,10**18) + rows = {int(t): n for t,n in bit['child_multiplicities'].items()} + self.assertLess(refine.exact_moment(bit['m'],bit['W'],rows,saving)['upper'], 1) + self.assertGreater(refine.exact_moment(bit['m'],bit['W'],rows,saving+grid)['lower'], 1) + for label, variant in ( + ('next_kappa', dict(kappa=kappa+grid)), + ('zero_backoff', dict(h=Fraction())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))): + call = dict(a_bit=saving, kappa=kappa, h=Fraction(1,10**12));call.update(variant) + with self.subTest(control=label), self.assertRaises(refine.balanced.InvalidAssembly): + refine.balanced.assembly(current['finite_bridge'], **call) + + def test_mass_preserving_profile_mutation_is_rejected(self): + from split_pair_compose import check_sources + profile_path = ROOT/'certificates/split-pair-profiles-23.json' + changed = json.loads(profile_path.read_text()) + before = sum(t*n for t,n in enumerate(changed['blocks'])) + changed['blocks'][2] += 3; changed['blocks'][3] -= 2 + self.assertTrue(all(n >= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'split-pair-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from split_pair_compose import check_sources + manifest_path = ROOT/'research/split-pair/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/split-pair-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import split_pair_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('split_pair_graph.py', 'split_pair_engine.py', 'split_pair_compiler.py', 'split_pair_arithmetic.py', 'split_pair_compose.py', 'verify_split_pair.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr71/tests/test_split_pair_pending.py b/references/frame-compiler/pr88/references/frame-compiler/pr71/tests/test_split_pair_pending.py new file mode 100644 index 0000000000..e6d63f72a4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr71/tests/test_split_pair_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/split_pair_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr74/FETCH.json b/references/frame-compiler/pr88/references/frame-compiler/pr74/FETCH.json new file mode 100644 index 0000000000..92196075e8 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr74/FETCH.json @@ -0,0 +1,72 @@ +{ + "pr": 74, + "commit": "3f78d8967c009153f2df5c6a6577b6ab1d37e2ca", + "files": [ + { + "path": "research/balanced-split-frames/producer.py", + "blob_sha": "8d68303a3be4ba2f15f3b54a74560c4310b0fc69", + "sha256": "ec94e4b7af370f7e921fffa3679e80d081a672dbd3ff198043edfb0dc7a9cc9d", 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Rank-first reclamation on interval-strip pair assembly, 8 October 2026 +Composition and exact profile witness: Dominik Scholz, with substantial OpenAI +GPT-6 Astra / Codex assistance. The PR #60 descending-frame-rank compiler by +Chafik Boukhalfa is reused unchanged on Avi Eisenberg's PR #62 scalar graph. +The joint frame compiler and paid reclamation are eumemic's PR #57, developed +with OpenAI Codex assistance. PR #62 records Anthropic Claude assistance. +This composition improves actual fixed-basis block profiles with unchanged +role counts; no new slot-priority rule or scalar graph is claimed. All prior +contributors, licenses, compiler arguments and conditional analytic/tape +interfaces remain credited. See research/rank-pair/PROOF.md. + +Ordered scalar frames, minimum-raise reclamation and coordinate relabeling +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. +The new finite construction and exact arithmetic certificates are in +research/ordered-frames, with an earlier parameter refinement in +research/rank-pair-refinement. These build on Dominik Scholz's PR #63 +composition, Chafik Boukhalfa's PR #60 reclamation compiler, Avi Eisenberg's +PR #62 scalar graph and eumemic's PR #57 reversible frame compiler. +Concurrent PR #65/#67 work is acknowledged in the proof. All inherited +licenses, author notices and conditional proof boundaries remain in force. + +Balanced split frames with core node ordering and coordinate relabeling +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. +This composition combines eumemic's PR69 coarse column sums, Chafik Boukhalfa's +PR71 anchored split/next-use-live compiler, and the earlier PR74 node ordering +and coordinate relabeling. Rohan Garg's PR59 split operation, Avi Eisenberg's +PR62 scalar graph, Rohan Arun's PR65/67 schedules and profile-cost selection, +Dominik Scholz's PR63/68 composition and pending controls, and eumemic's PR57 +compiler remain credited. Original source closures and notices are preserved +under references/frame-compiler/pr69 and pr71; all preceding licenses apply. +See research/balanced-split-frames/PROOF.md for the finite conditional scope. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr74/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr74/SOURCE.json new file mode 100644 index 0000000000..87bd75428a --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr74/SOURCE.json @@ -0,0 +1,19 @@ +{ + "commit": "3f78d8967c009153f2df5c6a6577b6ab1d37e2ca", + "files": { + "FETCH.json": "4aee950c461d4b46ca42d323d7a7041118ba2b1002d7a867616f3c7ea4d66c1c", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "c087c747998243c96db63203920affd28cec880b702c36017c40a3eb29947fa9", + "research/balanced-split-frames/PROOF.md": "f7a908eea56fdab2f2e8f4ce694a0132c37844ae1cb657962b6549f585bfcdfb", + "research/balanced-split-frames/README.md": "f620b1a18df2b6c0f5d179ebf50f90e630270bba90e14c0d4bff189e3056ee49", + "research/balanced-split-frames/SOURCE.json": "c933a96c636f1e22e02be6fb775a9da2cd14c11fa2d07ba75af17c7e99f00049", + "research/balanced-split-frames/certificate.json": "cec62c4ca612e458b638982056c80be8741ed634904077a5c220427e23cc3edd", + "research/balanced-split-frames/check.py": "45fb95cb2a6b0573efbe37938c149936f4aa4fff1a88425380af7bc59239b4ae", + "research/balanced-split-frames/producer.py": "ec94e4b7af370f7e921fffa3679e80d081a672dbd3ff198043edfb0dc7a9cc9d", + "research/balanced-split-frames/profile-23.json": "7f61525499f56ccc3a183a2741ef823cce30423475fa586ba7d36610b5b66844", + "research/balanced-split-frames/profile-25.json": "9b4d0647e3667af963c164c048c6ea750d90397b046336ede5a5b6902a9f6473", + "research/balanced-split-frames/selection.json": "cbc616540af0ff5b63a90a920c70acd660fbb67052e4dc19889fe0443f2129f4" + }, + "pr": 74, + "scope": "Exact attributed contributor inputs and reported comparison certificate, not a new audit of the entire foreign claim." +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/PROOF.md b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/PROOF.md new file mode 100644 index 0000000000..7244811413 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/PROOF.md @@ -0,0 +1,145 @@ +# A paid composition of balanced coarse sums, split recursion and frame order + +## Statement and boundary + +The complete finite profile below certifies + +`kappa = 10366199626713/200000000000000000` + +for the inherited conditional bound `T(n)=O(n(log n)^(1-kappa))`. +The all-size compiler, analytic transfer, fixed-alphabet tape simulation, +precision, routing, prime selection and exact recovery hypotheses are inherited. +Finite source checks and arithmetic do not establish those general hypotheses. + +## 1. Pinned ingredients + +PR #71 is frozen at `1bef94fd40a746452548c84a4a8f8834670a3113` in +`references/frame-compiler/pr71/`, including its complete consumed source +closure, selected words, data interfaces, licenses, notices and root documents. +Its own source manifest is preserved without re-pinning. PR #69's original +coarse-sum compiler and notices are frozen at +`91aa1f17e6e3fc063241686a41a34ddd0dc24c50` in the adjacent `pr69/` archive. + +The new producer reads PR #69's literal BEFORE/AFTER replacement, applies it +exactly once to the archived PR #62 scalar graph consumed by PR #71, and keeps +PR #71's `[1,1,2]` split choices and lowest-intact-pair anchoring. The original +source files are unchanged. After reordering, it uses the archived PR #71 +compiler and its next-use profile-cost selection unchanged. + +## 2. Shared intermediate sums preserve the scalar map + +For two disjoint groups A and B, replace the chain forming +`sum_{a in A,b in B} e(a,b)` by +`sum_{b in B} (sum_{a in A} e(a,b))`. +Each operand support occurs exactly once. The nested sums are disjoint, +so this is an equality over the inherited scalar field. Existing node +interning shares the column intermediates with later strip computations. +The singleton cases and strictly decreasing recursive partitions retain the +same identity. No negative coefficient or cancellation is introduced. + +`graph_audit.py` reconstructs dense global triple-coordinate supports using +its own recurrence. For each dimension it checks every input, addition, +core, cover and prescribed output, and compares the complete output support +inventory with original PR #71. This checks 67,460 / 94,993 additions and +5,336 / 6,925 outputs. Original PR #71 has 68,771 / 96,718 additions. + +## 3. Legal node order and fully charged live reclamation + +Keep source IDs fixed. Group remaining active nodes by their original +(core, cover), retaining their original order within each group. Sort groups +lexicographically by + +`(popcount(cover)-popcount(core), -core, cover, first_original_node)`. + +Remap every operand and output ID, clear support caches indexed by old IDs, +and verify again. The independent audit proves that each literal edge and +output is preserved, every operand precedes its consumer, every envelope is +unchanged, and this is exactly the selected renumbering. Matching is recomputed +on the resulting graph and the compiler uses its natural region order. + +PR #71's unchanged pending live controls enter a clearing basis only when +their current frame is contained in the present frame and that frame is +contained in their next-use frame. Controls retain their values. The complete +word contains every chosen clearing XOR and every required frame raise. +The discovery score is never substituted for the actual charged profile. + +Both complete words are regenerated with dirty-basis checks enabled. A +separate serialized-word checker replays every input and arbitrary dirty +basis column in both orientations. The final roles are 27,136 / 35,744. + +## 4. Coordinate relabeling and the data family + +Apply each selected permutation to the frame core/cover masks, source-triple +indices, scatter target-triple indices, output common points and output +triples. Literal XORs, scratch IDs and frame IDs remain unchanged. The complete +permutations are frozen in `selection.json`; both relabeled words are replayed. + +For permutation matrix P, both fixed bases `I+J` and the inverse metric +`I-J/9` commute with P. Envelope projectors therefore transform by conjugation. +Containment and every legal incidence remain valid. Ordered contiguous child +profiles can change, and every one is regenerated from the literal word +using the inherited exact bounded-minor/CRT profiler, with zero disagreements. + +Each coordinate permutation induces a bijection on the complete triple set. +Consequently the complete two-axis data-block family is only reindexed: its +aggregate inherited profile and rational recovery cases remain valid. Copied +centers, endpoints and data growth remain explicitly charged. + +## 5. Complete recurrence and assembly + +Let `N=4073300`, `m=575`, and let `R_h` and `b_{h,t}` be the verified role count +and exact internal profile. The physical width is + +`W = 2N + (N/1771)R_23 + (N/2300)R_25 = 133862024`. + +The complete child multiset includes: + +- data: `18N` children of size 1 and `2N` each of sizes 21, 17 and 481; +- paid endpoint copies: `N` additional size-1 children; +- internal axis h: `(N/binom(h,3))*b_{h,t}` children of size t; +- exterior axis h: `(N/binom(h,3))*R_h` each of sizes h and `m-2h`; +- data growth per axis: `2N` each of sizes 1 and `h-2`. + +The total rank is `76968816900 = mW-1846900`; maximum child size is 529. +The exact characteristic is +`M(a)=sum_t (t*n_t/(mW))*exp(a*log(m/t))`. +At `a=25916842362591/500000000000000000`, a rigorous upper bound is below 1. +At `a+10^-18`, a rigorous lower bound is above 1. Positive logarithms make +the characteristic increasing. The complete original PR #71 profile is +separately excluded at the new accepted saving. + +Production arithmetic uses the retained rational logarithm/exponential +helper. The independent checker derives the complete paid multiset and uses +40 exact atanh terms for logarithms and Taylor degree 10 with a geometric +exponential tail. It imports no production arithmetic and checks each of the +47 assembly slacks and seven margins independently. The next kappa grid value +is rejected. Negative controls reject omitted paid children, fabricated slacks +and incorrect source hashes. + +Use positive backoff `10^-18`. Since W is below `2^27`, its `bit_length()` is +27. The product-row coefficient becomes `9*27+20*30=843`. Keeping degree 2000 +and suffix slope 8000 gives degree gap `2000-(51/25)*843=7007/25`. +These values are derived and checked; no stale predecessor constants remain. +Arithmetic cutoff bounds are not complete operational runtime thresholds. + +## Credits + +The composition, core-order continuation, coordinate choices, packaging and +independent audits were prepared for Thomas DiFiore with substantial OpenAI +Codex assistance. Coarse-sum reassociation is eumemic's PR #69. Anchored split +frames and next-use-aware live selection are Chafik Boukhalfa's PR #71. +Rohan Garg supplied the split operation (#59); Avi Eisenberg supplied interval +strips and core-aware pair assembly (#62); Rohan Arun supplied region schedules +and profile-cost selection (#65/#67); Dominik Scholz supplied ranked composition +and pending live controls (#63/#68); eumemic supplied the reversible compiler +and physical/profile checking interfaces (#57). Our earlier PR #74 supplied the +core node ordering and coordinate-relabeling continuation used here. + +The preserved archives retain all earlier credits, including RaD/hipotures, +icekylinx, James Chang, Zhihao Chen, Aurel Prosz, Swapnil Jain, Alejandro Zarzuelo +Urdiales, Douglas Colkitt, OpenAI and Harvey–van der Hoeven, and predecessor +AI-assistance disclosures. No predecessor authorship or endorsement of this +composition is implied. Existing licenses and notices remain in force. + +Concurrent PR #75–#79 contributions, including carry exchanges, balanced split +constructions and coordinate flags, are acknowledged. No priority claim is made. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/README.md new file mode 100644 index 0000000000..5784b8b928 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/README.md @@ -0,0 +1,70 @@ +# Balanced split frames with shared sums and reusable live controls + +**κ = 10366199626713 / 200000000000000000 = 0.000051830998133565** + +The conditional bound is `T(n) = O(n (log n)^(1-kappa))`. +This is **0.9788258% above our original PR #74 result**, **0.8097927% above +pinned PR #71**, and **0.8082664% above PR #75's claim observed on 8 October +2026**. The later PR #79 claim `5.1745625472866e-5`, observed at 19:55 UTC on the same +date, is also below this result by **0.1649853%**. These compare asymptotic exponent savings; they are not measured +multiplication speedups. + +| Quantity | Original PR #74 | Pinned PR #71 | This composition | +| --- | ---: | ---: | ---: | +| h23 auxiliary roles | 27,698 | 27,455 | 27,136 | +| h25 auxiliary roles | 36,310 | 36,015 | 35,744 | +| Physical width | 136,157,010 | 135,075,665 | 133,862,024 | +| Conditional κ | 5.132858076595e-5 | 5.1414646104039e-5 | 5.1830998133565e-5 | + +## Construction + +Compose eumemic's PR #69 column-balanced coarse sums with Chafik Boukhalfa's +PR #71 anchored split recursion and next-use-aware live reclamation. Apply +our original-envelope node order before carrier matching, then relabel the +geometric coordinates and recompute the actual fixed-basis profiles. + +The balanced graph has 67,460 / 94,993 active additions, compared with +PR #71's 68,771 / 96,718. Every prescribed output is unchanged. The complete +physical words pay for all XORs, frame raises, copied centers and data blocks. +The width now lies below `2^27`; its role-logarithm and product-row constants +are recomputed in the exact certificate. + +## Evidence and reproduction + +- [Proof, scope and contributor credits](PROOF.md) +- [Exact certificate](certificate.json) +- [Selected graph and coordinate choices](selection.json) +- [Immutable source manifest](SOURCE.json) +- [Independent dense scalar audit](graph-audit.json) +- [Independent exact arithmetic audit](independent-audit.json) +- [Verification receipt](validation.json) and [raw log](verification.log) + +Use Python 3.11 or newer and a C++17 compiler with unsigned 128-bit support: + +```sh +make balanced-split-frames-verify +``` + +This regenerates both words from pinned sources, checks their selected raw +hashes, audits the complete scalar graph, independently replays every input +and dirty basis vector in both orientations, reconstructs every literal frame +transition and exact profile, and checks the full paid recurrence and assembly. +The two replay dimensions contain 30,678 / 40,344 basis coordinates. +Both profiles have zero CRT disagreements. Independent arithmetic verifies +all 47 strict inequalities, seven margins, adjacent-grid rejection, and +exclusion of the complete pinned PR #71 profile at the new bit saving. + +The earlier full-suite receipt in `../ordered-frames/validation.json` covers +that historical source state. Current upstream checks and formal packages +remain separate CI jobs. The new source archives retain original notices +and original root documentation so predecessor pins remain unchanged. + +All inherited analytic, all-size compiler, fixed-tape, precision, routing, +prime-selection and recovery hypotheses remain assumed. This is a verified +finite conditional witness, with no global-optimality or practical-speed claim. + +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. Original +PR #74 remains available in `../ordered-frames/`; all predecessor credits and +licenses remain applicable. + +Concurrent PR #75–#79 work is acknowledged; no priority claim is made. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/SOURCE.json new file mode 100644 index 0000000000..06404d9283 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/SOURCE.json @@ -0,0 +1,21 @@ +{ + "files": { + "references/frame-compiler/pr69/SOURCE.json": "928fa8cce0964a6894af3f40cbde6d983aac395336e5277f751c9cbf1b07957f", + "references/frame-compiler/pr71/SOURCE.json": "1c79309362044dd386f72946ccb2e258e98d07d7239ea89d8a8646338d24228a", + "research/balanced-split-frames/check.py": "45fb95cb2a6b0573efbe37938c149936f4aa4fff1a88425380af7bc59239b4ae", + "research/balanced-split-frames/graph_audit.py": "b95cf9269fbcaf7f7b9732b28d7a8b790feefc262e86a36de33a92ab7906a8b3", + "research/balanced-split-frames/independent_check.py": "02dd998ebe68f111a42657e1591416b28b618a8d58bbd4fb0686d3afd929db1a", + "research/balanced-split-frames/producer.py": "ec94e4b7af370f7e921fffa3679e80d081a672dbd3ff198043edfb0dc7a9cc9d", + "research/balanced-split-frames/profile-23.json": "7f61525499f56ccc3a183a2741ef823cce30423475fa586ba7d36610b5b66844", + "research/balanced-split-frames/profile-25.json": "9b4d0647e3667af963c164c048c6ea750d90397b046336ede5a5b6902a9f6473", + "research/balanced-split-frames/selection.json": "cbc616540af0ff5b63a90a920c70acd660fbb67052e4dc19889fe0443f2129f4", + "research/balanced-split-frames/transitions-23.json": "0e9b6bbb1f9f08b34077bb93a60b39c2d61cf8f1329c884fd47326bf32bfac60", + "research/balanced-split-frames/transitions-25.json": "3bffd56836edefb309825f4ba303dc27ae88455aa7c8fc918af3ef24d82caee3", + "research/balanced-split-frames/word-23.json.gz": "956b886339ccbd3d599c5e0ec403b870958d052f3442067e8f12a56318e9525d", + "research/balanced-split-frames/word-25.json.gz": "ea090af1c4b56b7dae31d1f0d3fece4417677160f07c372e0455d7f8ac31c7b0", + "research/rank-pair-refinement/refine.py": "a19a79ea064fe66cb5f4e2971d6ab277cdfd452975c539e23066174533430691" + }, + "pr69_commit": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "pr71_commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "scope": "Selected sources and finite inputs. The archived PR69 and PR71 manifests bind the complete inherited source closure; generated axis receipts and arithmetic/audit certificates are checked outputs." +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/certificate.json new file mode 100644 index 0000000000..6a3cfa48df --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/certificate.json @@ -0,0 +1,740 @@ +{ + "W": 133862024, + "accepted": { + "lower": "99999999999999999979924873504956311258242134978917/100000000000000000000000000000000000000000000000000", + "strict_gap": "20075126495043683558076755370663/100000000000000000000000000000000000000000000000000", + "terms": { + "1": { + "lower": "578243869104998674370968149468068831065643870861/25000000000000000000000000000000000000000000000000", + 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python3 +"""Screen complete paid profiles from independently replayed axis constructions.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions required') +from pathlib import Path +from collections import Counter +from fractions import Fraction as Q +import importlib.util,argparse,json,subprocess,tempfile,hashlib,os,shlex +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +from producer import check_sources +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m +exact=load('candidate_exact',ROOT/'research/rank-pair-refinement/refine.py') +balanced=load('candidate_assembly',DEP/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') + +def profile(path): + v=json.loads(Path(path).read_text()) + return v['profile'] if 'profile' in v else v + +def calculate(first,second): + profiles=[profile(first),profile(second)] + N=4073300;m=575 + assert [p['h'] for p in profiles]==[23,25] + W=2*N+sum(N//p['v']*p['R'] for p in profiles) + parts={'data':Counter({1:18*N,21:2*N,17:2*N,481:2*N}),'endpoint_copy':Counter({1:N})} + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 + assert p['rank_sum']==h*p['R']+p['loss']==sum(t*n for t,n in enumerate(p['blocks'])) + assert p['loss']==h*(h-1) + parts[f'internal_{h}']=Counter({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + parts[f'exterior_{h}']=Counter({h:bank,m-2*h:bank}) + parts[f'growth_{h}']=Counter({1:2*N,h-2:2*N}) + rows=sum(parts.values(),Counter());assert sum(t*n for t,n in rows.items())==m*W-1846900 + lo,hi,grid=1,71700000000000,10**18 + while lo+11 + result.update(status='Verified finite conditional witness; inherited all-size transfer remains assumed', + source_manifest_sha256=hashlib.sha256((HERE/'SOURCE.json').read_bytes()).hexdigest(), + axes=axes,eventual_bounds=balanced.cutoffs(result['finite_bridge'],result['assembly']), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113',pr71_kappa=Q(previous['kappa']), + relative_gain_pr71=result['kappa']/Q(previous['kappa'])-1, + pr71_complete_profile_exclusion_lower=old_lower)) + result=arithmetic.js(result) + path=HERE/'certificate.json' + if record:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:assert result==json.loads(path.read_text()) + print('PASS exact moment, next-grid exclusions, 47 inequalities and seven margins',flush=True) + return result + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--record',action='store_true');args=parser.parse_args();generate(args.record) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/producer.py b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/producer.py new file mode 100644 index 0000000000..8d68303a3b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/producer.py @@ -0,0 +1,132 @@ +#!/usr/bin/env python3 +"""Balanced coarse sums + anchored split/live frames + core ordering and coordinates. + +Composition for Thomas DiFiore with OpenAI Codex assistance. Apache-2.0. +PR69 coarse sums: eumemic. PR71 split/live composition: Chafik Boukhalfa. +Graph: Avi Eisenberg PR62; split operation: Rohan Garg PR59; reclamation: +Rohan Arun PR65/67, Dominik Scholz PR63/68, eumemic PR57. Original notices +and exact sources are retained under references/frame-compiler/pr69 and pr71. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +from hashlib import sha256 +import argparse,ast,gzip,importlib.util,json,types +from concurrent.futures import ProcessPoolExecutor +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +import split_pair_graph as provider +import split_pair_compiler as ancestor +from binary_frame_replay import replay + + +def check_sources(): + for folder in (DEP,ROOT/'references/frame-compiler/pr69'): + manifest=json.loads((folder/'SOURCE.json').read_text()) + for name,digest in manifest['files'].items(): + assert sha256((folder/name).read_bytes()).hexdigest()==digest,name + manifest=json.loads((HERE/'SOURCE.json').read_text()) + required={str((HERE/name).relative_to(ROOT)) for name in ('producer.py','check.py','graph_audit.py','independent_check.py','selection.json')} + assert required <= set(manifest['files']), 'Incomplete selected source closure' + for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + + +def reorder(c): + groups={} + for x in sorted(c.active): + if c.args[x]: groups.setdefault((c.core[x],c.union[x]),[]).append(x) + def key(item): + (core,cover),nodes=item + return cover.bit_count()-core.bit_count(),-core,cover,min(nodes) + ids=list(range(len(c.inputs)+1))+[x for _,nodes in sorted(groups.items(),key=key) for x in nodes] + mapping={x:i for i,x in enumerate(ids)} + args,core,cover,provenance=c.args,c.core,c.union,c.provenance + c.args=[tuple(mapping[y] for y in args[x]) if args[x] else None for x in ids] + c.core=[core[x] for x in ids];c.union=[cover[x] for x in ids] + c.provenance=[provenance[x] for x in ids] + c.active={mapping[x] for x in c.active};c.outputs={k:mapping[v] for k,v in c.outputs.items()} + c.support_in.cache_clear() + c.verify() + return c + + +def graph(h,ordered=True): + source=Path(provider._graph.__file__).read_text() + original=ROOT/'references/frame-compiler/pr69/scripts/experiments/balanced_coarse_compiler.py' + replacements={} + for node in ast.parse(original.read_text()).body: + if isinstance(node,ast.Assign): + for target in node.targets: + if isinstance(target,ast.Name) and target.id in ('BEFORE','AFTER'): + replacements[target.id]=ast.literal_eval(node.value) + assert source.count(replacements['BEFORE'])==1 + module=types.ModuleType('balanced_split_private_graph');module.__file__=provider._graph.__file__ + exec(compile(source.replace(replacements['BEFORE'],replacements['AFTER']),module.__file__+':balanced-coarse','exec'),module.__dict__) + previous=provider._graph + try: + provider._graph=module + c=provider.graph(h) + finally: + provider._graph=previous + return reorder(c) if ordered else c + + +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + +def compile_axis(h): + check_sources() + config=json.loads((HERE/'selection.json').read_text())['axes'][str(h)] + previous_graph,previous_order=provider.graph,provider.ordered_build + # graph() calls the original provider; keep that callable private while + # the inherited driver resolves the selected composed graph dynamically. + original_graph=previous_graph + def selected_graph(dimension): + provider.graph=original_graph + try:return graph(dimension) + finally:provider.graph=selected_graph + try: + provider.graph=selected_graph + provider.ordered_build=lambda original,dimension:original + compiled,word=ancestor.compile_axis(h) + finally: + provider.graph,provider.ordered_build=previous_graph,previous_order + compiled['graph_configuration']=config + word=relabel(word,config['coordinate_permutation']) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + path=HERE/f'word-{h}.json.gz' + with path.open('wb') as stream: + with gzip.GzipFile(filename='',fileobj=stream,mode='wb',mtime=0) as archive:archive.write(raw) + receipt=replay(path) + assert sha256(raw).hexdigest()==config['expected_word_sha256'] + axis=dict(configuration=config,compiled=compiled,replay=receipt, + word_sha256=sha256(raw).hexdigest(),gzip_sha256=sha256(path.read_bytes()).hexdigest()) + (HERE/f'axis-{h}.json').write_text(json.dumps(axis,indent=2)+'\n') + print(f'PASS fresh balanced/split/core word h={h}, roles={receipt["roles"]}',flush=True) + + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--h',type=int,choices=(23,25));args=parser.parse_args() + if args.h:compile_axis(args.h) + else: + with ProcessPoolExecutor(max_workers=2) as pool:list(pool.map(compile_axis,(23,25))) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/profile-23.json b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/profile-23.json new file mode 100644 index 0000000000..013f4e59c7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/profile-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27136,"loss":506,"rank_sum":624634,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38292,"crt_matrices":5488,"crt_disagreements":0,"blocks":[0,355721,21666,6948,6524,3093,4314,2400,3266,1501,2094,1008,1374,586,732,353,307,139,62,16,0,23,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/profile-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/profile-25.json new file mode 100644 index 0000000000..1e3b6b89aa --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/profile-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35744,"loss":600,"rank_sum":894200,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52202,"crt_matrices":7623,"crt_disagreements":0,"blocks":[0,490052,26188,13531,7191,4637,5355,4229,3705,2610,2620,2080,1814,1357,1070,868,612,463,233,56,141,0,71,25,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/selection.json b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/selection.json new file mode 100644 index 0000000000..57cf3b6b65 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr74/research/balanced-split-frames/selection.json @@ -0,0 +1,86 @@ +{ + "source_pr71": "1bef94fd40a746452548c84a4a8f8834670a3113", + "source_pr69": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "axes": { + "23": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 22, + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 20, + 19, + 21 + ], + "expected_word_sha256": "8dc6696a274e70ca0af3fc49c4bdede362adaedc8dc322f335e3dab499f1ed48" + }, + "25": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 2, + 1, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "expected_word_sha256": "2c923afe366219ee3fffc9db063c91e44cdf7cbbdb62246b8e6a297dc440b577" + } + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr78/FETCH.json b/references/frame-compiler/pr88/references/frame-compiler/pr78/FETCH.json new file mode 100644 index 0000000000..4db82db4a1 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr78/FETCH.json @@ -0,0 +1,48 @@ +{ + "pr": 78, + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf", + "files": [ + { + "path": "research/coordinate-flags/verify.py", + "blob_sha": "216ccd3d58c1331fffdb008df7547982cb43d2ae", + "sha256": "b59a5345c8684bb67a5ea666d5de11422c45cdf19f2c13de1520623a71bae7e1", + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf" + }, + { + "path": "research/coordinate-flags/order-23.json", + "blob_sha": "035f01df59be3312e30ec692754d3a331a766799", + "sha256": "def92cd69f3fba2986c7a230ece45f9eb63fd38fef512d055bf0adffe9edfa82", + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf" + }, + { + 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Coordinate-flag relabeling and finite verification: Rohan Arun with OpenAI Codex assistance. Based on Chafik Boukhalfa PR71 and the inherited contributions credited in research/coordinate-flags/README.md. Existing contributor originals are preserved. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr78/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr78/SOURCE.json new file mode 100644 index 0000000000..15f08e2813 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr78/SOURCE.json @@ -0,0 +1,15 @@ +{ + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf", + "files": { + "FETCH.json": "79d6b40af23f03d6737be9a072ebca4f96aa6a663895cffdee4052432b5d13b8", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "0a0e0314b9d1e23a193e92aa633fc50c432b6e3ea326f40d5cbb1ea538823149", + "research/coordinate-flags/README.md": "cbc4f20613e1dfafcce7c5f82c274fdd48898cc968d14fbea7bf9b1a47607e85", + "research/coordinate-flags/SOURCE.json": "c0ec88783c06431d95e1e8efabbb2928857f1d4ca8d0ada10206e99322ae78e2", + "research/coordinate-flags/order-23.json": "def92cd69f3fba2986c7a230ece45f9eb63fd38fef512d055bf0adffe9edfa82", + "research/coordinate-flags/order-25.json": "209dee5fac04fa91a5bf63ed0307a56e849cc6800fa543254590045e0c95d6a5", + "research/coordinate-flags/verify.py": "b59a5345c8684bb67a5ea666d5de11422c45cdf19f2c13de1520623a71bae7e1" + }, + "pr": 78, + "scope": "Exact attributed contributor inputs and reported comparison certificate, not a new audit of the entire foreign claim." +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr78/research/coordinate-flags/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr78/research/coordinate-flags/README.md new file mode 100644 index 0000000000..950f4eaa2d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr78/research/coordinate-flags/README.md @@ -0,0 +1,68 @@ +# Coordinate flags for the split-pair witness + +This finite conditional witness gives kappa = 12857195906507 / 250000000000000000 += 5.1428783626028e-5, about 0.02750% above PR71's 5.1414646104039e-5. +The bit saving is 25715714341 / 500000000000000. Roles, physical width, +recursive rank mass, scalar operations, paid clearing and copied endpoints +remain those of PR71. The changed object is the coordinate flag used to +decompose internal frame transitions into consecutive pivot blocks. + +## General relabeling argument + +Let P be a permutation matrix on the h coordinates. It commutes with J, +so P commutes with the fixed basis L = I+J and preserves the form I-J/9. +For a core/cover frame F(C,U), the relabeled projector is +P F(C,U) P^-1 = F(P C,P U). Consequently, every frame inclusion, rank, +nondegeneracy condition, projector denominator bound and elementary role +operation is preserved. The existing exact CRT bounds apply unchanged. + +Relabel each input triple T to P T, each output (c,T) to (P c,P T), +each frame mask by P, and each scatter row by the induced triple permutation. +The role slots and literal XOR operations do not change. This conjugates +the complete linear word by the input/output permutation and therefore +preserves its identity on every ordinary input and arbitrary dirty role. +The verifier independently replays that identity in both orientations. + +The data component sums over every pair of source triples. Independent +coordinate permutations on the two axes induce a bijection on that complete +Cartesian product. Hence its existing complete histogram, copied-center +costs and endpoint corrections are unchanged. This argument uses the full +case set; it would not justify retaining a selected subset's histogram. + +North-east corner rank profiles depend on the fixed coordinate order. +Conjugating by P can change which adjacent pivots form a recursive block, +even though total rank is unchanged. We regenerate these profiles from the +actual relabeled words rather than assuming their costs are invariant. +Both dimensions use the selected orders in order-23.json and order-25.json. + +## Verification and scope + +Run `make coordinate-flags-verify`. It checks source closure, regenerates +both words byte for byte, replays every ordinary and dirty basis vector in +both orientations, reconstructs physical transitions, and recomputes all +fixed-I+J profiles with the inherited exact CRT bounds. Six negative controls +reject inconsistent coordinates, missing source/output relabeling, missing +operations and aliased terminal roles. + +The complete paid child list is rebuilt independently. Directed rational +moment bounds, an independent logarithm/exponential computation, 47 strict +constraints, seven margins, both next-grid rejections and exclusion of +PR71's complete profile at the new saving are checked. + +The search used structured coordinate orders and bounded adjacent swaps. +No global optimum or practical speedup is claimed. This remains conditional +on the inherited all-size residual compiler, routing, recovery, prime +selection, fixed finite-alphabet multitape simulation and analytic transfer. +The full expanded repository rerun is pending; this package is a draft. + +## Credit + +Chafik Boukhalfa's PR71 supplies the split-pair graph and next-use scoring. +Rohan Garg introduced the split operation (PR59); Avi Eisenberg supplied +interval/pair assembly (PR62); Dominik Scholz supplied ranked frames and +pending controls (PR63/68); Rohan Arun supplied schedule and profile-cost +search (PR65/67); eumemic supplied the reversible compiler and physical +checkers (PR57). Credit also icekylinx, James Chang, Zhihao Chen, Aurel +Prosz/Paureel, Swapnil Jain, Alejandro Zarzuelo Urdiales, RaD/hipotures, +Douglas Colkitt, OpenAI and all inherited contributors. Existing sources, +licenses and notices are retained. 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b/references/frame-compiler/pr88/references/frame-compiler/pr78/research/coordinate-flags/order-23.json @@ -0,0 +1,53 @@ +{ + "h": 23, + "order": [ + 1, + 3, + 2, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 21, + 20, + 22, + 0 + ], + "mapping": { + "1": 0, + "3": 1, + "2": 2, + "4": 3, + "5": 4, + "6": 5, + "7": 6, + "8": 7, + "9": 8, + "10": 9, + "11": 10, + "12": 11, + "13": 12, + "14": 13, + "15": 14, + "16": 15, + "17": 16, + "18": 17, + "19": 18, + "21": 19, + "20": 20, + "22": 21, + "0": 22 + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr78/research/coordinate-flags/order-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr78/research/coordinate-flags/order-25.json new file mode 100644 index 0000000000..7c06a68e6e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr78/research/coordinate-flags/order-25.json @@ -0,0 +1,57 @@ +{ + "h": 25, + "order": [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 23, + 22, + 24, + 0 + ], + "mapping": { + "1": 0, + "2": 1, + "3": 2, + "4": 3, + "5": 4, + "6": 5, + "7": 6, + "8": 7, + "9": 8, + "10": 9, + "11": 10, + "12": 11, + "13": 12, + "14": 13, + "15": 14, + "16": 15, + "17": 16, + "18": 17, + "19": 18, + "20": 19, + "21": 20, + "23": 21, + "22": 22, + "24": 23, + "0": 24 + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr78/research/coordinate-flags/verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr78/research/coordinate-flags/verify.py new file mode 100644 index 0000000000..216ccd3d58 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr78/research/coordinate-flags/verify.py @@ -0,0 +1,89 @@ +"""Rebuild the coordinate-permuted PR71 words and their exact paid bound.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2];HERE=Path(__file__).resolve().parent +sys.path.insert(0,str(ROOT/'scripts/experiments')) +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +from split_pair_arithmetic import refine,audit +import binary_frame_math as arithmetic +from pin_split_pair_sources import required_paths +from fractions import Fraction as Q +from collections import Counter +from itertools import combinations +from math import comb +from hashlib import sha256 +import gzip,json,subprocess,tempfile + +def required(): + names=required_paths()|{'research/split-pair/SOURCE.json','certificates/split-pair-kappa.json', + '.github/workflows/verify.yml'} + names.update(str(p.relative_to(ROOT)) for p in HERE.iterdir() if p.is_file() and p.name not in ('SOURCE.json','validation.json')) + return names + +def sources(): + manifest=json.loads((HERE/'SOURCE.json').read_text()) + assert required()<=set(manifest['files']),'Source closure incomplete' + for name,digest in manifest['files'].items():assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + +def relabel(word,config): + h=word['h'];order=config['order'];assert sorted(order)==list(range(h)) + perm={old:new for new,old in enumerate(order)} + assert perm=={int(k):v for k,v in config['mapping'].items()} + triples=list(combinations(range(h),3));lookup={t:i for i,t in enumerate(triples)} + index={i:lookup[tuple(sorted(perm[x] for x in triple))] for i,triple in enumerate(triples)} + def mask(m):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(index[int(i)]):s for i,s in word['sources'].items()} + v=word['v'];word['scatter']=[[v+index[a-v],b] for a,b in word['scatter']] + word['outputs']=[[s,g,perm[c],sorted(perm[x] for x in triple)] for s,g,c,triple in word['outputs']] + return word + +def exact(profiles): + cert=json.loads((HERE/'certificate.json').read_text());baseline=json.loads((HERE/'baseline-pr71.json').read_text()) + N=comb(23,3)*comb(25,3);m=575;W=2*N+sum(N//p['v']*p['R'] for p in profiles) + L=sum(N//p['v']*p['loss'] for p in profiles) + rows=Counter({1:19*N,21:2*N,17:2*N,481:2*N}) + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 and p['v']==comb(h,3) + assert sum(t*n for t,n in enumerate(p['blocks']))==h*p['R']+h*(h-1)==p['rank_sum'] + rows.update({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + rows[h]+=bank;rows[m-2*h]+=bank;rows[1]+=2*N;rows[h-2]+=2*N + bit=dict(m=m,N=N,W=W,L=L,total_rank=sum(t*n for t,n in rows.items()),child_multiplicities=dict(sorted(rows.items()))) + assert bit['total_rank']==m*W-N+L + assert arithmetic.js(bit)==cert['bit'] + saving=Q(cert['bit_saving']);moment=refine.exact_moment(m,W,rows,saving) + rejected=refine.exact_moment(m,W,rows,saving+Q(1,10**18)) + assert moment['upper']<11 + print('PASS exact conditional kappa',result['kappa'],'47 constraints, seven margins, independent bounds and next-grid controls') + +def verify(): + sources();profiles=[] + with tempfile.TemporaryDirectory(prefix='coordinate-flags-') as directory: + work=Path(directory);exe=work/'profiles' + subprocess.run(['c++','-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'scripts/experiments/binary_frame_profiles.cpp'),'-o',str(exe)],check=True) + for h in (23,25): + original=json.loads(gzip.decompress((ROOT/f'certificates/split-pair-word-{h}.json.gz').read_bytes())) + config=json.loads((HERE/f'order-{h}.json').read_text());word=relabel(original,config) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + assert raw==gzip.decompress((HERE/f'word-{h}.json.gz').read_bytes()) + path=work/f'word-{h}.json';path.write_bytes(raw);checked=replay(path) + stored=json.loads((HERE/f'replay-{h}.json').read_text());assert arithmetic.js(checked)==stored['replay'] + trans=work/f'transitions-{h}.bin';receipt=prepare(path,trans);assert arithmetic.js(receipt)==stored['transitions'] + subprocess.run([str(exe),str(trans)],check=True) + profile=json.loads(Path(str(trans)+'.profiles.json').read_text());assert profile==json.loads((HERE/f'profiles-{h}.json').read_text()) + profiles.append(profile);print('PASS complete relabelled physical word and profile',h,flush=True) + exact(profiles) +if __name__=='__main__':verify() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/.gitattributes b/references/frame-compiler/pr88/references/frame-compiler/pr79/.gitattributes new file mode 100644 index 0000000000..48ba61f217 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/.gitattributes @@ -0,0 +1,15 @@ +* text=auto eol=lf +*.pdf binary +# Unified diffs require a leading space on blank context lines. +*.patch -whitespace +# Preserve the exact upstream bytes, including original whitespace. +upstream/** -whitespace +# Preserve the exact pinned third-party proof snapshots and notices. +references/copied-centers/pr29/** -whitespace +references/copied-centers/pr33/** -whitespace +references/semantic-bulk/** -whitespace + +# Immutable contributor archives retain original CRLF and whitespace bytes. +references/frame-compiler/pr69/** -text -whitespace +references/frame-compiler/pr70/** -text -whitespace +references/frame-compiler/pr71/** -text -whitespace diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/.github/workflows/verify.yml b/references/frame-compiler/pr88/references/frame-compiler/pr79/.github/workflows/verify.yml new file mode 100644 index 0000000000..33886a2cdf --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/.github/workflows/verify.yml @@ -0,0 +1,63 @@ +name: Verify research artifacts + +on: + push: + pull_request: + workflow_dispatch: + +permissions: + contents: read + +jobs: + verify: + runs-on: ubuntu-24.04 + timeout-minutes: 20 + strategy: + fail-fast: false + matrix: + python-version: ['3.11', '3.13', '3.14'] + group: [community, producers, certificates, ternary, research, tests, strips, clones, positive, joint, pair, balanced] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: ${{ matrix.python-version }} + - name: Install headers for the exact enlarged-frame profiler + if: matrix.group == 'positive' + run: | + if ! test -f /usr/include/boost/multiprecision/cpp_int.hpp; then + sudo apt-get update + sudo apt-get install -y libboost-dev + fi + - name: Check arithmetic, source hashes, finite identities, and patches + run: make verify-${{ matrix.group }} + - name: Require reproducible certificates and patches + run: git diff --exit-code + + formal: + runs-on: ubuntu-24.04 + timeout-minutes: 30 + strategy: + fail-fast: false + matrix: + package: [historical, gaussian, matrix] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: '3.13' + - name: Install elan; each project pins its Lean toolchain + run: | + curl --proto '=https' --tlsv1.2 -sSf https://raw.githubusercontent.com/leanprover/elan/0e36a07b9bbcc5381fa6250df109f9a4f94d7bac/elan-init.sh -o /tmp/elan-init.sh + sh /tmp/elan-init.sh -y --default-toolchain none + echo "$HOME/.elan/bin" >> "$GITHUB_PATH" + - name: Fetch pinned Mathlib build cache + if: matrix.package == 'historical' + working-directory: formal/lean + run: lake exe cache get + - name: Check formal package and theorem axiom dependencies + run: make formal-${{ matrix.package }}-verify diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/LICENSE b/references/frame-compiler/pr88/references/frame-compiler/pr79/LICENSE 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/Makefile b/references/frame-compiler/pr88/references/frame-compiler/pr79/Makefile new file mode 100644 index 0000000000..e2e2c38a36 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/Makefile @@ -0,0 +1,447 @@ +.PHONY: verify note audit-note tuned-note reuse-note incidence-note dag-note shared-point-note paired-note compact-note complex-note ternary-note fetch +.DEFAULT_GOAL := verify + +.PHONY: community-audit-check +community-audit-check: + python3 scripts/audit_community_candidate.py --check docs/research/community-audit-arithmetic.json + +.PHONY: community-followup-check +community-followup-check: + python3 scripts/audit_followup_candidate.py --candidate-root . --check docs/research/community-followup-arithmetic.json + +.PHONY: verify-community verify-producers verify-certificates verify-ternary verify-tests +# CI runs these in separate checkouts. Keep local verification sequential: +# different groups regenerate certificates that another group may read. +verify: + $(MAKE) verify-community + $(MAKE) verify-producers + $(MAKE) verify-certificates + $(MAKE) verify-ternary + $(MAKE) verify-research + $(MAKE) verify-strips + $(MAKE) verify-clones + $(MAKE) verify-positive + $(MAKE) verify-joint + $(MAKE) verify-pair + $(MAKE) verify-balanced + $(MAKE) verify-tests + +verify-community: community-audit-check community-followup-check copied-reversed-producer copied-reversed-check copied-fixed-reversed-producer copied-fixed-reversed-check + $(MAKE) copied-fixed-verify + $(MAKE) climbed-48-verify + +verify-producers: + $(MAKE) copied-centers-verify + $(MAKE) structured-bulk-verify + $(MAKE) endpoint-gauge-producer endpoint-gauge-certificate + $(MAKE) partial-swap-producer partial-swap-certificate + +verify-certificates: + python3 scripts/prime_field_network.py + python3 scripts/complex_network.py + python3 scripts/fast_gaussian.py + $(MAKE) batched-certificate batched-patch + python3 scripts/certify.py + python3 scripts/search_network.py + python3 scripts/make_patch.py + python3 scripts/nonadjacent.py + python3 scripts/make_nonadjacent_patch.py + python3 scripts/tune_routing.py + python3 scripts/research_networks.py + python3 scripts/search_network_variants.py + python3 scripts/block_label_targets.py + python3 scripts/audit_block_labels.py + python3 scripts/audit_additive_labels.py + python3 scripts/small_block_witness.py + python3 scripts/incidence_network.py + python3 scripts/make_incidence_patch.py + python3 scripts/search_incidence_partitions.py + python3 scripts/dag_network.py + python3 scripts/make_dag_patch.py + python3 scripts/shared_point_network.py + python3 scripts/make_shared_point_patch.py + python3 scripts/paired_network.py + python3 scripts/make_paired_patch.py + python3 scripts/prepare_layers.py + python3 scripts/audit_sparse_fusion.py + python3 scripts/audit_fused_block.py + python3 scripts/audit_short_guards.py + python3 scripts/audit_gather_schedules.py + python3 scripts/audit_coded_carries.py + python3 scripts/audit_cancellation.py + python3 scripts/audit_joint_frames.py + python3 scripts/audit_compact_controls.py + python3 scripts/compact_control_layer.py + python3 scripts/make_compact_control_patch.py + python3 scripts/audit_scratch_pooling.py + python3 scripts/reuse_network.py + python3 scripts/make_reuse_patch.py + +verify-ternary: + python3 scripts/complex_compression.py + python3 scripts/make_complex_compression_patch.py + python3 scripts/audit_ternary_side.py + python3 scripts/make_ternary_patch.py + +verify-tests: + python3 scripts/run_isolated_tests.py + git apply --check --directory=upstream patches/frozen-154.patch + git apply --check --directory=upstream patches/balanced-153.patch + git apply --check --directory=upstream patches/same-network-129.patch + git apply --check --directory=upstream patches/h46-111.patch + git apply --check --directory=upstream patches/h46-109.patch + git apply --check --directory=upstream patches/h46-108.patch + git apply --check --directory=upstream patches/h46-rational.patch + git apply --check --directory=upstream patches/nonadjacent-layout.patch + git apply --check --directory=upstream patches/frozen-nonadjacent-107.patch + git apply --check --directory=upstream patches/h46-nonadjacent-78.patch + git apply --check --directory=upstream patches/h46-nonadjacent-76.patch + git apply --check --directory=upstream patches/h46-shared-side-75.patch + git apply --check --directory=upstream patches/h46-incidence-67.patch + git apply --check --directory=upstream patches/h46-dag-63.patch + git apply --check --directory=upstream patches/h46-shared-point.patch + git apply --check --directory=upstream patches/h50-paired-59.patch + git apply --check --directory=upstream patches/compact-control-34.patch + git apply --check --directory=upstream patches/complex-compression-31.patch + git apply --check --directory=upstream patches/ternary-30.patch + git apply --check --directory=upstream patches/batched-23.patch + +note: + mkdir -p artifacts + tectonic --outdir artifacts notes/parameter-note.tex + +audit-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/nonadjacent-axis-note.tex + +tuned-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/routing-tuned-note.tex + +reuse-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/stage-reuse-note.tex + +incidence-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/incidence-note.tex + +dag-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/dag-note.tex + +shared-point-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/shared-point-note.tex + +paired-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/paired-note.tex + +compact-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/compact-control-note.tex + +complex-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/complex-compression-note.tex + +ternary-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/ternary-note.tex + +fetch: + python3 scripts/fetch_upstream.py + +.PHONY: batched-certificate batched-patch batched-note +PDFLATEX ?= pdflatex +TEX_ENGINE ?= pdflatex +TECTONIC ?= tectonic + +batched-certificate: + python3 scripts/controlled_bit_rank_moment.py --output certificates/controlled-bit-rank-moment.json > /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify + +.PHONY: balanced-split-verify verify-balanced +balanced-split-verify: + python3 scripts/experiments/verify_balanced_split.py + python3 scripts/experiments/audit_balanced_split_completion.py + python3 scripts/experiments/audit_balanced_split_exchange.py + python3 -m unittest discover -s tests -p 'test_balanced_split*.py' -v + +verify-balanced: balanced-split-verify diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/NOTICE b/references/frame-compiler/pr88/references/frame-compiler/pr79/NOTICE new file mode 100644 index 0000000000..8a6bef1613 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/NOTICE @@ -0,0 +1,337 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Balanced coarse split composition (2026-10-08) +--------------------------------------------- +Eumemic / @eumemic supplied PR69's balanced coarse sums, with OpenAI Codex +assistance. Alejandro Zarzuelo Urdiales / @alejandrozu supplied PR70's bounded +carry-exchange strategy with the AI disclosures retained in the source archive. +Chafik Boukhalfa / @chafreaky, with OpenAI Codex assistance, selected the row/ +half-plane coarse rules, future-compatible unit completion, exact integer-price +carry adaptation, composition and this certificate package. The PR71 anchored +split vector, schedules, arithmetic, pending controls and their contributor +chain are retained as credited above. Original PR69/70 sources, licenses and +notices and the complete published PR71 baseline are preserved under +references/frame-compiler. All earlier notices remain applicable. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr79/README.md new file mode 100644 index 0000000000..1bd7139657 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/README.md @@ -0,0 +1,184 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: balanced coarse split frames + +The [balanced-split proof and reproduction guide](research/balanced-split/README.md) +gives **κ=25872812736433/500000000000000000=5.1745625472866e-5**, approximately +**0.6437453019850683%** above the complete published PR71 witness. It composes +PR69 balanced coarse sums and a bounded PR70 carry exchange with PR71's +anchored split graph, future unit completion and profile-cost pending controls. +All actual words, dirty inputs, paid profiles and 47 strict assembly constraints +are checked by `make balanced-split-verify`. This finite conditional construction +retains the inherited all-size hypotheses and contributor notices. Chafik +Boukhalfa prepared the selected composition with OpenAI Codex assistance. + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/SOURCE.json new file mode 100644 index 0000000000..6ba76e935b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/SOURCE.json @@ -0,0 +1,257 @@ +{ + "commit": "9a58e62cf9e8954a4dde3c9b1372d733c276a6d1", + "files": { + ".gitattributes": "5f257f4e9e574ad5767f902242f519dad19cc455d6858f49234d0ccc345cabf1", + ".github/workflows/verify.yml": "1a9cccd742ba2a5aa5a5ac38c1b7559bc0dec46b23d3ce3ff3e26c3137e6c3a2", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "Makefile": "1bf5b63d413280a68fc2b91a7e83a6172632e50c8177ca097d9622af669ee8d6", + "NOTICE": 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No external claimed bound is imported as a proof." + }, + "split_operation": { + "author": "Rohan Garg / rohangar1 with OpenAI Codex assistance", + "commit": "641f22e52913db784f3b6ff1176b0c2945aae45b", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "f85437ee441f2a028660dd5e8dbdc0ec7b52bb55c04ea34fa4829c154bfd0ac1", + "research/split-skip/SOURCE.json": "7c2b4646a3ecfef6f881da5c43e4bd0fa9a4d1b00548b8ab458d897e16735134", + "research/split-skip/split_graph.py": "9b16ba907cbd58611fb64bfb9211be7809d54822d44c78fc6167cf4ba79eb905" + }, + "repo": "CrocSwap/integer-mult-bounds", + "scope": "Preserved original split-pair operation and attribution. These files document the adapted grouping operation; they are not imported by this producer. Actual imported source closure is PR65 plus shared PR48." + } + }, + "status": "Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/certificates/balanced-split-profiles-23.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/certificates/balanced-split-profiles-23.json new file mode 100644 index 0000000000..ee696ff2ba --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/certificates/balanced-split-profiles-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27297,"loss":506,"rank_sum":628337,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38540,"crt_matrices":5512,"crt_disagreements":0,"blocks":[0,357189,20828,8114,5378,4120,3708,3149,2526,2013,1694,1444,960,837,528,481,240,205,49,100,0,23,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/certificates/balanced-split-profiles-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/certificates/balanced-split-profiles-25.json new file mode 100644 index 0000000000..b0d73f3327 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/certificates/balanced-split-profiles-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35684,"loss":600,"rank_sum":892700,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":51168,"crt_matrices":7278,"crt_disagreements":0,"blocks":[0,491995,27247,10127,7839,5460,4947,4006,3802,2943,2456,2025,1787,1423,1124,867,560,478,221,170,46,59,0,25,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/certificates/balanced-split-repository-validation.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/certificates/balanced-split-repository-validation.json new file mode 100644 index 0000000000..8079dc012c --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/certificates/balanced-split-repository-validation.json @@ -0,0 +1,92 @@ +{ + "bit_saving": "51748303221339/1000000000000000000", + "certificate_sha256": "0c9ddf817a7198d597b65cd178873a36910188cfe9bdd2b22a3477ee84df5e88", + "ci": { + "required": "All twelve arithmetic groups on Python3.11/3.13/3.14 and all three inherited formal packages, plus any other triggered checks", + "status": "PENDING" + }, + "final_archive_binding": { + "all_staged_source_blobs_match_manifest": true, + "checked_utc": "2026-10-08T19:48:16.522765+00:00", + "controls_log_sha256": "e2e08dad6d7a59a4a8a8484510ce0717a32c6d5e8384c99c7cce614ef4e6a2a1", + "exact_composition_rechecked": true, + "focused_controls": 24, + "reason": "Preserve the original CRLF and whitespace bytes of the new contributor archives in Git; no graph, engine, physical word, profile or mathematical change.", + "source_manifest_sha256": 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/dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/SOURCE.json @@ -0,0 +1,16 @@ +{ + "files": { + "research/copied-fixed/balanced_assembly.py": "4d27575dcad2b45a281a34054d311409ecd954f373c0c3a62c29bcc843f06a86", + "research/copied-fixed/certificate.json": "33b3373c04e18a7f4cee33ba68da6ed71934acc3e0179cca6197696be4befa22", + "research/copied-fixed/changed_graph.py": "375a7ca6cac6d153c1880fd5ea5b4525e5dca9d4ee3018d24d679c219b59c5b3", + "research/copied-fixed/profiles.cpp": "b9fbd71c746609948b60c441ba4601e88436956fe636d1810f270ce4ce6a63a6", + "research/copied-fixed/verify.py": "44932182ce6c4d39776650311262ef0ac1ea9b5da7220bc0f728e2789881f84a", + "scripts/exclusion_circuit.py": "b253f9d7318becda1c1f3b24e2287ed44a9c27fcea00cf9d531afb950d0457a0", + "scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34" + }, + "head": "b7194b8586844956904b33e9fe18f0c75606c11b", + "scope": "Unmodified producer inputs for experimental frame compiler; attribution retained in each file", + "source_pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/48" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py new file mode 100644 index 0000000000..c7fd42867d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py @@ -0,0 +1,196 @@ +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit', 'complex'): + data = finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + 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"scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1", + "scripts/partial_swap/graph.py": "fd8c567759e26a10d2bad05508fd0355eb70fb116664d4e06e1858d0d8cb2ef9", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + } + }, + "status": "Conditional exact arithmetic witness; general transfer proofs are dependencies" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "PR48": { + "author": "Chafik Boukhalfa", + "commit": "b7194b8586844956904b33e9fe18f0c75606c11b", + 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Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + } + }, + "gzip_sha256": "4629d45d5074f87706db46be3aa3cd369071cd215bc6560d641115aadcce54a0", + "word_sha256": "bd0cbf73756f2e4f8d3879ec6c7a194990eb9ec40aaf3580bdded6994798d920" + }, + "25": { + "compiled": { + "h": 25, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 36586, + "baseline_pr48_roles": 48329, + "histogram": { + "1": 55478, + "0": 416276, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + }, + "rank_mass": 915250, + "elementary_xors": 205650, + "stats": { + "augmentations": 286, + "regions": 73695, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json new file mode 100644 index 0000000000..346cf87ea3 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json @@ -0,0 +1,1087 @@ +{ + "accepted_moment": { + "degree": 8, + "lower": "34287951499999999998997315662315085394575263036671/34287951500000000000000000000000000000000000000000", + "rounding_denominator": 10000000000000000000000000000000000000000, + "saving": "5103158916233/100000000000000000", + "strict_gap": "2278828040192983762647964739/77927162500000000000000000000000000000000000000", + "terms": { + "1": { + "exp_lower": "5001621630918375893019301295747281962987/5000000000000000000000000000000000000000", + "exp_upper": "10003243261836751786038602591494564437549/10000000000000000000000000000000000000000", + "log_lower": "3177185020398675220004135749131/500000000000000000000000000000", + "log_upper": "6354370040797350440008271498263/1000000000000000000000000000000", + "weight": "61988/2833715" + 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rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.", + "All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.", + "Neither global optimality nor measured practical speedup is claimed." + ], + "rejected_moment": { + "degree": 8, + "lower": "8571987875000000003683551653063012975552828889113/8571987875000000000000000000000000000000000000000", + "rounding_denominator": 10000000000000000000000000000000000000000, + "saving": "51031589162331/1000000000000000000", + "strict_gap": "-920887913265753353254538048853/2142996968750000000000000000000000000000000000000", + "terms": { + "1": { + "exp_lower": "2000648652367350369920582377063597092877/2000000000000000000000000000000000000000", + "exp_upper": "250081081545918796240072797132949649399/250000000000000000000000000000000000000", + "log_lower": "3177185020398675220004135749131/500000000000000000000000000000", + "log_upper": 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b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json new file mode 100644 index 0000000000..42958fc74b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json @@ -0,0 +1,195 @@ +{ + "artifact_sha256": { + "frame-profiles-23.json": "fec377bcf1512a427674983256b900229d4133026445b6e680c6e1e6dde5af7d", + "frame-profiles-25.json": 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orientations PASS", + "word_length": 621342 + }, + "schedule": "cover-core", + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4" + }, + "25": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 48329, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 41186, + "elementary_xors": 205977, + "h": 25, + "histogram": { + "0": 416741, + "1": 55478, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "2": 115781, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 915250, + "roles": 36586, + "stats": { + "augmentations": 286, + "clearing_xors": 2154, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "regions": 73695 + } + }, + "gzip_sha256": 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"3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "research/reordered-rank-pair/test_negative.py": "88832242e6f74e3fe08d109d4f21ff188a9ca0ae50c3e8f31da0243fe9501510", + "research/reordered-rank-pair/verify.py": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352", + "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3", + "scripts/experiments/binary_frame_profiles.cpp": "8e2e391d3ee57cbb1372c68e4aa031e1b861321536eabd642ada54e12e678669", + "scripts/experiments/binary_frame_replay.py": "392e78e62d7685c99a5888a7da743ea6c3dcad631af4a743c91e0c09348442bc", + "scripts/experiments/rank_pair_compiler.py": "9984aaccf880e4840402322d76678bfddb33ce7e494af78430a43429f51b85fd" + }, + "status": "Exact topological scheduling of unchanged PR63 graph/compiler; both physical orientations and fixed profiles checked" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json new file mode 100644 index 0000000000..3b648dbe21 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "loss": 506, + "rank_sum": 642620, + "field_prime": 2305843009213693951, + "frames": 52475, + "distinct_matrices": 36399, + "crt_matrices": 6049, + "crt_disagreements": 0, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json new file mode 100644 index 0000000000..19cc34b4ca --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json @@ -0,0 +1,40 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "loss": 600, + "rank_sum": 915250, + "field_prime": 2305843009213693951, + "frames": 73697, + "distinct_matrices": 50394, + "crt_matrices": 8127, + "crt_disagreements": 0, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json new file mode 100644 index 0000000000..2883a5f7c9 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "frames": 52475, + "distinct_transitions": 138016, + "singles": 15939, + "rank_mass": 642620, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 53320, + "2": 77409, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "21": 165, + "22": 23 + }, + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json new file mode 100644 index 0000000000..3b4bc33ff6 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json @@ -0,0 +1,35 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "frames": 73697, + "distinct_transitions": 190838, + "singles": 20700, + "rank_mass": 915250, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69278, + "2": 108881, + "3": 14362, + "4": 16908, + 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a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz new file mode 100644 index 0000000000..6a239a3e9f Binary files /dev/null and b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz differ diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + 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a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 at the new bit saving, +and the new complete profile has exact upper moment <1. All47 strict assembly +conditions and seven margins pass. **53 Lean endpoints** pass:34 new universal, +15 concrete,4 reused rational-helper lemmas. No omitted proof, project axiom or +native decision shortcut. The math scope includes dirty-word/complement safety, +coordinate conjugacy, fresh-kernel clearing, actual finite rounding and old-profile +rejection. It does not formalize the Python/C++ compiler or the all-size theorem. + +## Reproduce the accepted words + +Use an external checkout of frozen PR62 commit +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No newer sources are consumed. +See `verification/README.md` to compile its exact C++17 profiler, then run: + +``` +python verification/verify_words.py --upstream UPSTREAM --profiler PROFILER --word23 words/word-23.json.gz --word25 words/word-25.json.gz --output work/recheck +python verification/check_guards.py words/word-23.json.gz +python verification/check_guards.py words/word-25.json.gz +cd math +lake build Frozen62Research +``` + +The verifier checks immutable sources and its own adapter hashes, full input/dirty +bases in both orientations, exact source/scatter inventory, every literal frame +transition and all fixed-I+J profiles with bounded-minor and CRT checks. It rejects +optimized Python assertion mode. Use the supplied words for authoritative replay; +floating discovery prices propose candidates and have no trusted-proof role. +Discovery source snapshots, exact oracle fixtures (gzip-compressed) and matching +seeds retain original byte hashes. `discovery/SEARCH.md` explains the algorithms, +heuristic boundary and experimental commands. Historical workspace paths in the +source-generation receipts identify the original run; the accepted-word replay +uses the explicit upstream argument and needs no private directory layout. +Portable discovery regeneration: + +``` +python discovery/regenerate_portable.py --upstream UPSTREAM --work work/regenerate +``` + +This rewrites workspace paths only and checks both raw words and deterministic +gzip against the accepted words. Floating discovery is outside the trusted +certificate; the independent word/profile verifier establishes acceptance. + +The one-hour session froze information through #62. The unchanged data geometry +and its rational recovery are inherited; selected physical words/profile checks +are fresh. All-size analytic, compiler/frame transfer, finite-alphabet tape, +routing, prime selection/recovery and eventual-threshold contracts remain +conditional. No practical runtime or global-optimality claim is made. + +Alejandro Zarzuelo Urdiales is the human author/developer, following earlier +Archivara and personal July/October matrix/parity work developed with multiple +AI tools. This synthesis involved substantial OpenAI Codex assistance. Known +linear algebra, matroid exchange, dirty uncomputation and concavity principles +retain prior-work status. The finite construction credits Avi Eisenberg/ikeboy +(#62 interval/core-aware graph), eumemic (#57 frame compiler), Chafik Boukhalfa +(#60 ranking and earlier exact profiling), Rohan Arun and other retained notices. +The prior matrix/parity source is in `../matrix-exponent-synthesis/` and prior +Gaussian work in PR45. Its product counts retain their separate arithmetic scope. +The paper is supplied as LaTeX source; no newly compiled PDF is claimed. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md new file mode 100644 index 0000000000..b8dd669634 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md @@ -0,0 +1,136 @@ +# Local frame-compiler search, frozen through PR62 + +All experiments in this directory use the pinned PR62 pair graph at +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No later community source is consumed. +The original checkout is unchanged. Each emitted word and compiler copy has +a SHA256 recorded in its `compiled.json`; changed words are sent separately +to the independent literal replay and profile verifier. + +## New dependency-circuit choices + +The inherited compiler reduces retired fresh-signal rows against the current +live anchors and an echelon basis of compatible retired rows. Instead of +accepting the first dependent retired row, the new selectors collect the +available fundamental dependency circuits and choose a circuit by one of: + +- total charged target/provider rank growth (`all_growth`); +- number and rank growth of other retired providers (`all_collateral`); +- anchor-only dependence before general retired dependence (`anchor_first`); +- actual physical transition child-profile moment cost (`profile_cost*`). + +Every clearing XOR and every target/provider frame promotion is still emitted +and charged. A zero fresh-signal row can contain arbitrary physical dirty state; +its reuse is justified by the complete reversible word, not by claiming that +the physical register is initialized to zero. The compiler runs both complete +dirty-basis orientations, and the independent verifier repeats them. + +For the last selector let `C(A,B) = sum_t n_t(A,B) F_t`, where the `n_t` are +the exact inherited fixed-I+J pivot-run profile of the physical frame transition +and `F_t = t exp(a log(m/t))`. A candidate target `s` at old frame `A_s`, cleared +into frame `G` with providers `z`, is priced by + +``` +C(A_s,G) - C(A_s,I) + + sum_z [C(A_z,G) + C(G,I) - C(A_z,I)]. +``` + +This accounts for immediate promotions and the change in deferred cleanup, +assuming each other retired provider remains retired until cleanup. Future +reuse couples decisions, so this is a discovery heuristic, not an additive +global optimality certificate. Linear rank mass cancels between candidates; +`t*expm1(a*log(m/t))` avoids cancellation in floating discovery prices. +Missing transition profiles are recorded and collected for the next iteration. +Once a run has zero missing pairs, every local price uses an actual transition +profile. The final saving is accepted only through exact rational whole-profile +moment bounds and all assembly gates. + +`build_pair_oracle.py` is a local adaptation of the frozen C++ profiler that +additionally exports each transition histogram. It preserves the projector, +pivot, bounded-minor and three-prime CRT routines. Its synthetic transition-list +input is an oracle request, not a physical executable word. Each immutable +profile dump and the source/header hashes are recorded. + +## Moment-ordered carry selection + +The `--weighted` experiment orders the inherited linear/partition-matroid +candidate edges by their physical transition moment change before the original +greedy initialization and augmenting paths. For a value produced at `P`, +preserved through donor frame `G`, and carried to future target `T`, its +no-reclamation child-cost change is + +``` +C(G,T) - C(G,I) - C(0,P) - C(P,T). +``` + +At fixed cardinality, role and external-volume corrections are common to all +edge choices in the same axis. The inherited augmenting algorithm still seeks +maximum cardinality; it does not optimize the weights globally. Reclamation +adds coupling, so only the changed whole-word profile can establish an actual +improvement. This experiment makes no minimum-cost matroid claim. + +The `--exchange` variant starts from the frozen original maximum-cardinality +matching and tries bounded improving one-edge exchanges. A new edge may replace +the old donor of the same use when its donor block stays linearly independent; +or it may replace a selected edge in the same donor block and serve an unused +use. Both preserve cardinality and distinct-use constraints. The `--cycle` +variant additionally tests two-edge donor/use cycles, checking the independence +of both changed blocks. No improving two-edge cycle was found in the tested +native-price instance; this is not a proof that longer cycles cannot improve it. + +## Joint basis and schedule search + +`--basis shift1` profiles all candidate physical transitions after the point +permutation `i -> (i+1) mod h`, while preserving their original frame IDs. +Matching and reclamation are then priced in that basis. The emitted word is +renamed by `relabel_word.py`: all frame masks, canonical source/output triples, +common points and scatter port indices change together. Scratch slots and +literal XOR instructions are retained. The complete triple family and the +permutation-invariant `I+J` basis are inherited; every final renamed word still +gets fresh full-basis and actual physical-profile verification. + +This joint search differs from merely relabeling an already selected schedule: +the selected carries and clearing circuits are optimized under the new ordered +pivot-run prices. It remains a bounded discovery heuristic. + +## Regeneration + +The frozen graph/matching setup and a moment-cost exchange run are generated by: + +``` +python -S collect_matching_pairs.py --h 23 +python -S build_pair_oracle.py --h 23 --strategy matching_collect +python -S run_strategy.py --h 23 --strategy profile_cost --exchange +``` + +Repeat at `h=25`. For joint search, add `--basis shift1` to the oracle and +strategy commands. Reclamation may encounter transitions absent from the +initial carry-edge inventory. Run the oracle again on the emitted strategy +directory with `--incremental`, then run a new strategy label. The new label +must start with `profile_cost`; output directories are never overwritten. +`compiled.json` records the exact oracle dump hash, missing-pair count, word +hashes and source pin. Immutable earlier oracle dumps are retained by SHA256. +Use `--oracle path/to/the-immutable-dump.jsonl` to reproduce the prices of a +specific recorded run instead of consuming the subsequently enlarged cache. +The initial compiler matching cache is accepted only if its complete candidate +edge list matches the current frozen graph and every restored selected block +passes the same linear-independence check. + +The runner saves an immutable source copy and its hash for later runs. Floating +`expm1` prices at discovery saving `a=0.00005103` select proposals only. Neither +those prices nor their reported local gains are used as an arithmetic witness. + +## Acceptance boundary + +The independent verifier checks all input and dirty basis vectors in both +orientations, exact literal-scatter incidences, causal nested physical frames, +event equality reconstructed from the actual XOR word, rank mass, actual child +profiles and CRT agreement. It then computes the whole mixed-axis recurrence +and exact rational moment/assembly witnesses. Existing all-size geometry, +analytic envelopes, compiler/tape arguments and the surrounding reduction are +inherited from frozen PR62. A finite profile improvement does not by itself +formally prove those inherited hypotheses. + +Reduced XOR count alone is not accepted as an exponent improvement. In this +search `all_collateral` and `anchor_first` reduced clearing XORs but worsened +the certified characteristic. Actual child-size distributions decide the +saving, even when both physical-role counts and total rank mass are unchanged. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py new file mode 100644 index 0000000000..7c154b1a29 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py @@ -0,0 +1,275 @@ +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +import sys;sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'matrix-synthesis/bridge/pr62/references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s,add=True): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>s&1;e^=1<=prices[f]-1e-14:continue + if not can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:-prices[z])if prices[e] /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/NOTICE b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/NOTICE new file mode 100644 index 0000000000..8adab44ba3 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/NOTICE @@ -0,0 +1,324 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/README.md new file mode 100644 index 0000000000..4a9b481aa3 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/README.md @@ -0,0 +1,172 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/SOURCE.json new file mode 100644 index 0000000000..c8cc31f3d0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/SOURCE.json @@ -0,0 +1,120 @@ +{ + "commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "Makefile": "6e9e48a677b2f66643226840f574a6535e3564ffb0c72284b60302684a5dfbe4", + "NOTICE": "1e0702aa665673508fa91169163c5785d680637fff636fda01f36e3b127c3ee0", + "README.md": 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566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "rank_mass": 900975, + "singles": 20700, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 2300, + "word_sha256": "4c956749f0ec72c61875c51099afdf23e69ccea268a9b43b8d46da2ffdb24903" + } + } + }, + "bit_saving": "12854322426487/250000000000000000", + "certificate_sha256": "0fcb53fa374273efab6370953c966e8fa065dbfdba43691843a4788cb2cda42e", + "kappa": "51414646104039/1000000000000000000", + "margins": 7, + "producer_words_regenerated_and_matched": true, + "scope": "Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.", + "source_binding": "Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.", + "status": "PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly", + 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a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py new file mode 100644 index 0000000000..c7fd42867d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py @@ -0,0 +1,196 @@ +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit', 'complex'): + data = finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": 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b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": "41187950749917624099/1000000000000000000000000", + "cell_above_band": "666666666665666652937349833360791967/1333388250600666556832132000000000000", + "compact_leaf": "26927049500082375901/1000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "13729317166639208033/333347062650166639208033", + "epsilon_positive": "333333333333000000000000/333347062650166639208033", + "g1_above_kappa": "3408408254232349301008147/3333470626501666392080330000000000000", + "g2_above_kappa": "4241/2500000000000", + "g3_above_kappa": "74937627730682908927817/3333470626501666392080330000000000000", + "g4_above_kappa": "4241/2500000000000", + "g5_above_kappa": "5299956450675231223831763/13333882506006665568321320000000000000", + "g6_above_kappa": "11966897703678564007992423/13333882506006665568321320000000000000", + "g7_above_kappa": "3333196040161742016173902349301008147/3333470626501666392080330000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "13729317166639208033/333347062650166639208033", + "lambda_above_internal": "82375901/2000000000000000000000000", + "lambda_above_sigma": "61024099000082375901/2000000000000000000000000", + "lambda_above_tau": "82375901/2000000000000000000000000", + "lambda_prime_above_lambda": "82375901/2000000000000000000000000", + "lambda_prime_below_one": "41187950499917624099/1000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "21966907133275670202633360791967/533355300240266622732852800000000000", + "phase_leaf_above_bit": "53854099/2000000000000", + "phase_local": "109834536999766601613833360791967/2666776501201333113664264000000000000", + "prime_interval_packing": "13729317166639208033/333347062650166639208033", + "q_below_internal": "82375901/1000000000000000000000000", + "q_below_leaf": "26927049500082375901/1000000000000000000000000", + "q_below_reservations": "1/4000000000000", + "q_positive": "41187950499917624099/1000000000000000000000000", + "record_suffix": "13729317166639208033/333347062650166639208033", + "row_product_gap": "6548/25", + "short_record_fallback": "666639206901368489075295096355187267/666694125300333278416066000000000000", + "small_field_exposure": "1/1000000000000" + }, + "finite_bridge": { + "bit": { + "W": 177530859, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "degree": 2000, + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": 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b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": 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Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 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"multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json 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b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json new file mode 100644 index 0000000000..42958fc74b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json @@ -0,0 +1,195 @@ +{ + "artifact_sha256": { + "frame-profiles-23.json": "fec377bcf1512a427674983256b900229d4133026445b6e680c6e1e6dde5af7d", + "frame-profiles-25.json": "28b4b911e26fbc02dde0d2e1458ed16227f756126ab8144d6d45e164d1165262", + "frame-transitions-23.json": "86646f1110595294cccc15603c552f0a153574a690b69c3b144d84a449891103", + "frame-transitions-25.json": "c333c348665d12b95e168ca4fac48bfdca335104edd0f29c81fe94bec292e774", + "frame-word-23.json.gz": "a44e038e1c548ea8ac31dd04acc2bba7951b22e17df7b7ad3464ea2b504a8da4", + "frame-word-25.json.gz": "ad8b299697f90b185b6b791313b505586be97965519052100d097df6199e00c5", + "paired-candidate.json": "34a500d739537235dfc5d24325c22856ca4567b9eac998a3bce9b13db5501940" + }, + "axes": { + "23": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 36432, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 31460, + "elementary_xors": 149137, + "h": 23, + "histogram": { + "0": 302057, + "1": 42694, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "2": 82722, + "21": 165, + "22": 23, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 642620, + "roles": 27918, + "stats": { + "augmentations": 220, + "clearing_xors": 1577, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "regions": 52473 + } + }, + "gzip_sha256": "a44e038e1c548ea8ac31dd04acc2bba7951b22e17df7b7ad3464ea2b504a8da4", + "replay": { + "elementary_xors": 149137, + "full_basis_vectors": 31460, + "h": 23, + "histogram": { + "0": 162914, + "1": 42694, + "10": 442, + "11": 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orientations PASS", + "word_length": 856108 + }, + "schedule": "reverse-node", + "word_sha256": "a54443429f47c486016771ce0436effda098e142afc52861c20957e9ff8e086b" + } + }, + "source_sha256": { + "research/pair-assembly/frame/frame_verify.py": "fafe25d57166a747eeb847444a2e02dd7eed19038b93a2c495014d147d04a8fb", + "research/pair-assembly/pair_graph.py": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "research/reordered-rank-pair/test_negative.py": "88832242e6f74e3fe08d109d4f21ff188a9ca0ae50c3e8f31da0243fe9501510", + "research/reordered-rank-pair/verify.py": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352", + "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3", + "scripts/experiments/binary_frame_profiles.cpp": 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b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "loss": 506, + "rank_sum": 642620, + "field_prime": 2305843009213693951, + "frames": 52475, + "distinct_matrices": 36399, + "crt_matrices": 6049, + "crt_disagreements": 0, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json new file mode 100644 index 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b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json new file mode 100644 index 0000000000..2883a5f7c9 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "frames": 52475, + "distinct_transitions": 138016, + "singles": 15939, + "rank_mass": 642620, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 53320, + "2": 77409, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "21": 165, + "22": 23 + }, + "word_sha256": 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b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + "exponent": 5333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5715743812, + "rhs": 1792000000313576, + "rhs_bits": 51 + }, + "rows": { + "exponent": 5715743812, + "rhs": 896000000156824000, + "rhs_bits": 60 + } + } + }, + { + "log2_input": 224000000000000, + "powers": { + "alpha": { + "exponent": 11431487624, + "rhs": 1792000000156824, + "rhs_bits": 51 + }, + "compact": { + "exponent": 11431487624, + "rhs": 7168000000627232, + "rhs_bits": 53 + }, + "leaf": { + "exponent": 10666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11431487624, + "rhs": 3584000000313576, + "rhs_bits": 52 + }, + "rows": { + "exponent": 11431487624, + "rhs": 1792000000156824000, + "rhs_bits": 61 + } + } + }, + { + "log2_input": 448000000000000, + "powers": { + "alpha": { + "exponent": 22862975248, + "rhs": 3584000000156824, + "rhs_bits": 52 + }, + "compact": { + "exponent": 22862975248, + "rhs": 14336000000627232, + "rhs_bits": 54 + }, + "leaf": { + "exponent": 21333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 22862975248, + "rhs": 7168000000313576, + "rhs_bits": 53 + }, + "rows": { + "exponent": 22862975248, + "rhs": 3584000000156824000, + "rhs_bits": 62 + } + } + } + ], + "practical_runtime_claim": false + }, + "kappa": "40827/800000000", + "next_kappa": "318961/6250000000", + "next_kappa_rejection": "{'g1_above_kappa': '-25408022593116799041/7102635201420453820506250000000', 'g3_above_kappa': '-5201705247125960457841/1136421632227272611281000000000000', 'g5_above_kappa': '-7640875416065173165777/1818274611563636178049600000000000', 'g6_above_kappa': '-33658690551416775383761/9091373057818180890248000000000000'}", + "original_enclosure_control": { + "accepted_upper": "427922022655051425592169455669348999419009338821677321501934579031509793316011927849852932699225587520480274623290826519124585131702799274967695430254567113650998884459986946222692530282749027853246814000572815342011972280832203653626757194588235745687874105909336892415629002940540277569675953192803096179140323199169875932058482212840371519373866332987776983981442275480629595879092440778438065834410270423292532877965451564571150969903518733283745770147929604915103094966966240445718551419238205360172260389165815355293860586787487668007987689744585745259297708409486845374929838902410526770296527117452860612190765279746966315757114757646249443956020657651637850471083396567352186238660458491615294604389003317389825219053116168473153626947262543915434579501546193988862612230828605213616950127673267971569642351835151332191639228898384399684069201926146521990048728093044781289653532998958679374426311189560250341590145887508815021337226982815008224357898461730107482372032845888428476273500999760300211786400006201411895378711403441679516543048925021677151249124774565210588951830515783148269750340702961227551/427922022656065148722015624802653702889498564421131911283499341667573520226931037010841800905471906532344178836996138043716400845851217866305783744362952178488692163617667760947934446961428764096857095662125776648371730944750850740376437391609342381012534311915175448066736517476339673099556706774420618964194148648273392198066357729130169733561134843302857240883248026154958104699812690626052696940220399106081385425042375485602542555097186568052507330835744941604979041042724146442866160606543845260686788873587136675704407457814823973491248098778928607362558510538701395621352496475077156310639504247824069338077266718928997258973439362819271794470658904562860362470215133491491305622841328989108583065554731667738937158958161399293136952726957825424616696098290625805073806865420810062253320746566043770582998650738545122821954094593047815197564256009823257422725379706679933315631514838786135447434356419391187561619401952168548631044553632502869921434523792993783307013326156305798890689568359302672301544894715282222433613932715358768884516049207059704442128612279932500000000000000000000000000000000000000000", + "next_bit_lower": "374050380000830479912607937870818083834173718615907103079616878943322706260497332605534066060136407627149268792108716494485294881071/374050380000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + } + }, + "comparison": { + "additional_precision_gain": "2116843/200000000000000000", + "difference": "1238116843/200000000000000000", + "difference_pr65": "59693903/12500000000000000", + "kappa": "10206752116843/200000000000000000", + "pr63_kappa": "5102757/100000000000", + "pr65_kappa": "2041159402879/40000000000000000", + "structural_gain_on_original_grid": "309/50000000000" + }, + "grid_denominator": 1000000000000000000, + "next_bit_saving": "5103636516201/100000000000000000", + "preferred": { + "assembly": { + "absorption_gap": "12957517239351787231794417587/100005103636516190692726967598200000000000000000", + "constraints": { + "K_dominates_log": "25518182705927945452132037536365162009/500025518182580953463634837991000000000000", + "K_geometry": "375025518182705953463634837991/500025518182580953463634837991000000000000", + "a_below_b": "20663634837991/1000000000000000000", + "a_positive": "51036365162009/1000000000000000000", + "alpha_below_one": "999999999999500025518182580953463634837991/1000051036365161906927269675982000000000000", + "alpha_below_one_fourth": "249961722725628595322730323966963634837991/1000051036365161906927269675982000000000000", + "alpha_positive": "51036365661881409087095028536365162009/1000051036365161906927269675982000000000000", + "artificial_boundary": "28001633163690681098227177374284390904513973/4000204145460647627709078703928000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "499974481817294046536365162009/500000000000000000000000000000", + "c_positive": "25518182705953463634837991/500000000000000000000000000000", + "cell_above_band": "999999999998499974481817419046536365162009/2000102072730323813854539351964000000000000", + "compact_leaf": "8539317419046536365162009/500000000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "25518183080953463634837991/500025518182580953463634837991", + "epsilon_positive": "499999999999500000000000000000/500025518182580953463634837991", + "g1_above_kappa": "100005116594033430044514199392617587/100005103636516190692726967598200000000000000000", + "g2_above_kappa": "1302288897/500000000000000000", + "g3_above_kappa": "12957517239351787231794417587/100005103636516190692726967598200000000000000000", + "g4_above_kappa": "1302288897/500000000000000000", + "g5_above_kappa": "37501926821210810861559844643742587/100005103636516190692726967598200000000000000000", + "g6_above_kappa": "87504478639468906207923328442842587/100005103636516190692726967598200000000000000000", + "g7_above_kappa": "99994896363383814423867065831844514199392617587/100005103636516190692726967598200000000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "25518183080953463634837991/500025518182580953463634837991", + "lambda_above_internal": "51036365162009/1000000000000000000000000000000", + "lambda_above_sigma": "20663634838042036365162009/1000000000000000000000000000000", + "lambda_above_tau": "51036365162009/1000000000000000000000000000000", + "lambda_prime_above_lambda": "51036365162009/1000000000000000000000000000000", + "lambda_prime_below_one": "25518182580953463634837991/500000000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "40829092429500023633159832136365162009/800040829092129525541815740785600000000000", + "phase_leaf_above_bit": "17078634837991/1000000000000000000", + "phase_local": "204145464147602190896122974536365162009/4000204145460647627709078703928000000000000", + "prime_interval_packing": "25518183080953463634837991/500025518182580953463634837991", + "q_below_internal": "51036365162009/500000000000000000000000000000", + "q_below_leaf": "8539317419046536365162009/500000000000000000000000000000", + "q_below_reservations": "1/4000000000000", + "q_positive": "25518182580953463634837991/500000000000000000000000000000", + "record_suffix": "25518183080953463634837991/500025518182580953463634837991", + "row_product_gap": "6548/25", + "short_record_fallback": "499974480514563711027641740160491885440816916081/500025518182580953463634837991000000000000000000", + "small_field_exposure": "1/1000000000000" + }, + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "margins": { + "g1": "25518183080953463634837991/500025518182580953463634837991", + "g2": "51036365162009/1000000000000000000", + "g3": "25518182580927945452257037536365162009/500025518182580953463634837991000000000000", + "g4": "51036365162009/1000000000000000000", + "g5": "40829092429500023633159832136365162009/800040829092129525541815740785600000000000", + "g6": "204145464147602190896122974536365162009/4000204145460647627709078703928000000000000", + "g7": "499999999999500000000000000000/500025518182580953463634837991" + }, + "minimum_margin": "25518182580927945452257037536365162009/500025518182580953463634837991000000000000", + "parameters": { + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": "1", + "a_bit": "51036365162009/1000000000000000000", + "a_complex": "717/10000000", + "alpha_squared_power": "51036365661881409087095028536365162009/1000051036365161906927269675982000000000000", + "beta": "1/20", + "c": "25518182705953463634837991/500000000000000000000000000000", + "delta": "1/8000000000000", + "epsilon": "499999999999500000000000000000/500025518182580953463634837991", + "h": "1/1000000000000", + "kappa": "10206752116843/200000000000000000", + "lambda_": "999948963634838042036365162009/1000000000000000000000000000000", + "lambda_prime": "499974481817419046536365162009/500000000000000000000000000000", + "q": "25518182580953463634837991/500000000000000000000000000000", + "sigma": "9999283/10000000", + "tau": "999948963634837991/1000000000000000000" + }, + "recurrence": { + "internal": "999948963634837991/1000000000000000000", + "leaf": "199986377/200000000", + "reservations": "499974481817294046536365162009/500000000000000000000000000000" + }, + "scoped_limit": "51036365162009/1000051036365162009" + }, + "eventual_bounds": { + "additional_eventual_conditions": [ + "BHP prime threshold and distinct-prime packing", + "Fixed rational basis, eligible common prime and native table setup", + "Catalogue/descriptor domination, logarithm absorption, exact recovery" + ], + "all_interval_argument": "For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). Successive intervals double LHS; the positive affine RHS grows at most linearly, so 2^j >= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956143, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + "exponent": 5333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5715743812, + "rhs": 1792000000313576, + "rhs_bits": 51 + }, + "rows": { + "exponent": 5715743812, + "rhs": 896000000156824000, + "rhs_bits": 60 + } + } + }, + { + "log2_input": 224000000000000, + "powers": { + "alpha": { + "exponent": 11431487624, + "rhs": 1792000000156824, + "rhs_bits": 51 + }, + "compact": { + "exponent": 11431487624, + "rhs": 7168000000627232, + "rhs_bits": 53 + }, + "leaf": { + "exponent": 10666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11431487624, + "rhs": 3584000000313576, + "rhs_bits": 52 + }, + "rows": { + "exponent": 11431487624, + "rhs": 1792000000156824000, + "rhs_bits": 61 + } + } + }, + { + "log2_input": 448000000000000, + "powers": { + "alpha": { + "exponent": 22862975248, + "rhs": 3584000000156824, + "rhs_bits": 52 + }, + "compact": { + "exponent": 22862975248, + "rhs": 14336000000627232, + "rhs_bits": 54 + }, + "leaf": { + "exponent": 21333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 22862975248, + "rhs": 7168000000313576, + "rhs_bits": 53 + }, + "rows": { + "exponent": 22862975248, + "rhs": 3584000000156824000, + "rhs_bits": 62 + } + } + } + ], + "practical_runtime_claim": false + }, + "kappa": "10206752116843/200000000000000000", + "next_kappa": "6379220073027/125000000000000000", + "next_kappa_rejection": "{'g3_above_kappa': '-54404741498227752163082843757/62503189772822619182954354748875000000000000000'}" + }, + "profile_path": "research/slot-cost-rank-pair/paired-candidate.json", + "profile_sha256": "be0322ad60f73923953f242eaffaf114ff12438e8617dae38888b77fa03184cc", + "proof_limits": [ + "The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.", + 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a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) ++ slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();pending={};stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): +@@ -149,7 +151,8 @@ + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 +- return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) ++ endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 ++ return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} +@@ -161,6 +164,9 @@ + old,e=bb[p];row^=old;expr^=e + return expr + for s in anchors:ins(s) ++ for s,target in pending.items(): ++ if contains(blocks[frames[s]]['frame'],blocks[g]['frame']) and contains(blocks[g]['frame'],blocks[target]['frame']): ++ ins(s);stats['live_anchor_candidates']+=1 + best=None + # Inspect every eligible dependent candidate across all retired ranks. + # Rank the actual fixed-basis growth/cleanup profiles by an integer entropy score. +@@ -176,7 +182,9 @@ + if best is None or key= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and kappa > previous_kappa + bridge = json.loads((OLD/'certificate.json').read_text())['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/split-pair/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr67_commit='b3745601e947a94316bf25c2c6263d93c06e3364', + pr67_kappa=previous_kappa, ratio_pr67=kappa/previous_kappa, + absolute_gain_pr67=kappa-previous_kappa, + pr67_complete_profile_exclusion_lower=prior65_lower, + full_pr67_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected split-pair partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'split-pair-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py new file mode 100644 index 0000000000..1290ef2eb8 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py @@ -0,0 +1,275 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py new file mode 100644 index 0000000000..7908c963a4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py @@ -0,0 +1,78 @@ +#!/usr/bin/env python3 +"""Replay the aligned split-pair/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from split_pair_compose import compose, check_sources +from split_pair_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'split-pair-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='split-pair-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + 'c++', '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'split-pair-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'split-pair-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'split-pair-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'split-pair-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'split-pair-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair.py new file mode 100644 index 0000000000..5088cff133 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair.py @@ -0,0 +1,238 @@ +"""Physical and exact-arithmetic controls for the aligned split/pair witness.""" +from copy import deepcopy +from fractions import Fraction +from itertools import combinations +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile +import unittest +from unittest.mock import patch + +ROOT = Path(__file__).resolve().parents[1] +EXPERIMENTS = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXPERIMENTS)) +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from binary_frame_math import moment + + +class SplitPairControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.words = {h: json.loads(gzip.decompress((ROOT/f'certificates/split-pair-word-{h}.json.gz').read_bytes())) + for h in (23,25)} + + def reject_mutation(self, mutate, checker='both'): + for h, original in self.words.items(): + with self.subTest(h=h), tempfile.TemporaryDirectory() as directory: + changed = deepcopy(original) + mutate(changed) + path = Path(directory)/'word.json' + path.write_text(json.dumps(changed, separators=(',', ':'))+'\n') + with self.assertRaises((AssertionError, ValueError, IndexError, KeyError)): + if checker != 'transitions': + replay(path) + if checker != 'replay': + prepare(path, Path(directory)/'transitions.bin') + + def test_selected_words_pass_independent_replay(self): + recorded = json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + actual = replay(ROOT/f'certificates/split-pair-word-{h}.json.gz') + self.assertEqual(json.loads(json.dumps(actual)), recorded['axes'][str(h)]['replay']) + + def test_omitted_literal_xor_is_rejected(self): + self.reject_mutation(lambda word: word['ops'].pop(0)) + + def test_self_xor_is_rejected(self): + def mutate(word): + word['ops'][0][1] = word['ops'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_non_nested_operation_frame_is_rejected(self): + def mutate(word): + narrow = next(i for i,(core,cover) in enumerate(word['frames']) if core == cover) + operation = next(op for op in word['ops'] if word['frames'][op[2]][0] != word['frames'][op[2]][1]) + operation[2] = narrow + self.reject_mutation(mutate) + + def test_aliased_terminal_role_is_rejected(self): + def mutate(word): + word['outputs'][1][0] = word['outputs'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_missing_copied_center_is_rejected(self): + def mutate(word): + index = next(i for i,(_,_,_,target) in enumerate(word['outputs']) if len(target) == 1) + word['outputs'].pop(index) + self.reject_mutation(mutate) + + def test_omitted_transition_cannot_reduce_paid_profile(self): + self.reject_mutation(lambda word: word['events'].pop(0), 'transitions') + + def test_understated_physical_width_is_rejected(self): + def mutate(word): + word['R'] -= 1 + self.reject_mutation(mutate) + + def test_complete_pr67_profile_fails_new_bit_saving(self): + from split_pair_arithmetic import refine + previous = json.loads((ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/paired-candidate.json').read_text())['bit'] + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + result = refine.exact_moment(previous['m'], previous['W'], {int(t): n for t,n in previous['child_multiplicities'].items()}, Fraction(current['bit_saving'])) + self.assertGreater(result['lower'], 1) + self.assertGreater(Fraction(current['kappa']), Fraction(current['comparison']['pr67_kappa'])) + + def test_private_import_preserves_path_and_arithmetic_module(self): + import split_pair_graph as provider + import split_pair_arithmetic as arithmetic + sentinel = object() + existing = sys.modules.get('refine', sentinel) + previous_path = sys.path[:] + graph, schedule = provider._private_modules() + refine, audit = arithmetic.private_arithmetic() + self.assertIs(audit.refine, refine) + self.assertIs(sys.modules.get('refine', sentinel), existing) + self.assertEqual(sys.path, previous_path) + + def test_failed_graph_build_restores_original_providers(self): + import split_pair_graph as provider + previous_class, previous_points = provider._graph.circuit_class, provider._graph.alternating_points + with patch.object(provider._graph, 'graph', side_effect=RuntimeError('deliberate graph failure')): + with self.assertRaises(RuntimeError): + provider.graph(23) + self.assertIs(provider._graph.circuit_class, previous_class) + self.assertIs(provider._graph.alternating_points, previous_points) + + def test_failed_compilation_restores_engine_graph_and_schedule(self): + import split_pair_compiler as producer + previous_graph, previous_build = producer.compiler.graph, producer.compiler.build + missing = object() + runtime = {name:getattr(producer.compiler,name,missing) for name in ('PENDING_COST','ORACLE_EXE','ORACLE_INPUT','oracles')} + with patch.object(producer.compiler, 'compile_', side_effect=RuntimeError('deliberate compiler failure')): + with self.assertRaises(RuntimeError): + producer.compile_axis(23) + self.assertIs(producer.compiler.graph, previous_graph) + self.assertIs(producer.compiler.build, previous_build) + for name,value in runtime.items(): + self.assertIs(getattr(producer.compiler,name,missing),value) + + def test_uncertified_configurations_are_rejected(self): + import split_pair_graph as provider + wrong_anchor = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_anchor['anchor'] = False + boolean_group = deepcopy(provider.EXPECTED_CONFIGS[23]); boolean_group['groups'][0] = True + changed_schedule = deepcopy(provider.EXPECTED_CONFIGS[23]); changed_schedule['schedule'] = 'reverse-node' + for changed in (wrong_anchor, boolean_group, changed_schedule): + with self.subTest(configuration=changed), patch.object(provider.json, 'loads', return_value=changed): + with self.assertRaises(ValueError): + provider.configuration(23) + for dimension in (True, 22, 24, '23'): + with self.subTest(dimension=dimension), self.assertRaises(ValueError): + provider.configuration(dimension) + + def test_recursive_weighted_exclusions_and_contraction(self): + import split_pair_graph as provider + for h in (23,25): + block_sizes = [] + parent = provider._graph.circuit_class(h) + selected = provider.split_class(parent, provider.configuration(h)['groups']) + case = self + class Audited(selected): + def grouping(self, points): + groups = super().grouping(points) + case.assertEqual([x for group in groups for x in group], list(points)) + case.assertLess(len(groups), len(points)) + return groups + + def _block(self, points, edges, weights, level): + def expected(omitted): + values = [value for pair,value in edges.items() if not set(pair) & omitted] + values += [value for point,value in weights.items() if point not in omitted] + support = 0 + for value in values: + case.assertEqual(support & self.support[value], 0) + support |= self.support[value] + return support + total, single, pairs = super()._block(points, edges, weights, level) + case.assertEqual(self.support[total], expected(set())) + case.assertEqual(set(single), set(points)) + for a in points: + case.assertEqual(self.support[single[a]], expected({a})) + case.assertEqual(set(pairs), set(combinations(points,2))) + for a,b in combinations(points,2): + case.assertEqual(self.support[pairs[a,b]], expected({a,b})) + block_sizes.append(len(points)) + return total, single, pairs + local = Audited(h-1) + block_sizes.clear() + local.pair(list(range(h-1))) + self.assertEqual(sorted(block_sizes, reverse=True), [h-1, 12 if h==23 else 13, 7 if h==23 else 8, 5, 3, 2]) + + def test_next_fine_grid_points_and_old_assembly_controls_reject(self): + from split_pair_arithmetic import refine + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + bit = current['bit']; saving = Fraction(current['bit_saving']); kappa = Fraction(current['kappa']) + grid = Fraction(1,10**18) + rows = {int(t): n for t,n in bit['child_multiplicities'].items()} + self.assertLess(refine.exact_moment(bit['m'],bit['W'],rows,saving)['upper'], 1) + self.assertGreater(refine.exact_moment(bit['m'],bit['W'],rows,saving+grid)['lower'], 1) + for label, variant in ( + ('next_kappa', dict(kappa=kappa+grid)), + ('zero_backoff', dict(h=Fraction())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))): + call = dict(a_bit=saving, kappa=kappa, h=Fraction(1,10**12));call.update(variant) + with self.subTest(control=label), self.assertRaises(refine.balanced.InvalidAssembly): + refine.balanced.assembly(current['finite_bridge'], **call) + + def test_mass_preserving_profile_mutation_is_rejected(self): + from split_pair_compose import check_sources + profile_path = ROOT/'certificates/split-pair-profiles-23.json' + changed = json.loads(profile_path.read_text()) + before = sum(t*n for t,n in enumerate(changed['blocks'])) + changed['blocks'][2] += 3; changed['blocks'][3] -= 2 + self.assertTrue(all(n >= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'split-pair-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from split_pair_compose import check_sources + manifest_path = ROOT/'research/split-pair/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/split-pair-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import split_pair_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('split_pair_graph.py', 'split_pair_engine.py', 'split_pair_compiler.py', 'split_pair_arithmetic.py', 'split_pair_compose.py', 'verify_split_pair.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair_pending.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair_pending.py new file mode 100644 index 0000000000..e6d63f72a4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/split_pair_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/research/balanced-split/PROOF.md b/references/frame-compiler/pr88/references/frame-compiler/pr79/research/balanced-split/PROOF.md new file mode 100644 index 0000000000..c34f8542cc --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/research/balanced-split/PROOF.md @@ -0,0 +1,251 @@ +# Finite certificate and inherited scope + +## 1. Exact change and provenance + +This construction preserves PR71's anchored `[1,1,2]` split recursion, +PR65 region schedules, PR67 profile-cost reclamation and PR68 pending live +controls with next-use scoring. It composes three finite choices: PR69's +balanced coarse parenthesization, future-compatible unit completion, and a +bounded adaptation of PR70 carry exchanges. The contributor originals, +licenses and notices are retained in hash-checked archives. The published +PR71 source, words and complete arithmetic certificate are preserved at +`1bef94fd40a746452548c84a4a8f8834670a3113` for the full-profile comparison. +The new namespace is `balanced-split`. Two portable engines differ from the +independently audited discovery engines only in the repository-relative ROOT +constant; their relocation patches and SHA256s are recorded. + +The h23 coarse cell uses columns when `i+jstep and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority):''' +check(s.count(completion)==1 and s.count(changed_start)==1,'Changed source not uniquely recognized') +check(s.replace(changed_start,old_start).replace(completion,' for i in range(len(ins)):')==old,'Compiler changed beyond the claimed unit-completion priority') +tree=ast.parse(s) +helpers=[n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name in ('basis','independent')] +namespace={};exec(compile(ast.Module(body=helpers,type_ignores=[]),str(SOURCE),'exec'),namespace) +basis=namespace['basis'];independent=namespace['independent'] +future=next(n for n in ast.walk(tree) if isinstance(n,ast.FunctionDef) and n.name=='future_priority') +contains=lambda a,b:not(b[0]&~a[0]) and not(a[1]&~b[1]) +# Actual-use fixtures distinguish future compatible uses from backward or nonnested uses. +ns=dict(position={0:0,1:1,2:2,3:3},step=1,b={'frame':(1,3),'inputs':[10,11,12,13]},blocks=[{'frame':(1,3)},{'frame':(1,3)},{'frame':(1,7)},{'frame':(1,5)}],uses=[(10,2,None),(10,2,('terminal',)),(11,2,None),(11,0,None),(12,3,None),(13,3,None)],value_uses={10:[0,1],11:[2,3],12:[4],13:[5]},contains=contains,slots=[7,1,3,3],ins=[0,1,2,3]) +exec(compile(ast.Module(body=[future],type_ignores=[]),str(SOURCE),'exec'),ns) +check([ns['future_priority'](i) for i in range(4)]==[(-2,3,0),(-1,1,1),(0,2,2),(0,2,3)],'Priority does not use compatible actual future uses, symbolic support, index') +check(sorted(range(4),key=ns['future_priority'])==[0,1,2,3],'Priority is not deterministic') +# General span argument is below; these adversarial numerical fixtures check the actual helpers and literal synthesis. +rng=Random(20261008);cases=0;operations=0 +for n in range(1,10): + for trial in range(250): + rows=[] + for _ in range(rng.randrange(n+1)*3): + candidate=rng.randrange(1,1<>i&1) + if j!=i: + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];ops.append((a,z)) + for j in range(n): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];ops.append((j,i)) + check(rr==[1< 1 and kappa > previous_kappa + bridge = finite_bridge(p['W']) + validate_bridge(bridge, p['W']) + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/balanced-split/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113', + pr71_kappa=previous_kappa, ratio_pr71=kappa/previous_kappa, + absolute_gain_pr71=kappa-previous_kappa, + pr71_complete_profile_exclusion_lower=prior71_lower, + full_pr71_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected balanced-split partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring, PR69 balanced coarse sums, future unit completion and bounded PR70 carry exchanges; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'balanced-split-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/scripts/experiments/balanced_split_engine.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/scripts/experiments/balanced_split_engine.py new file mode 100644 index 0000000000..e1a9883726 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/scripts/experiments/balanced_split_engine.py @@ -0,0 +1,278 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + _graph = _graphs[h] + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/scripts/experiments/binary_frame_math.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/scripts/experiments/binary_frame_math.py new file mode 100644 index 0000000000..b87855e808 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/scripts/experiments/binary_frame_math.py @@ -0,0 +1,87 @@ +"""Exact rational helpers extracted without body changes from pinned PR48 verify.py. +Credits: icekylinx PR32/36, Dominik Scholz PR35, Zhihao Chen PR29/23, +Paureel/Aurel Prosz, Swapnil Jain, Rohan Arun PR25/31, RaD/hipotures, +Chafik Boukhalfa and inherited notices in references/frame-compiler/pr48. +Prepared with OpenAI Codex assistance; no formal theorem claim. +""" +from fractions import Fraction as Q +from functools import lru_cache +from math import comb, factorial, isqrt, prod + +def js(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):js(v)for k,v in x.items()} + if isinstance(x,(list,tuple)):return [js(v)for v in x] + return x + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def mersenne(exponent): + require(exponent >= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr79/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'balanced-split-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from balanced_split_compose import check_sources + manifest_path = ROOT/'research/balanced-split/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/balanced-split-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import balanced_split_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_all_threshold_dependent_bridge_fields_are_checked(self): + from balanced_split_compose import finite_bridge, validate_bridge + expected = finite_bridge(134126064) + self.assertTrue(validate_bridge(expected, 134126064)) + for section,key in (('bit','wire_bits'),('rows','coefficient'),('rows','degree'),('rows','degree_gap'),('rows','suffix_slope')): + changed = deepcopy(expected) + changed[section][key] = Fraction(changed[section][key])+1 + with self.subTest(field=section+'.'+key), self.assertRaisesRegex(AssertionError, 'Stale finite bridge'): + validate_bridge(changed, 134126064) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('balanced_split_graph.py', 'balanced_split_engine.py', 'balanced_split_compiler.py', 'split_pair_arithmetic.py', 'balanced_split_exchange_engine.py', 'balanced_split_compose.py', 'verify_balanced_split.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr79/tests/test_balanced_split_pending.py b/references/frame-compiler/pr88/references/frame-compiler/pr79/tests/test_balanced_split_pending.py new file mode 100644 index 0000000000..cce267112e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr79/tests/test_balanced_split_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/balanced_split_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/balanced-split-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr82/FETCH.json b/references/frame-compiler/pr88/references/frame-compiler/pr82/FETCH.json new file mode 100644 index 0000000000..0dccc67c62 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr82/FETCH.json @@ -0,0 +1,43 @@ +{ + "commit": "3410b940aa26e5876202152dfa7c4f66451ee22c", + "files": { + "LICENSE": { + "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64", + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4" + }, + "NOTICE": { + "git_blob": "8a6bef1613ee24ca140ea612af48fb51d8cd9000", + "sha256": "ef6c74f5103d624f1a9910668d4124b213775e9b7e24edde089d9f4d1377abbb" + }, + "research/envelope-balanced/README.md": { + "git_blob": "77486a38c26058fa5690952254a056c1035b6e30", + "sha256": "ed0a825837ca352dda60fc6d0bf977881466d2edeb2c906983d9b2678a34bd12" + }, + "research/envelope-balanced/SOURCE.json": { + "git_blob": "6b7fbca6d08b8da17bb79439a93bbd0f5262e330", + "sha256": "ede836ef555e700601810f4beea31057af88ce7ff4dae21fceba44918be26551" + }, + "research/envelope-balanced/compiler.py": { + "git_blob": "b4d43e88aaa65aad4b3d83decd3f34947b4b6962", + "sha256": "1716168a06fa5385c41232b40f343a98b322dec3718cb641f0042aa8f5610738" + }, + "research/envelope-balanced/flag_engine.py": { + "git_blob": "d210d9336bf92edf03eb9b6d89b9e66b22a15a54", + "sha256": "e42a43947c8d575b764683d88ddc26a290618ac79028337b3b50daedc8475183" + }, + "research/envelope-balanced/order-23.json": { + "git_blob": "035f01df59be3312e30ec692754d3a331a766799", + "sha256": "def92cd69f3fba2986c7a230ece45f9eb63fd38fef512d055bf0adffe9edfa82" + }, + "research/envelope-balanced/order-25.json": { + "git_blob": "ec2a8aa14c0b0c07de47b7314b535aa1385c0756", + "sha256": "47632a745319452f4237754ccb1793e7d0ae455654b68c6a31eb2a79a0f98b9f" + }, + "research/envelope-balanced/verify.py": { + "git_blob": "e74b03c41417c914bcf0e4e8fd0150a27e61aaef", + "sha256": "bd767d460a85414ca320a449705860a376bee42cb8ce0734233a8e9706ad4fc5" + } + }, + "repo": "rohanarun/integer-mult-bounds", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/82" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr82/LICENSE b/references/frame-compiler/pr88/references/frame-compiler/pr82/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr82/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Balanced coarse split composition (2026-10-08) +--------------------------------------------- +Eumemic / @eumemic supplied PR69's balanced coarse sums, with OpenAI Codex +assistance. Alejandro Zarzuelo Urdiales / @alejandrozu supplied PR70's bounded +carry-exchange strategy with the AI disclosures retained in the source archive. +Chafik Boukhalfa / @chafreaky, with OpenAI Codex assistance, selected the row/ +half-plane coarse rules, future-compatible unit completion, exact integer-price +carry adaptation, composition and this certificate package. The PR71 anchored +split vector, schedules, arithmetic, pending controls and their contributor +chain are retained as credited above. Original PR69/70 sources, licenses and +notices and the complete published PR71 baseline are preserved under +references/frame-compiler. All earlier notices remain applicable. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr82/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr82/SOURCE.json new file mode 100644 index 0000000000..99c32c3c37 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr82/SOURCE.json @@ -0,0 +1,17 @@ +{ + "commit": "3410b940aa26e5876202152dfa7c4f66451ee22c", + "files": { + "FETCH.json": "e3c49a0759e5539c0c6d665278dae83cd9f0c4f614f322b76df5abc4e2404d0b", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "ef6c74f5103d624f1a9910668d4124b213775e9b7e24edde089d9f4d1377abbb", + "research/envelope-balanced/README.md": "ed0a825837ca352dda60fc6d0bf977881466d2edeb2c906983d9b2678a34bd12", + "research/envelope-balanced/SOURCE.json": "ede836ef555e700601810f4beea31057af88ce7ff4dae21fceba44918be26551", + "research/envelope-balanced/compiler.py": "1716168a06fa5385c41232b40f343a98b322dec3718cb641f0042aa8f5610738", + "research/envelope-balanced/flag_engine.py": "e42a43947c8d575b764683d88ddc26a290618ac79028337b3b50daedc8475183", + "research/envelope-balanced/order-23.json": "def92cd69f3fba2986c7a230ece45f9eb63fd38fef512d055bf0adffe9edfa82", + "research/envelope-balanced/order-25.json": "47632a745319452f4237754ccb1793e7d0ae455654b68c6a31eb2a79a0f98b9f", + "research/envelope-balanced/verify.py": "bd767d460a85414ca320a449705860a376bee42cb8ce0734233a8e9706ad4fc5" + }, + "pr": 82, + "scope": "Exact credited coordinate-aware pricing source and notices; reported foreign witness accepted without producer replay." +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr82/research/envelope-balanced/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr82/research/envelope-balanced/README.md new file mode 100644 index 0000000000..77486a38c2 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr82/research/envelope-balanced/README.md @@ -0,0 +1,127 @@ +# Envelope ordering inside balanced split compilation + +The finite conditional witness gives **kappa = 5203279888519/100000000000000000 = 5.2032798885190e-05**, +0.49049670% above PR80. Bit saving is 13008876609597/250000000000000000. +This is a draft pending the full expanded repository verification. + +PR80 selected already-compiled axes from PR76 and PR79. Here we compose +their construction methods before compilation on both axes: PR79's balanced +coarse graph and future-compatible unit completion; PR76/PR74's envelope +node ordering; three passes of PR79/PR70's bounded carry exchanges; and +PR78's geometric coordinate flags. h23 uses the half-plane coarse choice +and cover-core schedule; h25 uses row coarse sums and reverse-node schedule. +Both retain the anchored [1,1,2] split vector and exact next-use profile costs. +All archived sources are unchanged. `compiler.py` is the portable composition. +At h25 the discovery oracle receives coordinate-permuted frame masks, so its +costs refer to the final flag rather than the original coordinate order. +`flag_engine.py` differs from PR79's engine only in that oracle frame writer +and an attribution comment; operations, eligibility, independence and dirty +checks are unchanged. This changes only heuristic selection among legal +choices. Its final word is still independently replayed and exactly priced. +At h23 oracle pricing retains the original coordinate order. + +| Quantity | PR80 | This witness | +|---|---:|---:| +| h23 auxiliary roles | 27256 | 27075 | +| h25 auxiliary roles | 35684 | 35500 | +| Physical width | 134031764 | 133289600 | +| Total recursive rank | 77066417400 | 76639673100 | +| Deficit | 1846900 | 1846900 | + +## General compatibility argument + +Balanced coarse parenthesization changes only how the same Cartesian-product +edge sums are evaluated. The weighted scalar identities and recursively +contracting anchored partition are inherited from PR79's proof. Envelope +ordering then applies a bijection to non-source scalar node IDs, grouping +nodes by (core, cover), preserving the order inside each group and every +argument, output and provenance reference. It changes no scalar linear form +or frame. The graph verifier is rerun after this relabeling. Dependency and +carrier-eligibility checks in the compiler remain enabled. + +Future-compatible completion chooses independent unit rows after the desired +outputs and retained carriers. Any accepted independent completion is a full +invertible basis; the unchanged synthesis emits its literal XOR operations. +Bounded carrier exchanges preserve matching cardinality, unique uses and +independence of the output-plus-retained-input rows. These choices can change +each other's costs, so the words are recompiled and every profile recomputed; +we do not add reported savings or assume independent numerical gains. + +All clearing targets and controls remain charged. Both frame-containment +checks for pending controls remain enabled. The compiler and independent +replay verify the full arbitrary-dirty-role wrapper in both orientations. +Independent axis implementations expose the same source triple lines, fixed +I+J basis, terminal frames and scatter identity. Hence the complete tensor/data +construction is unchanged. Every endpoint/copy/data-growth/complex term is +retained exactly once. The fixed-width bridge is derived from the actual W. + +## General relabeling argument + +Let P be a permutation matrix on the h coordinates. It commutes with J, +so P commutes with the fixed basis L = I+J and preserves the form I-J/9. +For a core/cover frame F(C,U), the relabeled projector is +P F(C,U) P^-1 = F(P C,P U). Consequently, every frame inclusion, rank, +nondegeneracy condition, projector denominator bound and elementary role +operation is preserved. The existing exact CRT bounds apply unchanged. + +Relabel each input triple T to P T, each output (c,T) to (P c,P T), +each frame mask by P, and each scatter row by the induced triple permutation. +The role slots and literal XOR operations do not change. This conjugates +the complete linear word by the input/output permutation and therefore +preserves its identity on every ordinary input and arbitrary dirty role. +The verifier independently replays that identity in both orientations. + +The data component sums over every pair of source triples. Independent +coordinate permutations on the two axes induce a bijection on that complete +Cartesian product. Hence its existing complete histogram, copied-center +costs and endpoint corrections are unchanged. This argument uses the full +case set; it would not justify retaining a selected subset's histogram. + +North-east corner rank profiles depend on the fixed coordinate order. +Conjugating by P can change which adjacent pivots form a recursive block, +even though total rank is unchanged. We regenerate these profiles from the +actual relabeled words rather than assuming their costs are invariant. +Both dimensions use the selected orders in order-23.json and order-25.json. + +## Reproduction and validation + +From the repository root with assert-enabled Python 3.11+ and C++17: + +```sh +python3 research/envelope-balanced/verify.py --regenerate +(cd research/envelope-balanced && python3 -m unittest test_controls -v) +make verify +``` + +The regeneration option launches two isolated compiler processes and requires +both original words to reproduce byte-for-byte. The verifier then regenerates +the coordinate-permuted words, performs independent full input/dirty replay, +reconstructs all transitions, and regenerates exact bounded-minor/CRT profiles. +The complete paid child list is reconstructed; independent rational moment +bounds, 47 strict inequalities, seven margins and both next-grid exclusions +are checked. The complete PR76, PR79 and PR80 child lists are each excluded at +the new bit saving using their own width. Six physical/coordinate failure +controls and three stale bridge controls run separately. A dedicated +three-version CI workflow retains every inherited workflow. + +The bounded searches are not proofs of global optimality. All inherited +all-size residual compiler, routing, recovery, prime selection, finite +alphabet/tape, precision and analytic transfer interfaces remain hypotheses. +No unconditional multiplication theorem or practical speedup is claimed. + +## Attribution + +Thomas DiFiore (PR74) introduced the envelope ordering; Dominik Scholz +(PR76) composed it with carried exchanges; Chafik Boukhalfa (PR79/71) +provided balanced/future/exchange and anchored split compilation; eumemic +(PR69/57) provided balanced coarse sums and reversible compilation; +Alejandro Zarzuelo Urdiales (PR70) supplied the carry-exchange strategy; +Rohan Arun (PR78/80/65/67) supplied coordinate flags, axis selection, +schedules and profile-cost reclamation. This new pre-compilation composition +and finite selection were prepared by Rohan Arun with OpenAI Codex assistance. + +Credit also Rohan Garg, Avi Eisenberg, icekylinx, James Chang, Zhihao Chen, +Aurel Prosz/Paureel, Swapnil Jain, RaD/hipotures, Douglas Colkitt, OpenAI, +Harvey–van der Hoeven and all inherited contributors. Original licenses, +author and AI-assistance notices remain preserved. Tested PR75 zero-circuit +variants were not selected for this witness and are not claimed as its method. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr82/research/envelope-balanced/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr82/research/envelope-balanced/SOURCE.json new file mode 100644 index 0000000000..6b7fbca6d0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr82/research/envelope-balanced/SOURCE.json @@ -0,0 +1,304 @@ +{ + "parent_pr80": "a9ed157ff106fd35557b5896197f66a1272f7f13", + "files": { + ".gitattributes": "5f257f4e9e574ad5767f902242f519dad19cc455d6858f49234d0ccc345cabf1", + ".github/workflows/combined-flags.yml": "53d0f33c83356b2764f3cb332892690ff74ffa0e68b9ae1203fe837979c15396", + ".github/workflows/envelope-balanced.yml": "d658c2f91e1377eac5288cff7725ae1e573efdff70dac5472e6a4060085ab7fc", + ".github/workflows/verify.yml": "1a9cccd742ba2a5aa5a5ac38c1b7559bc0dec46b23d3ce3ff3e26c3137e6c3a2", 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"scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3", + "scripts/experiments/binary_frame_profiles.cpp": "8e2e391d3ee57cbb1372c68e4aa031e1b861321536eabd642ada54e12e678669", + "scripts/experiments/binary_frame_replay.py": "392e78e62d7685c99a5888a7da743ea6c3dcad631af4a743c91e0c09348442bc", + "scripts/experiments/joint_dual_reclaim_compiler.py": "9984aaccf880e4840402322d76678bfddb33ce7e494af78430a43429f51b85fd", + "scripts/experiments/pin_balanced_split_sources.py": "1ad34c438f3900379b0c3679d1bc9307a520896153247b3949c0a625036545f1", + "scripts/experiments/split_pair_arithmetic.py": "fb982a0ac8758b2e308dc8bd145f21548c28f4f2ee97d28e77fa849b9560de4a", + "scripts/experiments/split_pair_engine.py": "58f13f82ce1bb7f2b5549e17628bc6034e5e05cb24db2acb9a91c24820872f70", + "scripts/experiments/verify_balanced_split.py": "954795a732a39e716e6a35e0aaba7f9c95a5bc8d7fb91abfff7c4d7346c60dc5", + "tests/test_balanced_split.py": "9664bd572123cd525f1d2b0e60f928d000fd3093d4d1f322cf946791b5b4969e", + "tests/test_balanced_split_pending.py": "29139af10f899ae1738183b22439a888d89d1941f75573e5013fbfb579934524" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr82/research/envelope-balanced/compiler.py b/references/frame-compiler/pr88/references/frame-compiler/pr82/research/envelope-balanced/compiler.py new file mode 100644 index 0000000000..b4d43e88aa --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr82/research/envelope-balanced/compiler.py @@ -0,0 +1,51 @@ +"""Portable composition of PR79 balanced/future/exchange engine and PR76 ordering. +All inherited sources and notices remain unmodified. Composition by Rohan Arun +with OpenAI Codex assistance. Apache-2.0; finite conditional witness only. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2] +sys.path.insert(0,str(ROOT/'scripts/experiments')) +import balanced_split_graph as graph +import balanced_split_exchange_engine as baseline_engine +import flag_engine +sys.path.insert(0,str(ROOT/'references/frame-compiler/pr76/research/round7-scheduling')) +from schedule_variant import reorder +import argparse,gzip,json,subprocess,os,shlex + +def check_flag_engine(): + original=(ROOT/'scripts/experiments/balanced_split_exchange_engine.py').read_text() + before="for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank']))" + after="for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank']))" + assert original.count(before)==1 + expected='# Coordinate-conjugated oracle pricing by Rohan Arun with OpenAI Codex.\n'+original.replace(before,after) + assert (Path(__file__).parent/'flag_engine.py').read_text()==expected,'Flag engine contains changes beyond oracle coordinate pricing' + +def compile_axis(h,work): + check_flag_engine() + engine=flag_engine if h==25 else baseline_engine + if h==25: + cfg=json.loads((ROOT/f'research/envelope-balanced/order-{h}.json').read_text()) + assert sorted(cfg['order'])==list(range(h)) + engine.COORD_MAP={int(k):v for k,v in cfg['mapping'].items()} + assert engine.COORD_MAP=={old:new for new,old in enumerate(cfg['order'])} + work.mkdir(parents=True,exist_ok=True) + oracle=work/'oracle' + subprocess.run([*shlex.split(os.environ.get('CXX','c++')),'-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/profile_oracle.cpp'),'-o',str(oracle)],check=True) + engine.graph=lambda dimension:reorder(graph.graph(dimension)) + engine.build=graph.ordered_build(engine.build,h) + engine.ORACLE_EXE=str(oracle);engine.ORACLE_INPUT=str(work/'oracle.bin');engine.PENDING_COST=True;engine.oracles=[] + try:result,word=engine.compile_(h,matching=True,reclaim=True,dirty=True) + finally: + for process in engine.oracles: + process.stdin.close();assert process.wait(timeout=10)==0 + result.pop('seconds',None);result['scalar']=engine.graph(h).verify() + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + (work/'word.json.gz').write_bytes(gzip.compress(raw,mtime=0)) + (work/'compiler.json').write_text(json.dumps(result,indent=2)+'\n') + print('PASS compiled envelope-balanced axis',h,result['roles'],flush=True) + +if __name__=='__main__': + p=argparse.ArgumentParser();p.add_argument('--h',type=int,choices=(23,25),required=True);p.add_argument('--work',type=Path,required=True);args=p.parse_args();compile_axis(args.h,args.work) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr82/research/envelope-balanced/flag_engine.py b/references/frame-compiler/pr88/references/frame-compiler/pr82/research/envelope-balanced/flag_engine.py new file mode 100644 index 0000000000..d210d9336b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr82/research/envelope-balanced/flag_engine.py @@ -0,0 +1,312 @@ +# Coordinate-conjugated oracle pricing by Rohan Arun with OpenAI Codex. +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(index[int(i)]):s for i,s in word['sources'].items()} + v=word['v'];word['scatter']=[[v+index[a-v],b] for a,b in word['scatter']] + word['outputs']=[[s,g,perm[c],sorted(perm[x] for x in triple)] for s,g,c,triple in word['outputs']] + return word + +def exact(profiles): + cert=json.loads((HERE/'certificate.json').read_text()) + N=comb(23,3)*comb(25,3);m=575;W=2*N+sum(N//p['v']*p['R'] for p in profiles) + L=sum(N//p['v']*p['loss'] for p in profiles) + rows=Counter({1:19*N,21:2*N,17:2*N,481:2*N}) + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 and p['v']==comb(h,3) + assert sum(t*n for t,n in enumerate(p['blocks']))==h*p['R']+h*(h-1)==p['rank_sum'] + rows.update({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + rows[h]+=bank;rows[m-2*h]+=bank;rows[1]+=2*N;rows[h-2]+=2*N + bit=dict(m=m,N=N,W=W,L=L,total_rank=sum(t*n for t,n in rows.items()),child_multiplicities=dict(sorted(rows.items()))) + assert bit['total_rank']==m*W-N+L + assert arithmetic.js(bit)==cert['bit'] + saving=Q(cert['bit_saving']);moment=refine.exact_moment(m,W,rows,saving) + rejected=refine.exact_moment(m,W,rows,saving+Q(1,10**18)) + assert moment['upper']<11 + assert Q(cert['kappa'])>Q(old['kappa']) + print('PASS exact conditional kappa',result['kappa'],'47 constraints, seven margins, independent bounds and next-grid controls') + +def verify(regenerate=False): + sources();profiles=[] + with tempfile.TemporaryDirectory(prefix='coordinate-flags-') as directory: + work=Path(directory);exe=work/'profiles' + subprocess.run(['c++','-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'scripts/experiments/binary_frame_profiles.cpp'),'-o',str(exe)],check=True) + if regenerate: + jobs=[] + for h in (23,25): + axis=work/str(h);axis.mkdir() + jobs.append(subprocess.Popen([sys.executable,str(HERE/'compiler.py'),'--h',str(h),'--work',str(axis)])) + for job in jobs:assert job.wait()==0,'Portable compiler regeneration failed' + for h in (23,25): + assert gzip.decompress((work/str(h)/'word.json.gz').read_bytes())==gzip.decompress(original_path(h).read_bytes()),'Regenerated physical word changed' + print('PASS portable deterministic regeneration of both unpermuted words',flush=True) + for h in (23,25): + original=json.loads(gzip.decompress((original_path(h)).read_bytes())) + config=json.loads((HERE/f'order-{h}.json').read_text());word=relabel(original,config) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + assert raw==gzip.decompress((HERE/f'word-{h}.json.gz').read_bytes()) + path=work/f'word-{h}.json';path.write_bytes(raw);checked=replay(path) + stored=json.loads((HERE/f'replay-{h}.json').read_text());assert arithmetic.js(checked)==stored['replay'] + trans=work/f'transitions-{h}.bin';receipt=prepare(path,trans);assert arithmetic.js(receipt)==stored['transitions'] + subprocess.run([str(exe),str(trans)],check=True) + profile=json.loads(Path(str(trans)+'.profiles.json').read_text());assert profile==json.loads((HERE/f'profiles-{h}.json').read_text()) + profiles.append(profile);print('PASS complete relabelled physical word and profile',h,flush=True) + exact(profiles) +if __name__=='__main__': + import argparse + parser=argparse.ArgumentParser();parser.add_argument('--regenerate',action='store_true');args=parser.parse_args();verify(args.regenerate) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/.gitattributes b/references/frame-compiler/pr88/references/frame-compiler/pr84/.gitattributes new file mode 100644 index 0000000000..6ef147f1f0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/.gitattributes @@ -0,0 +1,23 @@ +* text=auto eol=lf +*.pdf binary +# Unified diffs require a leading space on blank context lines. +*.patch -whitespace +# Preserve the exact upstream bytes, including original whitespace. +upstream/** -whitespace +# Preserve the exact pinned third-party proof snapshots and notices. +references/copied-centers/pr29/** -whitespace +references/copied-centers/pr33/** -whitespace +references/semantic-bulk/** -whitespace + +# Immutable contributor archives retain original CRLF and whitespace bytes. +references/frame-compiler/pr69/** -text -whitespace +references/frame-compiler/pr70/** -text -whitespace +references/frame-compiler/pr71/** -text -whitespace + +# Preserve original contributor and frozen discovery bytes. +references/frame-compiler/pr74/** -text -whitespace +references/frame-compiler/pr78/** -text -whitespace +references/frame-compiler/pr79/** -text -whitespace +references/frame-compiler/indexed-r5/** -text -whitespace +# Byte-identical credited PR74 extracts retain original trailing blank lines. +scripts/experiments/indexed_cycle_nodeops.py -whitespace diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/.github/workflows/verify.yml b/references/frame-compiler/pr88/references/frame-compiler/pr84/.github/workflows/verify.yml new file mode 100644 index 0000000000..58b21a1373 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/.github/workflows/verify.yml @@ -0,0 +1,63 @@ +name: Verify research artifacts + +on: + push: + pull_request: + workflow_dispatch: + +permissions: + contents: read + +jobs: + verify: + runs-on: ubuntu-24.04 + timeout-minutes: 20 + strategy: + fail-fast: false + matrix: + python-version: ['3.11', '3.13', '3.14'] + group: [community, producers, certificates, ternary, research, tests, strips, clones, positive, joint, pair, balanced, indexed] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: ${{ matrix.python-version }} + - name: Install headers for the exact enlarged-frame profiler + if: matrix.group == 'positive' + run: | + if ! test -f /usr/include/boost/multiprecision/cpp_int.hpp; then + sudo apt-get update + sudo apt-get install -y libboost-dev + fi + - name: Check arithmetic, source hashes, finite identities, and patches + run: make verify-${{ matrix.group }} + - name: Require reproducible certificates and patches + run: git diff --exit-code + + formal: + runs-on: ubuntu-24.04 + timeout-minutes: 30 + strategy: + fail-fast: false + matrix: + package: [historical, gaussian, matrix] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: '3.13' + - name: Install elan; each project pins its Lean toolchain + run: | + curl --proto '=https' --tlsv1.2 -sSf https://raw.githubusercontent.com/leanprover/elan/0e36a07b9bbcc5381fa6250df109f9a4f94d7bac/elan-init.sh -o /tmp/elan-init.sh + sh /tmp/elan-init.sh -y --default-toolchain none + echo "$HOME/.elan/bin" >> "$GITHUB_PATH" + - name: Fetch pinned Mathlib build cache + if: matrix.package == 'historical' + working-directory: formal/lean + run: lake exe cache get + - name: Check formal package and theorem axiom dependencies + run: make formal-${{ matrix.package }}-verify diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/LICENSE b/references/frame-compiler/pr88/references/frame-compiler/pr84/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Keep local verification sequential: +# different groups regenerate certificates that another group may read. +verify: + $(MAKE) verify-community + $(MAKE) verify-producers + $(MAKE) verify-certificates + $(MAKE) verify-ternary + $(MAKE) verify-research + $(MAKE) verify-strips + $(MAKE) verify-clones + $(MAKE) verify-positive + $(MAKE) verify-joint + $(MAKE) verify-pair + $(MAKE) verify-balanced + $(MAKE) verify-indexed + $(MAKE) verify-tests + +verify-community: community-audit-check community-followup-check copied-reversed-producer copied-reversed-check copied-fixed-reversed-producer copied-fixed-reversed-check + $(MAKE) copied-fixed-verify + $(MAKE) climbed-48-verify + +verify-producers: + $(MAKE) copied-centers-verify + $(MAKE) structured-bulk-verify + $(MAKE) endpoint-gauge-producer endpoint-gauge-certificate + $(MAKE) partial-swap-producer partial-swap-certificate + +verify-certificates: + python3 scripts/prime_field_network.py + python3 scripts/complex_network.py + python3 scripts/fast_gaussian.py + $(MAKE) batched-certificate batched-patch + python3 scripts/certify.py + python3 scripts/search_network.py + python3 scripts/make_patch.py + python3 scripts/nonadjacent.py + python3 scripts/make_nonadjacent_patch.py + python3 scripts/tune_routing.py + python3 scripts/research_networks.py + python3 scripts/search_network_variants.py + python3 scripts/block_label_targets.py + python3 scripts/audit_block_labels.py + python3 scripts/audit_additive_labels.py + python3 scripts/small_block_witness.py + python3 scripts/incidence_network.py + python3 scripts/make_incidence_patch.py + python3 scripts/search_incidence_partitions.py + python3 scripts/dag_network.py + python3 scripts/make_dag_patch.py + python3 scripts/shared_point_network.py + python3 scripts/make_shared_point_patch.py + python3 scripts/paired_network.py + python3 scripts/make_paired_patch.py + python3 scripts/prepare_layers.py + python3 scripts/audit_sparse_fusion.py + python3 scripts/audit_fused_block.py + python3 scripts/audit_short_guards.py + python3 scripts/audit_gather_schedules.py + python3 scripts/audit_coded_carries.py + python3 scripts/audit_cancellation.py + python3 scripts/audit_joint_frames.py + python3 scripts/audit_compact_controls.py + python3 scripts/compact_control_layer.py + python3 scripts/make_compact_control_patch.py + python3 scripts/audit_scratch_pooling.py + python3 scripts/reuse_network.py + python3 scripts/make_reuse_patch.py + +verify-ternary: + python3 scripts/complex_compression.py + python3 scripts/make_complex_compression_patch.py + python3 scripts/audit_ternary_side.py + python3 scripts/make_ternary_patch.py + +verify-tests: + python3 scripts/run_isolated_tests.py + git apply --check --directory=upstream patches/frozen-154.patch + git apply --check --directory=upstream patches/balanced-153.patch + git apply --check --directory=upstream patches/same-network-129.patch + git apply --check --directory=upstream patches/h46-111.patch + git apply --check --directory=upstream patches/h46-109.patch + git apply --check --directory=upstream patches/h46-108.patch + git apply --check --directory=upstream patches/h46-rational.patch + git apply --check --directory=upstream patches/nonadjacent-layout.patch + git apply --check --directory=upstream patches/frozen-nonadjacent-107.patch + git apply --check --directory=upstream patches/h46-nonadjacent-78.patch + git apply --check --directory=upstream patches/h46-nonadjacent-76.patch + git apply --check --directory=upstream patches/h46-shared-side-75.patch + git apply --check --directory=upstream patches/h46-incidence-67.patch + git apply --check --directory=upstream patches/h46-dag-63.patch + git apply --check --directory=upstream patches/h46-shared-point.patch + git apply --check --directory=upstream patches/h50-paired-59.patch + git apply --check --directory=upstream patches/compact-control-34.patch + git apply --check --directory=upstream patches/complex-compression-31.patch + git apply --check --directory=upstream patches/ternary-30.patch + git apply --check --directory=upstream patches/batched-23.patch + +note: + mkdir -p artifacts + tectonic --outdir artifacts notes/parameter-note.tex + +audit-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/nonadjacent-axis-note.tex + +tuned-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/routing-tuned-note.tex + +reuse-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/stage-reuse-note.tex + +incidence-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/incidence-note.tex + +dag-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/dag-note.tex + +shared-point-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/shared-point-note.tex + +paired-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/paired-note.tex + +compact-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/compact-control-note.tex + +complex-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/complex-compression-note.tex + +ternary-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/ternary-note.tex + +fetch: + python3 scripts/fetch_upstream.py + +.PHONY: batched-certificate batched-patch batched-note +PDFLATEX ?= pdflatex +TEX_ENGINE ?= pdflatex +TECTONIC ?= tectonic + +batched-certificate: + python3 scripts/controlled_bit_rank_moment.py --output certificates/controlled-bit-rank-moment.json > /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify + +.PHONY: balanced-split-verify verify-balanced +balanced-split-verify: + python3 scripts/experiments/verify_balanced_split.py + python3 scripts/experiments/audit_balanced_split_completion.py + python3 scripts/experiments/audit_balanced_split_exchange.py + python3 -m unittest discover -s tests -p 'test_balanced_split*.py' -v + +verify-balanced: balanced-split-verify + +.PHONY: indexed-cycle-verify verify-indexed +indexed-cycle-verify: + python3 scripts/experiments/verify_indexed_cycle.py + python3 scripts/experiments/audit_indexed_cycle_completion.py + python3 scripts/experiments/audit_indexed_cycle_exchange.py + python3 scripts/experiments/audit_indexed_cycle_cycles.py + python3 scripts/experiments/audit_indexed_cycle_retired.py + python3 scripts/experiments/audit_indexed_cycle_pending.py + python3 -m unittest discover -s tests -p 'test_indexed_cycle*.py' -v + +verify-indexed: indexed-cycle-verify diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/NOTICE b/references/frame-compiler/pr88/references/frame-compiler/pr84/NOTICE new file mode 100644 index 0000000000..70f4d45ed6 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/NOTICE @@ -0,0 +1,339 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Balanced coarse split composition (2026-10-08) +--------------------------------------------- +Eumemic / @eumemic supplied PR69's balanced coarse sums, with OpenAI Codex +assistance. Alejandro Zarzuelo Urdiales / @alejandrozu supplied PR70's bounded +carry-exchange strategy with the AI disclosures retained in the source archive. +Chafik Boukhalfa / @chafreaky, with OpenAI Codex assistance, selected the row/ +half-plane coarse rules, future-compatible unit completion, exact integer-price +carry adaptation, composition and this certificate package. The PR71 anchored +split vector, schedules, arithmetic, pending controls and their contributor +chain are retained as credited above. Original PR69/70 sources, licenses and +notices and the complete published PR71 baseline are preserved under +references/frame-compiler. All earlier notices remain applicable. + +Indexed two-cycle composition (2026-10-08): Chafik Boukhalfa with OpenAI Codex assistance. Thomas DiFiore (@tomdif, PR74) supplied exact node ordering and coordinate relabeling, including the selected h25 permutation. Rohan Arun (@rohanarun, PR78) supplied the coordinate-flag search idea. Balanced multi-splits, exact retired/pending indices, bounded two-cycles, late-output routing and selected-coordinate certification compose inherited PR57/59/60/62/63/65/67/68/69/70/71/79 work. All original authorship, Apache-2.0 and AI disclosures remain in unchanged contributor archives. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/README.md new file mode 100644 index 0000000000..d48659c758 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/README.md @@ -0,0 +1,188 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: balanced coarse split frames + +The [balanced-split proof and reproduction guide](research/balanced-split/README.md) +gives **κ=25872812736433/500000000000000000=5.1745625472866e-5**, approximately +**0.6437453019850683%** above the complete published PR71 witness. It composes +PR69 balanced coarse sums and a bounded PR70 carry exchange with PR71's +anchored split graph, future unit completion and profile-cost pending controls. +All actual words, dirty inputs, paid profiles and 47 strict assembly constraints +are checked by `make balanced-split-verify`. This finite conditional construction +retains the inherited all-size hypotheses and contributor notices. Chafik +Boukhalfa prepared the selected composition with OpenAI Codex assistance. + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. + +### Indexed two-cycle finite witness + +[Indexed-cycle proof and evidence](research/indexed-cycle/README.md) gives κ = 261356445457/5000000000000000 with W=132466108. It combines attributed balanced multi-splits, exact frame indexes, bounded carry two-cycles, PR74 node ordering and coordinate flags; all-size transfer remains inherited. Verify with `make indexed-cycle-verify`. 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a/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-exchange-validation.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-exchange-validation.json new file mode 100644 index 0000000000..95821eb28c --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-exchange-validation.json @@ -0,0 +1,13 @@ +{ + "exercised_exchange_types": { + "different_region": 103, + "new_future_use": 582, + "same_future_use": 205, + "same_region": 684 + }, + "random_matroid_cases": 800, + "source_sha256": "a4a582339430662e13c905d5a4701f4e488ff1830a72dc1c71da57066ad2ea38", + "status": "PASS actual bounded single-exchange legality", + "targeted_cases": 5, + "total_exchanges_checked": 787 +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-kappa.json 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All-size residual compiler, recursion, finite scalar overhead, routing, prime selection, recovery, fixed-tape and analytic transfer remain inherited; arithmetic cutoffs are not full operational thresholds.", + "recorded_utc": "2026-10-08T20:32:01.926652+00:00", + "source_files": 580, + "source_manifest_sha256": "c5b314b4acff73f8fcd31802db2609f848ef6fcc2b63740fd985c353d994a612", + "status": "PASS focused portable witness and independent frozen-selection review; expanded full repository and published-head CI pending" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-retired-index-validation.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-retired-index-validation.json new file mode 100644 index 0000000000..20f20bf26a --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-retired-index-validation.json @@ -0,0 +1,7 @@ +{ + "actual_raise_fixture": true, + "mutations": 23572, + "ordered_queries": 11799, + "source_sha256": "a4a582339430662e13c905d5a4701f4e488ff1830a72dc1c71da57066ad2ea38", + "status": "PASS actual ordered retired index and frame lifecycle" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-transitions-23.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-transitions-23.json new file mode 100644 index 0000000000..613d5ace9b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 26834, + "frames": 65728, + "distinct_transitions": 163929, + "singles": 15939, + "rank_mass": 617688, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 83674, + "2": 73284, + "3": 9345, + "4": 14768, + "5": 5655, + "6": 2630, + "7": 906, + "8": 1692, + "9": 1014, + "10": 793, + "11": 207, + "12": 370, + "13": 104, + "14": 1219, + "15": 400, + "16": 493, + "17": 1036, + "18": 2643, + "19": 5609, + "21": 384, + "22": 23 + }, + "word_sha256": "c67fb6efa490db56814c743a48044c99397f3067f0038ce80673930c2f0ed829", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-transitions-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-transitions-25.json new file mode 100644 index 0000000000..89ef405538 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-transitions-25.json @@ -0,0 +1,37 @@ +{ + "h": 25, + "v": 2300, + "R": 35348, + "frames": 86507, + "distinct_transitions": 215055, + "singles": 20700, + "rank_mass": 884300, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 92777, + "2": 115704, + "3": 13298, + "4": 15384, + "5": 8687, + "6": 1876, + "7": 609, + "8": 2952, + "9": 849, + "10": 987, + "11": 156, + "12": 1101, + "13": 318, + "14": 575, + "15": 208, + "16": 1351, + "17": 472, + "18": 673, + "19": 779, + "20": 4243, + "21": 8332, + "23": 495, + "24": 25 + }, + "word_sha256": "ec153b2cd0ef6edeb626dbb2831abc5ce7a59c99870ec6a5e08afb5a1530c845", + "copied_centers": 25, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-two-cycle-validation.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-two-cycle-validation.json new file mode 100644 index 0000000000..4a80e9d18b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-two-cycle-validation.json @@ -0,0 +1,7 @@ +{ + "accepted_cycles_checked": 231, + "cases": 1204, + "duplicate_group_use_key_rejected": true, + "source_sha256": "a4a582339430662e13c905d5a4701f4e488ff1830a72dc1c71da57066ad2ea38", + "status": "PASS actual atomic two-cycle legality and adverse fixtures" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-validation.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-validation.json new file mode 100644 index 0000000000..68d9bc8540 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-validation.json @@ -0,0 +1,237 @@ +{ + "axes": { + "23": { + "profile": { + "R": 26834, + "blocks": [ + 0, + 360947, + 18308, + 10287, + 5376, + 3976, + 3779, + 2686, + 2296, + 1754, + 1371, + 1322, + 902, + 790, + 495, + 433, + 233, + 96, + 102, + 0, + 90, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 5567, + "distinct_matrices": 38555, + "field_prime": 2305843009213693951, + "frames": 65728, + "h": 23, + "loss": 506, + "rank_sum": 617688, + "v": 1771 + }, + "replay": { + "elementary_xors": 176951, + "full_basis_vectors": 30376, + "h": 23, + "histogram": { + "0": 192243, + "1": 73048, + "2": 78597, + "3": 9345, + "4": 14768, + "5": 5655, + "6": 2630, + "7": 906, + "8": 1692, + "9": 1014, + "10": 793, + "11": 207, + "12": 370, + "13": 104, + "14": 1219, + "15": 400, + "16": 493, + "17": 1036, + "18": 2643, + "19": 5609, + "21": 384, + "22": 23 + }, + "output_roles": 5336, + "rank_mass": 617688, + "roles": 26834, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 732598 + }, + "transitions": { + "R": 26834, + "copied_centers": 23, + "distinct_transitions": 163929, + "frames": 65728, + "h": 23, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 83674, + "2": 73284, + "3": 9345, + "4": 14768, + "5": 5655, + "6": 2630, + "7": 906, + "8": 1692, + "9": 1014, + "10": 793, + "11": 207, + "12": 370, + "13": 104, + "14": 1219, + "15": 400, + "16": 493, + "17": 1036, + "18": 2643, + "19": 5609, + "21": 384, + "22": 23 + }, + "rank_mass": 617688, + "singles": 15939, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 1771, + "word_sha256": "c67fb6efa490db56814c743a48044c99397f3067f0038ce80673930c2f0ed829" + } + }, + "25": { + "profile": { + "R": 35348, + "blocks": [ + 0, + 492700, + 23012, + 12086, + 6121, + 4924, + 5649, + 4980, + 3550, + 2660, + 2408, + 2123, + 1685, + 1370, + 958, + 775, + 544, + 438, + 260, + 97, + 130, + 0, + 126, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 7465, + "distinct_matrices": 48221, + "field_prime": 2305843009213693951, + "frames": 86507, + "h": 25, + "loss": 600, + "rank_sum": 884300, + "v": 2300 + }, + "replay": { + "elementary_xors": 234549, + "full_basis_vectors": 39948, + "h": 25, + "histogram": { + "0": 255645, + "1": 78977, + "2": 122604, + "3": 13298, + "4": 15384, + "5": 8687, + "6": 1876, + "7": 609, + "8": 2952, + "9": 849, + "10": 987, + "11": 156, + "12": 1101, + "13": 318, + "14": 575, + "15": 208, + "16": 1351, + "17": 472, + "18": 673, + "19": 779, + "20": 4243, + "21": 8332, + "23": 495, + "24": 25 + }, + "output_roles": 6925, + "rank_mass": 884300, + "roles": 35348, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 970396 + }, + "transitions": { + "R": 35348, + "copied_centers": 25, + "distinct_transitions": 215055, + "frames": 86507, + "h": 25, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 92777, + "2": 115704, + "3": 13298, + "4": 15384, + "5": 8687, + "6": 1876, + "7": 609, + "8": 2952, + "9": 849, + "10": 987, + "11": 156, + "12": 1101, + "13": 318, + "14": 575, + "15": 208, + "16": 1351, + "17": 472, + "18": 673, + "19": 779, + "20": 4243, + "21": 8332, + "23": 495, + "24": 25 + }, + "rank_mass": 884300, + "singles": 20700, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 2300, + "word_sha256": "ec153b2cd0ef6edeb626dbb2831abc5ce7a59c99870ec6a5e08afb5a1530c845" + } + } + }, + "bit_saving": "408390793141/7812500000000000", + "certificate_sha256": "c2ca8f70fd7bfc962b675d4784941a93d4d756530d7b4ec26a116bdb2c6f8315", + "kappa": "261356445457/5000000000000000", + "margins": 7, + "producer_words_regenerated_and_matched": true, + "scope": "Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.", + "source_binding": "Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.", + "status": "PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly", + "strict_constraints": 47 +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-word-23.json.gz b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-word-23.json.gz new file mode 100644 index 0000000000..3260f9aef6 Binary files /dev/null and b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-word-23.json.gz differ diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-word-25.json.gz b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-word-25.json.gz new file mode 100644 index 0000000000..074ec5c508 Binary files /dev/null and b/references/frame-compiler/pr88/references/frame-compiler/pr84/certificates/indexed-cycle-word-25.json.gz differ diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/EXPERIMENT.txt b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/EXPERIMENT.txt new file mode 100644 index 0000000000..ad69d585b0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/EXPERIMENT.txt @@ -0,0 +1 @@ +Compose Thomas DiFiore PR74 exact node-envelope renumbering with independently audited two-cycle matching, future completion, exact indexed reclamation, and selected h25 late output-use routing. Test six grouping structures and three coarse-sum orientations per dimension. Canary retains unchanged earlier cycles112 graph/schedule and hashes. Every new scalar graph and dirty physical word is independently checked and CPU CRT profiles/certificates are rebuilt. Imported PR74 functions and source/credits are preserved exactly. No imported claim is re-verified as a gate. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/LICENSE b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/NOTICE b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/NOTICE new file mode 100644 index 0000000000..e75caef6fe --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/NOTICE @@ -0,0 +1,241 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. 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a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/profiles.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/profiles.json new file mode 100644 index 0000000000..7baddf40c6 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/profiles.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27285,"loss":506,"rank_sum":628061,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38513,"crt_matrices":5538,"crt_disagreements":0,"blocks":[0,356669,20912,7996,5407,4043,3702,3146,2579,1990,1706,1444,980,839,542,483,239,205,49,97,0,23,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/replay.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/replay.json new file mode 100644 index 0000000000..d37ffd1add --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/replay.json @@ -0,0 +1,34 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27285, + "output_roles": 5336, + "elementary_xors": 160435, + "word_length": 666534, + "full_basis_vectors": 30827, + "rank_mass": 628061, + "histogram": { + "1": 58281, + "0": 171307, + "2": 80793, + "4": 14511, + "3": 10007, + "5": 6429, + "6": 2036, + "8": 1110, + "10": 535, + "9": 471, + "12": 661, + "14": 1868, + "13": 193, + "16": 431, + "11": 120, + "17": 574, + "18": 3412, + "15": 334, + "19": 6482, + "22": 23, + "21": 393, + "7": 627 + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/result.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/result.json new file mode 100644 index 0000000000..349e949822 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h23/result.json @@ -0,0 +1,19 @@ +{ + "h": 23, + "roles": 27285, + "stats": { + "augmentations": 13, + "regions": 59801, + "matched": 41730, + "multi_node_regions": 8694, + "carry_exchanges": 644, + "carry_two_cycles": 52, + "live_anchor_candidates": 72361, + "reclaimed": 2125, + "clearing_xors": 3916, + "live_anchor_xors": 76 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "word_sha256": "3f58db33edc2059ad6ca01cf8c36dd8cd8ae12149e1072e1f42757ca4ef17b82" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/profiles.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/profiles.json new file mode 100644 index 0000000000..2be4368700 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/profiles.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35684,"loss":600,"rank_sum":892700,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":51168,"crt_matrices":7278,"crt_disagreements":0,"blocks":[0,491871,27309,10127,7839,5460,4947,4006,3802,2943,2456,2025,1787,1423,1124,867,560,478,221,170,46,59,0,25,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/replay.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/replay.json new file mode 100644 index 0000000000..3ec3c54dc6 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/replay.json @@ -0,0 +1,36 @@ +{ + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 35684, + "output_roles": 6925, + "elementary_xors": 224161, + "word_length": 928844, + "full_basis_vectors": 40284, + "rank_mass": 892700, + "histogram": { + "1": 77041, + "0": 238437, + "2": 118217, + "3": 13314, + "4": 18459, + "6": 3215, + "5": 8388, + "7": 948, + "8": 1195, + "9": 721, + "10": 828, + "12": 708, + "13": 182, + "14": 653, + "16": 2171, + "18": 506, + "19": 981, + "17": 633, + "15": 187, + "11": 15, + "20": 4464, + "21": 8405, + "24": 25, + "23": 463 + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/result.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/result.json new file mode 100644 index 0000000000..50b259fcd7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/baseline/h25/result.json @@ -0,0 +1,19 @@ +{ + "h": 25, + "roles": 35684, + "stats": { + "augmentations": 16, + "regions": 84843, + "matched": 60971, + "multi_node_regions": 11575, + "carry_exchanges": 1000, + "carry_two_cycles": 62, + "live_anchor_candidates": 98464, + "reclaimed": 3263, + "clearing_xors": 6027, + "live_anchor_xors": 132 + }, + "full_physical_replay": "PASS both orientations", + "exact_CRT_profiles": "PASS", + "word_sha256": "7c60369042197c356dfac3516ae396d68dc92edbc5824b6078dce0e6676f7f79" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/batch.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/batch.py new file mode 100644 index 0000000000..1f994fa396 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/batch.py @@ -0,0 +1,113 @@ +"""Durable independent CPU search over pinned current two-cycle construction. +Each accepted case regenerates and independently replays the literal word, +reconstructs paid frames, computes CPU CRT profiles and exact inequalities. +""" +from pathlib import Path +from hashlib import sha256 +from concurrent.futures import ProcessPoolExecutor,as_completed +import argparse,ast,cProfile,gzip,importlib.util,json,os,pstats,subprocess,sys,time,types +ROOT=Path(__file__).resolve().parent +sys.path.insert(0,str(ROOT/'scripts/experiments')) + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m + +def generate(h,groups,profile=False,mode="baseline"): + started=time.monotonic();out=ROOT/'results'/f'{h}-{groups}-{mode}';out.mkdir(parents=True,exist_ok=True) + compiler=load('search_compiler',ROOT/'scripts/experiments/compiler.py') + source=(ROOT/'research/pair-assembly/pair_graph.py').read_text() + donor=ROOT/'references/pr69/balanced_coarse_compiler.py' + constants={n.targets[0].id:ast.literal_eval(n.value) for n in ast.parse(donor.read_text()).body if isinstance(n,ast.Assign) and isinstance(n.targets[0],ast.Name) and n.targets[0].id in ('BEFORE','AFTER')} + replacement=constants['AFTER'];needle='columns = [self.total([e(a,b) for a in groups[i]]) for b in groups[j]]' + orientation=mode.removeprefix('envelope-') if mode.startswith('envelope-') else ('half' if h==23 else 'row') + if orientation=='half': + replacement=replacement.replace(needle,'columns = ([self.total([e(a,b) for a in groups[i]]) for b in groups[j]] if i+j < ng-1 else [self.total([e(a,b) for b in groups[j]]) for a in groups[i]])') + elif orientation=='row':replacement=replacement.replace(needle,'columns = [self.total([e(a,b) for b in groups[j]]) for a in groups[i]]') + assert source.count(constants['BEFORE'])==1 + graph=types.ModuleType('balanced_graph');graph.__file__=str(ROOT/'research/pair-assembly/pair_graph.py');exec(compile(source.replace(constants['BEFORE'],replacement),graph.__file__,'exec'),graph.__dict__) + original=graph.circuit_class + def subclass(dim): + parent=original(dim) + class Split(parent): + def grouping(self,points): + result=super().grouping(points);choices=[int(x) for x in groups];choice=choices[self._level] if self._level3 and choice: + first,mid,last=0,(len(result)-1)//2,len(result)-1 + requested={1:[first],2:[mid],3:[last],4:[first,mid],5:[first,last],6:[mid,last],7:[first,mid,last],8:[first,first+1],9:[last-1,last]}[choice] + chosen=[] + for k in requested: + if k not in chosen and 0<=k1:hi=mid + else:raise ArithmeticError('Enclosure inconclusive') + a=Q(lo,den);bridge=deepcopy(baseline['finite_bridge']);bridge['bit']['W']=p['W'] + bridge['bit']['wire_bits']=p['W'].bit_length() + bridge['rows']['coefficient']=sum(bridge[name]['halving_degree']*bridge[name]['wire_bits'] for name in ('bit','complex')) + bridge['rows']['degree_gap']=Q(bridge['rows']['degree'])-Q(51,25)*bridge['rows']['coefficient'] + bridge['rows']['suffix_slope']=4*bridge['rows']['degree'] + accepted=refine.exact_moment(m,p['W'],rows,a);rejected=refine.exact_moment(m,p['W'],rows,Q(hi,den));assert accepted['upper']<1prior and best['prior65_moment']['lower']>1 + for r in rows: + r['moment_at_best_bit']=refine.exact_moment(m,r['bit']['W'],r['bit']['child_multiplicities'],best['bit_saving']) + output={'verified_baseline':{'pr':65,'commit':'49e84f939d15b618b50714eb039cabf97c74256a','kappa':prior},'best':best,'rows':rows,'cases':len(rows)} + (HERE/'fine-pair-comparison.json').write_text(json.dumps(refine.arithmetic.js(output),indent=2,sort_keys=True)+'\n') + (HERE/'selected-exact-result.json').write_text(json.dumps(refine.arithmetic.js(best),indent=2,sort_keys=True)+'\n') + print('BEST',json.dumps({'pair':best['pair'],'kappa':str(best['kappa']),'bit_saving':str(best['bit_saving']),'W':best['bit']['W'],'gain_percent_vs_verified65':float(100*(best['kappa']/prior-1))},sort_keys=True),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/nodeops.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/nodeops.py new file mode 100644 index 0000000000..fa6164310d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/nodeops.py @@ -0,0 +1,40 @@ +# Exact function extracts from Thomas DiFiore PR74,3f78d8967c009153f2df5c6a6577b6ab1d37e2ca. Apache-2.0; original source and notices retained. + +def reorder(c): + groups={} + for x in sorted(c.active): + if c.args[x]: groups.setdefault((c.core[x],c.union[x]),[]).append(x) + def key(item): + (core,cover),nodes=item + return cover.bit_count()-core.bit_count(),-core,cover,min(nodes) + ids=list(range(len(c.inputs)+1))+[x for _,nodes in sorted(groups.items(),key=key) for x in nodes] + mapping={x:i for i,x in enumerate(ids)} + args,core,cover,provenance=c.args,c.core,c.union,c.provenance + c.args=[tuple(mapping[y] for y in args[x]) if args[x] else None for x in ids] + c.core=[core[x] for x in ids];c.union=[cover[x] for x in ids] + c.provenance=[provenance[x] for x in ids] + c.active={mapping[x] for x in c.active};c.outputs={k:mapping[v] for k,v in c.outputs.items()} + c.support_in.cache_clear() + c.verify() + return c + + +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/original/carry_cycle_compiler.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/original/carry_cycle_compiler.py new file mode 100644 index 0000000000..d883cbc71d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/original/carry_cycle_compiler.py @@ -0,0 +1,338 @@ +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path('/Users/chafreaky/Documents/personal/integer-mult-research-20261008/joint-reclaim/references/frame-compiler/pr48') +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000000000, + "cutoff_log2_input": { + "alpha": 5956134977, + "compact": 23824539905, + "geometry": 3999930893196446780, + "guard": 4283152, + "log_p": 25, + "normalization": 14000000000000000000, + "period": 47649079809, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000000000, + "powers": { + "alpha": { + "exponent": 725614180574271, + "rhs": 112000000000000154416, + "rhs_bits": 67 + }, + "compact": { + "exponent": 725614180574271, + "rhs": 448000000000000617600, + "rhs_bits": 69 + }, + "leaf": { + "exponent": 666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 725614180574271, + "rhs": 224000000000000308760, + "rhs_bits": 68 + }, + "rows": { + "exponent": 725614180574271, + "rhs": 112000000000000154416000, + "rhs_bits": 77 + } + } + }, + { + "log2_input": 28000000000000000000, + "powers": { + "alpha": { + "exponent": 1451228361148543, + "rhs": 224000000000000154416, + "rhs_bits": 68 + }, + "compact": { + "exponent": 1451228361148543, + "rhs": 896000000000000617600, + "rhs_bits": 70 + }, + "leaf": { + "exponent": 1333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1451228361148543, + "rhs": 448000000000000308760, + "rhs_bits": 69 + }, + "rows": { + "exponent": 1451228361148543, + "rhs": 224000000000000154416000, + "rhs_bits": 78 + } + } + }, + { + "log2_input": 56000000000000000000, + "powers": { + "alpha": { + "exponent": 2902456722297087, + "rhs": 448000000000000154416, + "rhs_bits": 69 + }, + "compact": { + "exponent": 2902456722297087, + "rhs": 1792000000000000617600, + "rhs_bits": 71 + }, + "leaf": { + "exponent": 2666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2902456722297087, + "rhs": 896000000000000308760, + "rhs_bits": 70 + }, + "rows": { + "exponent": 2902456722297087, + "rhs": 448000000000000154416000, + "rhs_bits": 79 + } + } + }, + { + "log2_input": 112000000000000000000, + "powers": { + "alpha": { + "exponent": 5804913444594174, + "rhs": 896000000000000154416, + "rhs_bits": 70 + }, + "compact": { + "exponent": 5804913444594174, + "rhs": 3584000000000000617600, + "rhs_bits": 72 + }, + "leaf": { + "exponent": 5333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5804913444594174, + "rhs": 1792000000000000308760, + "rhs_bits": 71 + }, + "rows": { + "exponent": 5804913444594174, + "rhs": 896000000000000154416000, + "rhs_bits": 80 + } + } + }, + { + "log2_input": 224000000000000000000, + "powers": { + "alpha": { + "exponent": 11609826889188348, + "rhs": 1792000000000000154416, + "rhs_bits": 71 + }, + "compact": { + "exponent": 11609826889188348, + "rhs": 7168000000000000617600, + "rhs_bits": 73 + }, + "leaf": { + "exponent": 10666666666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11609826889188348, + "rhs": 3584000000000000308760, + "rhs_bits": 72 + }, + "rows": { + "exponent": 11609826889188348, + "rhs": 1792000000000000154416000, + "rhs_bits": 81 + } + } + }, + { + "log2_input": 448000000000000000000, + "powers": { + "alpha": { + "exponent": 23219653778376697, + "rhs": 3584000000000000154416, + "rhs_bits": 72 + }, + "compact": { + "exponent": 23219653778376697, + "rhs": 14336000000000000617600, + "rhs_bits": 74 + }, + "leaf": { + "exponent": 21333333333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 23219653778376697, + "rhs": 7168000000000000308760, + "rhs_bits": 73 + }, + "rows": { + "exponent": 23219653778376697, + "rhs": 3584000000000000154416000, + "rhs_bits": 82 + } + } + } + ], + "practical_runtime_claim": false + }, + "finite_bridge": { + "bit": { + "W": 133862024, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 27 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 843, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "7007/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "10366199626713/200000000000000000", + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "endpoint_copy": { + "1": 4073300 + }, + "exterior_23": { + "23": 62412800, + "529": 62412800 + }, + "exterior_25": { + "25": 63302624, + "525": 63302624 + }, + "growth_23": { + "1": 8146600, + "21": 8146600 + }, + "growth_25": { + "1": 8146600, + "23": 8146600 + }, + "internal_23": { + "1": 818158300, + "10": 4816200, + 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witness; inherited all-size transfer remains assumed" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/check.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/check.py new file mode 100644 index 0000000000..0630cfc19a --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/check.py @@ -0,0 +1,104 @@ +#!/usr/bin/env python3 +"""Screen complete paid profiles from independently replayed axis constructions.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions required') +from pathlib import Path +from collections import Counter +from fractions import Fraction as Q +import importlib.util,argparse,json,subprocess,tempfile,hashlib,os,shlex +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +from producer import check_sources +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m +exact=load('candidate_exact',ROOT/'research/rank-pair-refinement/refine.py') +balanced=load('candidate_assembly',DEP/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') + +def profile(path): + v=json.loads(Path(path).read_text()) + return v['profile'] if 'profile' in v else v + +def calculate(first,second): + profiles=[profile(first),profile(second)] + N=4073300;m=575 + assert [p['h'] for p in profiles]==[23,25] + W=2*N+sum(N//p['v']*p['R'] for p in profiles) + parts={'data':Counter({1:18*N,21:2*N,17:2*N,481:2*N}),'endpoint_copy':Counter({1:N})} + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 + assert p['rank_sum']==h*p['R']+p['loss']==sum(t*n for t,n in enumerate(p['blocks'])) + assert p['loss']==h*(h-1) + parts[f'internal_{h}']=Counter({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + parts[f'exterior_{h}']=Counter({h:bank,m-2*h:bank}) + parts[f'growth_{h}']=Counter({1:2*N,h-2:2*N}) + rows=sum(parts.values(),Counter());assert sum(t*n for t,n in rows.items())==m*W-1846900 + lo,hi,grid=1,71700000000000,10**18 + while lo+11 + result.update(status='Verified finite conditional witness; inherited all-size transfer remains assumed', + source_manifest_sha256=hashlib.sha256((HERE/'SOURCE.json').read_bytes()).hexdigest(), + axes=axes,eventual_bounds=balanced.cutoffs(result['finite_bridge'],result['assembly']), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113',pr71_kappa=Q(previous['kappa']), + relative_gain_pr71=result['kappa']/Q(previous['kappa'])-1, + pr71_complete_profile_exclusion_lower=old_lower)) + result=arithmetic.js(result) + path=HERE/'certificate.json' + if record:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:assert result==json.loads(path.read_text()) + print('PASS exact moment, next-grid exclusions, 47 inequalities and seven margins',flush=True) + return result + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--record',action='store_true');args=parser.parse_args();generate(args.record) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/producer.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/producer.py new file mode 100644 index 0000000000..8d68303a3b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/producer.py @@ -0,0 +1,132 @@ +#!/usr/bin/env python3 +"""Balanced coarse sums + anchored split/live frames + core ordering and coordinates. + +Composition for Thomas DiFiore with OpenAI Codex assistance. Apache-2.0. +PR69 coarse sums: eumemic. PR71 split/live composition: Chafik Boukhalfa. +Graph: Avi Eisenberg PR62; split operation: Rohan Garg PR59; reclamation: +Rohan Arun PR65/67, Dominik Scholz PR63/68, eumemic PR57. Original notices +and exact sources are retained under references/frame-compiler/pr69 and pr71. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +from hashlib import sha256 +import argparse,ast,gzip,importlib.util,json,types +from concurrent.futures import ProcessPoolExecutor +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +import split_pair_graph as provider +import split_pair_compiler as ancestor +from binary_frame_replay import replay + + +def check_sources(): + for folder in (DEP,ROOT/'references/frame-compiler/pr69'): + manifest=json.loads((folder/'SOURCE.json').read_text()) + for name,digest in manifest['files'].items(): + assert sha256((folder/name).read_bytes()).hexdigest()==digest,name + manifest=json.loads((HERE/'SOURCE.json').read_text()) + required={str((HERE/name).relative_to(ROOT)) for name in ('producer.py','check.py','graph_audit.py','independent_check.py','selection.json')} + assert required <= set(manifest['files']), 'Incomplete selected source closure' + for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + + +def reorder(c): + groups={} + for x in sorted(c.active): + if c.args[x]: groups.setdefault((c.core[x],c.union[x]),[]).append(x) + def key(item): + (core,cover),nodes=item + return cover.bit_count()-core.bit_count(),-core,cover,min(nodes) + ids=list(range(len(c.inputs)+1))+[x for _,nodes in sorted(groups.items(),key=key) for x in nodes] + mapping={x:i for i,x in enumerate(ids)} + args,core,cover,provenance=c.args,c.core,c.union,c.provenance + c.args=[tuple(mapping[y] for y in args[x]) if args[x] else None for x in ids] + c.core=[core[x] for x in ids];c.union=[cover[x] for x in ids] + c.provenance=[provenance[x] for x in ids] + c.active={mapping[x] for x in c.active};c.outputs={k:mapping[v] for k,v in c.outputs.items()} + c.support_in.cache_clear() + c.verify() + return c + + +def graph(h,ordered=True): + source=Path(provider._graph.__file__).read_text() + original=ROOT/'references/frame-compiler/pr69/scripts/experiments/balanced_coarse_compiler.py' + replacements={} + for node in ast.parse(original.read_text()).body: + if isinstance(node,ast.Assign): + for target in node.targets: + if isinstance(target,ast.Name) and target.id in ('BEFORE','AFTER'): + replacements[target.id]=ast.literal_eval(node.value) + assert source.count(replacements['BEFORE'])==1 + module=types.ModuleType('balanced_split_private_graph');module.__file__=provider._graph.__file__ + exec(compile(source.replace(replacements['BEFORE'],replacements['AFTER']),module.__file__+':balanced-coarse','exec'),module.__dict__) + previous=provider._graph + try: + provider._graph=module + c=provider.graph(h) + finally: + provider._graph=previous + return reorder(c) if ordered else c + + +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + +def compile_axis(h): + check_sources() + config=json.loads((HERE/'selection.json').read_text())['axes'][str(h)] + previous_graph,previous_order=provider.graph,provider.ordered_build + # graph() calls the original provider; keep that callable private while + # the inherited driver resolves the selected composed graph dynamically. + original_graph=previous_graph + def selected_graph(dimension): + provider.graph=original_graph + try:return graph(dimension) + finally:provider.graph=selected_graph + try: + provider.graph=selected_graph + provider.ordered_build=lambda original,dimension:original + compiled,word=ancestor.compile_axis(h) + finally: + provider.graph,provider.ordered_build=previous_graph,previous_order + compiled['graph_configuration']=config + word=relabel(word,config['coordinate_permutation']) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + path=HERE/f'word-{h}.json.gz' + with path.open('wb') as stream: + with gzip.GzipFile(filename='',fileobj=stream,mode='wb',mtime=0) as archive:archive.write(raw) + receipt=replay(path) + assert sha256(raw).hexdigest()==config['expected_word_sha256'] + axis=dict(configuration=config,compiled=compiled,replay=receipt, + word_sha256=sha256(raw).hexdigest(),gzip_sha256=sha256(path.read_bytes()).hexdigest()) + (HERE/f'axis-{h}.json').write_text(json.dumps(axis,indent=2)+'\n') + print(f'PASS fresh balanced/split/core word h={h}, roles={receipt["roles"]}',flush=True) + + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--h',type=int,choices=(23,25));args=parser.parse_args() + if args.h:compile_axis(args.h) + else: + with ProcessPoolExecutor(max_workers=2) as pool:list(pool.map(compile_axis,(23,25))) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-23.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-23.json new file mode 100644 index 0000000000..013f4e59c7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27136,"loss":506,"rank_sum":624634,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38292,"crt_matrices":5488,"crt_disagreements":0,"blocks":[0,355721,21666,6948,6524,3093,4314,2400,3266,1501,2094,1008,1374,586,732,353,307,139,62,16,0,23,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-25.json new file mode 100644 index 0000000000..1e3b6b89aa --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/profile-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35744,"loss":600,"rank_sum":894200,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52202,"crt_matrices":7623,"crt_disagreements":0,"blocks":[0,490052,26188,13531,7191,4637,5355,4229,3705,2610,2620,2080,1814,1357,1070,868,612,463,233,56,141,0,71,25,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/selection.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/selection.json new file mode 100644 index 0000000000..57cf3b6b65 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/references/pr74/research/balanced-split-frames/selection.json @@ -0,0 +1,86 @@ +{ + "source_pr71": "1bef94fd40a746452548c84a4a8f8834670a3113", + "source_pr69": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "axes": { + "23": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 22, + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 20, + 19, + 21 + ], + "expected_word_sha256": "8dc6696a274e70ca0af3fc49c4bdede362adaedc8dc322f335e3dab499f1ed48" + }, + "25": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 2, + 1, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "expected_word_sha256": "2c923afe366219ee3fffc9db063c91e44cdf7cbbdb62246b8e6a297dc440b577" + } + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/arithmetic/refine.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/indexed-r5/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + 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"scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1", + "scripts/partial_swap/graph.py": "fd8c567759e26a10d2bad05508fd0355eb70fb116664d4e06e1858d0d8cb2ef9", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + } + }, + "status": "Conditional exact arithmetic witness; general transfer proofs are dependencies" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "PR48": { + "author": "Chafik Boukhalfa", + "commit": "b7194b8586844956904b33e9fe18f0c75606c11b", + 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Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + } + }, + "gzip_sha256": "4629d45d5074f87706db46be3aa3cd369071cd215bc6560d641115aadcce54a0", + "word_sha256": "bd0cbf73756f2e4f8d3879ec6c7a194990eb9ec40aaf3580bdded6994798d920" + }, + "25": { + "compiled": { + "h": 25, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 36586, + "baseline_pr48_roles": 48329, + "histogram": { + "1": 55478, + "0": 416276, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + }, + "rank_mass": 915250, + "elementary_xors": 205650, + "stats": { + "augmentations": 286, + "regions": 73695, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json new file mode 100644 index 0000000000..346cf87ea3 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json @@ -0,0 +1,1087 @@ +{ + "accepted_moment": { + "degree": 8, + "lower": "34287951499999999998997315662315085394575263036671/34287951500000000000000000000000000000000000000000", + "rounding_denominator": 10000000000000000000000000000000000000000, + "saving": "5103158916233/100000000000000000", + "strict_gap": "2278828040192983762647964739/77927162500000000000000000000000000000000000000", + "terms": { + "1": { + "exp_lower": "5001621630918375893019301295747281962987/5000000000000000000000000000000000000000", + "exp_upper": "10003243261836751786038602591494564437549/10000000000000000000000000000000000000000", + "log_lower": "3177185020398675220004135749131/500000000000000000000000000000", + "log_upper": "6354370040797350440008271498263/1000000000000000000000000000000", + "weight": "61988/2833715" + 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rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.", + "All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.", + "Neither global optimality nor measured practical speedup is claimed." + ], + "rejected_moment": { + "degree": 8, + "lower": "8571987875000000003683551653063012975552828889113/8571987875000000000000000000000000000000000000000", + "rounding_denominator": 10000000000000000000000000000000000000000, + "saving": "51031589162331/1000000000000000000", + "strict_gap": "-920887913265753353254538048853/2142996968750000000000000000000000000000000000000", + "terms": { + "1": { + "exp_lower": "2000648652367350369920582377063597092877/2000000000000000000000000000000000000000", + "exp_upper": "250081081545918796240072797132949649399/250000000000000000000000000000000000000", + "log_lower": "3177185020398675220004135749131/500000000000000000000000000000", + "log_upper": 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json new file mode 100644 index 0000000000..42958fc74b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json @@ -0,0 +1,195 @@ +{ + "artifact_sha256": { + "frame-profiles-23.json": "fec377bcf1512a427674983256b900229d4133026445b6e680c6e1e6dde5af7d", + "frame-profiles-25.json": 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orientations PASS", + "word_length": 621342 + }, + "schedule": "cover-core", + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4" + }, + "25": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 48329, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 41186, + "elementary_xors": 205977, + "h": 25, + "histogram": { + "0": 416741, + "1": 55478, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "2": 115781, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 915250, + "roles": 36586, + "stats": { + "augmentations": 286, + "clearing_xors": 2154, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "regions": 73695 + } + }, + "gzip_sha256": "ad8b299697f90b185b6b791313b505586be97965519052100d097df6199e00c5", + "replay": { + "elementary_xors": 205977, + "full_basis_vectors": 41186, + "h": 25, + "histogram": { + "0": 224465, + "1": 55478, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "2": 115781, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569 + }, + "output_roles": 6925, + "rank_mass": 915250, + "roles": 36586, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 856108 + }, + "schedule": "reverse-node", + "word_sha256": "a54443429f47c486016771ce0436effda098e142afc52861c20957e9ff8e086b" + } + }, + "source_sha256": { + "research/pair-assembly/frame/frame_verify.py": "fafe25d57166a747eeb847444a2e02dd7eed19038b93a2c495014d147d04a8fb", + "research/pair-assembly/pair_graph.py": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "research/reordered-rank-pair/test_negative.py": "88832242e6f74e3fe08d109d4f21ff188a9ca0ae50c3e8f31da0243fe9501510", + "research/reordered-rank-pair/verify.py": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352", + "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3", + "scripts/experiments/binary_frame_profiles.cpp": "8e2e391d3ee57cbb1372c68e4aa031e1b861321536eabd642ada54e12e678669", + "scripts/experiments/binary_frame_replay.py": "392e78e62d7685c99a5888a7da743ea6c3dcad631af4a743c91e0c09348442bc", + "scripts/experiments/rank_pair_compiler.py": "9984aaccf880e4840402322d76678bfddb33ce7e494af78430a43429f51b85fd" + }, + "status": "Exact topological scheduling of unchanged PR63 graph/compiler; both physical orientations and fixed profiles checked" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json new file mode 100644 index 0000000000..3b648dbe21 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "loss": 506, + "rank_sum": 642620, + "field_prime": 2305843009213693951, + "frames": 52475, + "distinct_matrices": 36399, + "crt_matrices": 6049, + "crt_disagreements": 0, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json new file mode 100644 index 0000000000..19cc34b4ca --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json @@ -0,0 +1,40 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "loss": 600, + "rank_sum": 915250, + "field_prime": 2305843009213693951, + "frames": 73697, + "distinct_matrices": 50394, + "crt_matrices": 8127, + "crt_disagreements": 0, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json new file mode 100644 index 0000000000..2883a5f7c9 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "frames": 52475, + "distinct_transitions": 138016, + "singles": 15939, + "rank_mass": 642620, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 53320, + "2": 77409, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "21": 165, + "22": 23 + }, + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json new file mode 100644 index 0000000000..3b4bc33ff6 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json @@ -0,0 +1,35 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "frames": 73697, + "distinct_transitions": 190838, + "singles": 20700, + "rank_mass": 915250, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69278, + "2": 108881, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25 + }, + "word_sha256": "a54443429f47c486016771ce0436effda098e142afc52861c20957e9ff8e086b", + "copied_centers": 25, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz new file mode 100644 index 0000000000..3a7c7c41c1 Binary files /dev/null and b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz differ diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz new file mode 100644 index 0000000000..6a239a3e9f Binary files /dev/null and b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz differ diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + 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a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 at the new bit saving, +and the new complete profile has exact upper moment <1. All47 strict assembly +conditions and seven margins pass. **53 Lean endpoints** pass:34 new universal, +15 concrete,4 reused rational-helper lemmas. No omitted proof, project axiom or +native decision shortcut. The math scope includes dirty-word/complement safety, +coordinate conjugacy, fresh-kernel clearing, actual finite rounding and old-profile +rejection. It does not formalize the Python/C++ compiler or the all-size theorem. + +## Reproduce the accepted words + +Use an external checkout of frozen PR62 commit +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No newer sources are consumed. +See `verification/README.md` to compile its exact C++17 profiler, then run: + +``` +python verification/verify_words.py --upstream UPSTREAM --profiler PROFILER --word23 words/word-23.json.gz --word25 words/word-25.json.gz --output work/recheck +python verification/check_guards.py words/word-23.json.gz +python verification/check_guards.py words/word-25.json.gz +cd math +lake build Frozen62Research +``` + +The verifier checks immutable sources and its own adapter hashes, full input/dirty +bases in both orientations, exact source/scatter inventory, every literal frame +transition and all fixed-I+J profiles with bounded-minor and CRT checks. It rejects +optimized Python assertion mode. Use the supplied words for authoritative replay; +floating discovery prices propose candidates and have no trusted-proof role. +Discovery source snapshots, exact oracle fixtures (gzip-compressed) and matching +seeds retain original byte hashes. `discovery/SEARCH.md` explains the algorithms, +heuristic boundary and experimental commands. Historical workspace paths in the +source-generation receipts identify the original run; the accepted-word replay +uses the explicit upstream argument and needs no private directory layout. +Portable discovery regeneration: + +``` +python discovery/regenerate_portable.py --upstream UPSTREAM --work work/regenerate +``` + +This rewrites workspace paths only and checks both raw words and deterministic +gzip against the accepted words. Floating discovery is outside the trusted +certificate; the independent word/profile verifier establishes acceptance. + +The one-hour session froze information through #62. The unchanged data geometry +and its rational recovery are inherited; selected physical words/profile checks +are fresh. All-size analytic, compiler/frame transfer, finite-alphabet tape, +routing, prime selection/recovery and eventual-threshold contracts remain +conditional. No practical runtime or global-optimality claim is made. + +Alejandro Zarzuelo Urdiales is the human author/developer, following earlier +Archivara and personal July/October matrix/parity work developed with multiple +AI tools. This synthesis involved substantial OpenAI Codex assistance. Known +linear algebra, matroid exchange, dirty uncomputation and concavity principles +retain prior-work status. The finite construction credits Avi Eisenberg/ikeboy +(#62 interval/core-aware graph), eumemic (#57 frame compiler), Chafik Boukhalfa +(#60 ranking and earlier exact profiling), Rohan Arun and other retained notices. +The prior matrix/parity source is in `../matrix-exponent-synthesis/` and prior +Gaussian work in PR45. Its product counts retain their separate arithmetic scope. +The paper is supplied as LaTeX source; no newly compiled PDF is claimed. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md new file mode 100644 index 0000000000..b8dd669634 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md @@ -0,0 +1,136 @@ +# Local frame-compiler search, frozen through PR62 + +All experiments in this directory use the pinned PR62 pair graph at +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No later community source is consumed. +The original checkout is unchanged. Each emitted word and compiler copy has +a SHA256 recorded in its `compiled.json`; changed words are sent separately +to the independent literal replay and profile verifier. + +## New dependency-circuit choices + +The inherited compiler reduces retired fresh-signal rows against the current +live anchors and an echelon basis of compatible retired rows. Instead of +accepting the first dependent retired row, the new selectors collect the +available fundamental dependency circuits and choose a circuit by one of: + +- total charged target/provider rank growth (`all_growth`); +- number and rank growth of other retired providers (`all_collateral`); +- anchor-only dependence before general retired dependence (`anchor_first`); +- actual physical transition child-profile moment cost (`profile_cost*`). + +Every clearing XOR and every target/provider frame promotion is still emitted +and charged. A zero fresh-signal row can contain arbitrary physical dirty state; +its reuse is justified by the complete reversible word, not by claiming that +the physical register is initialized to zero. The compiler runs both complete +dirty-basis orientations, and the independent verifier repeats them. + +For the last selector let `C(A,B) = sum_t n_t(A,B) F_t`, where the `n_t` are +the exact inherited fixed-I+J pivot-run profile of the physical frame transition +and `F_t = t exp(a log(m/t))`. A candidate target `s` at old frame `A_s`, cleared +into frame `G` with providers `z`, is priced by + +``` +C(A_s,G) - C(A_s,I) + + sum_z [C(A_z,G) + C(G,I) - C(A_z,I)]. +``` + +This accounts for immediate promotions and the change in deferred cleanup, +assuming each other retired provider remains retired until cleanup. Future +reuse couples decisions, so this is a discovery heuristic, not an additive +global optimality certificate. Linear rank mass cancels between candidates; +`t*expm1(a*log(m/t))` avoids cancellation in floating discovery prices. +Missing transition profiles are recorded and collected for the next iteration. +Once a run has zero missing pairs, every local price uses an actual transition +profile. The final saving is accepted only through exact rational whole-profile +moment bounds and all assembly gates. + +`build_pair_oracle.py` is a local adaptation of the frozen C++ profiler that +additionally exports each transition histogram. It preserves the projector, +pivot, bounded-minor and three-prime CRT routines. Its synthetic transition-list +input is an oracle request, not a physical executable word. Each immutable +profile dump and the source/header hashes are recorded. + +## Moment-ordered carry selection + +The `--weighted` experiment orders the inherited linear/partition-matroid +candidate edges by their physical transition moment change before the original +greedy initialization and augmenting paths. For a value produced at `P`, +preserved through donor frame `G`, and carried to future target `T`, its +no-reclamation child-cost change is + +``` +C(G,T) - C(G,I) - C(0,P) - C(P,T). +``` + +At fixed cardinality, role and external-volume corrections are common to all +edge choices in the same axis. The inherited augmenting algorithm still seeks +maximum cardinality; it does not optimize the weights globally. Reclamation +adds coupling, so only the changed whole-word profile can establish an actual +improvement. This experiment makes no minimum-cost matroid claim. + +The `--exchange` variant starts from the frozen original maximum-cardinality +matching and tries bounded improving one-edge exchanges. A new edge may replace +the old donor of the same use when its donor block stays linearly independent; +or it may replace a selected edge in the same donor block and serve an unused +use. Both preserve cardinality and distinct-use constraints. The `--cycle` +variant additionally tests two-edge donor/use cycles, checking the independence +of both changed blocks. No improving two-edge cycle was found in the tested +native-price instance; this is not a proof that longer cycles cannot improve it. + +## Joint basis and schedule search + +`--basis shift1` profiles all candidate physical transitions after the point +permutation `i -> (i+1) mod h`, while preserving their original frame IDs. +Matching and reclamation are then priced in that basis. The emitted word is +renamed by `relabel_word.py`: all frame masks, canonical source/output triples, +common points and scatter port indices change together. Scratch slots and +literal XOR instructions are retained. The complete triple family and the +permutation-invariant `I+J` basis are inherited; every final renamed word still +gets fresh full-basis and actual physical-profile verification. + +This joint search differs from merely relabeling an already selected schedule: +the selected carries and clearing circuits are optimized under the new ordered +pivot-run prices. It remains a bounded discovery heuristic. + +## Regeneration + +The frozen graph/matching setup and a moment-cost exchange run are generated by: + +``` +python -S collect_matching_pairs.py --h 23 +python -S build_pair_oracle.py --h 23 --strategy matching_collect +python -S run_strategy.py --h 23 --strategy profile_cost --exchange +``` + +Repeat at `h=25`. For joint search, add `--basis shift1` to the oracle and +strategy commands. Reclamation may encounter transitions absent from the +initial carry-edge inventory. Run the oracle again on the emitted strategy +directory with `--incremental`, then run a new strategy label. The new label +must start with `profile_cost`; output directories are never overwritten. +`compiled.json` records the exact oracle dump hash, missing-pair count, word +hashes and source pin. Immutable earlier oracle dumps are retained by SHA256. +Use `--oracle path/to/the-immutable-dump.jsonl` to reproduce the prices of a +specific recorded run instead of consuming the subsequently enlarged cache. +The initial compiler matching cache is accepted only if its complete candidate +edge list matches the current frozen graph and every restored selected block +passes the same linear-independence check. + +The runner saves an immutable source copy and its hash for later runs. Floating +`expm1` prices at discovery saving `a=0.00005103` select proposals only. Neither +those prices nor their reported local gains are used as an arithmetic witness. + +## Acceptance boundary + +The independent verifier checks all input and dirty basis vectors in both +orientations, exact literal-scatter incidences, causal nested physical frames, +event equality reconstructed from the actual XOR word, rank mass, actual child +profiles and CRT agreement. It then computes the whole mixed-axis recurrence +and exact rational moment/assembly witnesses. Existing all-size geometry, +analytic envelopes, compiler/tape arguments and the surrounding reduction are +inherited from frozen PR62. A finite profile improvement does not by itself +formally prove those inherited hypotheses. + +Reduced XOR count alone is not accepted as an exponent improvement. In this +search `all_collateral` and `anchor_first` reduced clearing XORs but worsened +the certified characteristic. Actual child-size distributions decide the +saving, even when both physical-role counts and total rank mass are unchanged. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py new file mode 100644 index 0000000000..7c154b1a29 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py @@ -0,0 +1,275 @@ +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +import sys;sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'matrix-synthesis/bridge/pr62/references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s,add=True): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>s&1;e^=1<=prices[f]-1e-14:continue + if not can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:-prices[z])if prices[e] /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/NOTICE b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/NOTICE new file mode 100644 index 0000000000..8adab44ba3 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/NOTICE @@ -0,0 +1,324 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/README.md new file mode 100644 index 0000000000..4a9b481aa3 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/README.md @@ -0,0 +1,172 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/SOURCE.json new file mode 100644 index 0000000000..c8cc31f3d0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/SOURCE.json @@ -0,0 +1,120 @@ +{ + "commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "Makefile": "6e9e48a677b2f66643226840f574a6535e3564ffb0c72284b60302684a5dfbe4", + "NOTICE": "1e0702aa665673508fa91169163c5785d680637fff636fda01f36e3b127c3ee0", + "README.md": 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566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "rank_mass": 900975, + "singles": 20700, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 2300, + "word_sha256": "4c956749f0ec72c61875c51099afdf23e69ccea268a9b43b8d46da2ffdb24903" + } + } + }, + "bit_saving": "12854322426487/250000000000000000", + "certificate_sha256": "0fcb53fa374273efab6370953c966e8fa065dbfdba43691843a4788cb2cda42e", + "kappa": "51414646104039/1000000000000000000", + "margins": 7, + "producer_words_regenerated_and_matched": true, + "scope": "Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.", + "source_binding": "Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.", + "status": "PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly", + 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a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py new file mode 100644 index 0000000000..c7fd42867d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py @@ -0,0 +1,196 @@ +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit', 'complex'): + data = finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": "41187950749917624099/1000000000000000000000000", + "cell_above_band": "666666666665666652937349833360791967/1333388250600666556832132000000000000", + "compact_leaf": "26927049500082375901/1000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "13729317166639208033/333347062650166639208033", + "epsilon_positive": "333333333333000000000000/333347062650166639208033", + "g1_above_kappa": "3408408254232349301008147/3333470626501666392080330000000000000", + "g2_above_kappa": "4241/2500000000000", + "g3_above_kappa": "74937627730682908927817/3333470626501666392080330000000000000", + "g4_above_kappa": "4241/2500000000000", + "g5_above_kappa": "5299956450675231223831763/13333882506006665568321320000000000000", + "g6_above_kappa": "11966897703678564007992423/13333882506006665568321320000000000000", + "g7_above_kappa": "3333196040161742016173902349301008147/3333470626501666392080330000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "13729317166639208033/333347062650166639208033", + "lambda_above_internal": "82375901/2000000000000000000000000", + "lambda_above_sigma": "61024099000082375901/2000000000000000000000000", + "lambda_above_tau": "82375901/2000000000000000000000000", + "lambda_prime_above_lambda": "82375901/2000000000000000000000000", + "lambda_prime_below_one": "41187950499917624099/1000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "21966907133275670202633360791967/533355300240266622732852800000000000", + "phase_leaf_above_bit": "53854099/2000000000000", + "phase_local": "109834536999766601613833360791967/2666776501201333113664264000000000000", + "prime_interval_packing": "13729317166639208033/333347062650166639208033", + "q_below_internal": "82375901/1000000000000000000000000", + "q_below_leaf": "26927049500082375901/1000000000000000000000000", + "q_below_reservations": "1/4000000000000", + "q_positive": "41187950499917624099/1000000000000000000000000", + "record_suffix": "13729317166639208033/333347062650166639208033", + "row_product_gap": "6548/25", + "short_record_fallback": "666639206901368489075295096355187267/666694125300333278416066000000000000", + "small_field_exposure": "1/1000000000000" + }, + "finite_bridge": { + "bit": { + "W": 177530859, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "degree": 2000, + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": 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Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 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"multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json new file mode 100644 index 0000000000..42958fc74b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json @@ -0,0 +1,195 @@ +{ + "artifact_sha256": { + "frame-profiles-23.json": "fec377bcf1512a427674983256b900229d4133026445b6e680c6e1e6dde5af7d", + "frame-profiles-25.json": "28b4b911e26fbc02dde0d2e1458ed16227f756126ab8144d6d45e164d1165262", + "frame-transitions-23.json": "86646f1110595294cccc15603c552f0a153574a690b69c3b144d84a449891103", + "frame-transitions-25.json": "c333c348665d12b95e168ca4fac48bfdca335104edd0f29c81fe94bec292e774", + "frame-word-23.json.gz": "a44e038e1c548ea8ac31dd04acc2bba7951b22e17df7b7ad3464ea2b504a8da4", + "frame-word-25.json.gz": "ad8b299697f90b185b6b791313b505586be97965519052100d097df6199e00c5", + "paired-candidate.json": "34a500d739537235dfc5d24325c22856ca4567b9eac998a3bce9b13db5501940" + }, + "axes": { + "23": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 36432, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 31460, + "elementary_xors": 149137, + "h": 23, + "histogram": { + "0": 302057, + "1": 42694, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "2": 82722, + "21": 165, + "22": 23, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 642620, + "roles": 27918, + "stats": { + "augmentations": 220, + "clearing_xors": 1577, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "regions": 52473 + } + }, + "gzip_sha256": "a44e038e1c548ea8ac31dd04acc2bba7951b22e17df7b7ad3464ea2b504a8da4", + "replay": { + "elementary_xors": 149137, + "full_basis_vectors": 31460, + "h": 23, + "histogram": { + "0": 162914, + "1": 42694, + "10": 442, + "11": 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orientations PASS", + "word_length": 856108 + }, + "schedule": "reverse-node", + "word_sha256": "a54443429f47c486016771ce0436effda098e142afc52861c20957e9ff8e086b" + } + }, + "source_sha256": { + "research/pair-assembly/frame/frame_verify.py": "fafe25d57166a747eeb847444a2e02dd7eed19038b93a2c495014d147d04a8fb", + "research/pair-assembly/pair_graph.py": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "research/reordered-rank-pair/test_negative.py": "88832242e6f74e3fe08d109d4f21ff188a9ca0ae50c3e8f31da0243fe9501510", + "research/reordered-rank-pair/verify.py": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352", + "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3", + "scripts/experiments/binary_frame_profiles.cpp": 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "loss": 506, + "rank_sum": 642620, + "field_prime": 2305843009213693951, + "frames": 52475, + "distinct_matrices": 36399, + "crt_matrices": 6049, + "crt_disagreements": 0, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json new file mode 100644 index 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json new file mode 100644 index 0000000000..2883a5f7c9 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "frames": 52475, + "distinct_transitions": 138016, + "singles": 15939, + "rank_mass": 642620, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 53320, + "2": 77409, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "21": 165, + "22": 23 + }, + "word_sha256": 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + "exponent": 5333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5715743812, + "rhs": 1792000000313576, + "rhs_bits": 51 + }, + "rows": { + "exponent": 5715743812, + "rhs": 896000000156824000, + "rhs_bits": 60 + } + } + }, + { + "log2_input": 224000000000000, + "powers": { + "alpha": { + "exponent": 11431487624, + "rhs": 1792000000156824, + "rhs_bits": 51 + }, + "compact": { + "exponent": 11431487624, + "rhs": 7168000000627232, + "rhs_bits": 53 + }, + "leaf": { + "exponent": 10666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11431487624, + "rhs": 3584000000313576, + "rhs_bits": 52 + }, + "rows": { + "exponent": 11431487624, + "rhs": 1792000000156824000, + "rhs_bits": 61 + } + } + }, + { + "log2_input": 448000000000000, + "powers": { + "alpha": { + "exponent": 22862975248, + "rhs": 3584000000156824, + "rhs_bits": 52 + }, + "compact": { + "exponent": 22862975248, + "rhs": 14336000000627232, + "rhs_bits": 54 + }, + "leaf": { + "exponent": 21333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 22862975248, + "rhs": 7168000000313576, + "rhs_bits": 53 + }, + "rows": { + "exponent": 22862975248, + "rhs": 3584000000156824000, + "rhs_bits": 62 + } + } + } + ], + "practical_runtime_claim": false + }, + "kappa": "40827/800000000", + "next_kappa": "318961/6250000000", + "next_kappa_rejection": "{'g1_above_kappa': '-25408022593116799041/7102635201420453820506250000000', 'g3_above_kappa': '-5201705247125960457841/1136421632227272611281000000000000', 'g5_above_kappa': '-7640875416065173165777/1818274611563636178049600000000000', 'g6_above_kappa': '-33658690551416775383761/9091373057818180890248000000000000'}", + "original_enclosure_control": { + "accepted_upper": "427922022655051425592169455669348999419009338821677321501934579031509793316011927849852932699225587520480274623290826519124585131702799274967695430254567113650998884459986946222692530282749027853246814000572815342011972280832203653626757194588235745687874105909336892415629002940540277569675953192803096179140323199169875932058482212840371519373866332987776983981442275480629595879092440778438065834410270423292532877965451564571150969903518733283745770147929604915103094966966240445718551419238205360172260389165815355293860586787487668007987689744585745259297708409486845374929838902410526770296527117452860612190765279746966315757114757646249443956020657651637850471083396567352186238660458491615294604389003317389825219053116168473153626947262543915434579501546193988862612230828605213616950127673267971569642351835151332191639228898384399684069201926146521990048728093044781289653532998958679374426311189560250341590145887508815021337226982815008224357898461730107482372032845888428476273500999760300211786400006201411895378711403441679516543048925021677151249124774565210588951830515783148269750340702961227551/427922022656065148722015624802653702889498564421131911283499341667573520226931037010841800905471906532344178836996138043716400845851217866305783744362952178488692163617667760947934446961428764096857095662125776648371730944750850740376437391609342381012534311915175448066736517476339673099556706774420618964194148648273392198066357729130169733561134843302857240883248026154958104699812690626052696940220399106081385425042375485602542555097186568052507330835744941604979041042724146442866160606543845260686788873587136675704407457814823973491248098778928607362558510538701395621352496475077156310639504247824069338077266718928997258973439362819271794470658904562860362470215133491491305622841328989108583065554731667738937158958161399293136952726957825424616696098290625805073806865420810062253320746566043770582998650738545122821954094593047815197564256009823257422725379706679933315631514838786135447434356419391187561619401952168548631044553632502869921434523792993783307013326156305798890689568359302672301544894715282222433613932715358768884516049207059704442128612279932500000000000000000000000000000000000000000", + "next_bit_lower": "374050380000830479912607937870818083834173718615907103079616878943322706260497332605534066060136407627149268792108716494485294881071/374050380000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + } + }, + "comparison": { + "additional_precision_gain": "2116843/200000000000000000", + "difference": "1238116843/200000000000000000", + "difference_pr65": "59693903/12500000000000000", + "kappa": "10206752116843/200000000000000000", + "pr63_kappa": "5102757/100000000000", + "pr65_kappa": "2041159402879/40000000000000000", + "structural_gain_on_original_grid": "309/50000000000" + }, + "grid_denominator": 1000000000000000000, + "next_bit_saving": "5103636516201/100000000000000000", + "preferred": { + "assembly": { + "absorption_gap": "12957517239351787231794417587/100005103636516190692726967598200000000000000000", + "constraints": { + "K_dominates_log": "25518182705927945452132037536365162009/500025518182580953463634837991000000000000", + "K_geometry": "375025518182705953463634837991/500025518182580953463634837991000000000000", + "a_below_b": "20663634837991/1000000000000000000", + "a_positive": "51036365162009/1000000000000000000", + "alpha_below_one": "999999999999500025518182580953463634837991/1000051036365161906927269675982000000000000", + "alpha_below_one_fourth": "249961722725628595322730323966963634837991/1000051036365161906927269675982000000000000", + "alpha_positive": "51036365661881409087095028536365162009/1000051036365161906927269675982000000000000", + "artificial_boundary": "28001633163690681098227177374284390904513973/4000204145460647627709078703928000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "499974481817294046536365162009/500000000000000000000000000000", + "c_positive": "25518182705953463634837991/500000000000000000000000000000", + "cell_above_band": "999999999998499974481817419046536365162009/2000102072730323813854539351964000000000000", + "compact_leaf": "8539317419046536365162009/500000000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "25518183080953463634837991/500025518182580953463634837991", + "epsilon_positive": "499999999999500000000000000000/500025518182580953463634837991", + "g1_above_kappa": "100005116594033430044514199392617587/100005103636516190692726967598200000000000000000", + "g2_above_kappa": "1302288897/500000000000000000", + "g3_above_kappa": "12957517239351787231794417587/100005103636516190692726967598200000000000000000", + "g4_above_kappa": "1302288897/500000000000000000", + "g5_above_kappa": "37501926821210810861559844643742587/100005103636516190692726967598200000000000000000", + "g6_above_kappa": "87504478639468906207923328442842587/100005103636516190692726967598200000000000000000", + "g7_above_kappa": "99994896363383814423867065831844514199392617587/100005103636516190692726967598200000000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "25518183080953463634837991/500025518182580953463634837991", + "lambda_above_internal": "51036365162009/1000000000000000000000000000000", + "lambda_above_sigma": "20663634838042036365162009/1000000000000000000000000000000", + "lambda_above_tau": "51036365162009/1000000000000000000000000000000", + "lambda_prime_above_lambda": "51036365162009/1000000000000000000000000000000", + "lambda_prime_below_one": "25518182580953463634837991/500000000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "40829092429500023633159832136365162009/800040829092129525541815740785600000000000", + "phase_leaf_above_bit": "17078634837991/1000000000000000000", + "phase_local": "204145464147602190896122974536365162009/4000204145460647627709078703928000000000000", + "prime_interval_packing": "25518183080953463634837991/500025518182580953463634837991", + "q_below_internal": "51036365162009/500000000000000000000000000000", + "q_below_leaf": "8539317419046536365162009/500000000000000000000000000000", + "q_below_reservations": "1/4000000000000", + "q_positive": "25518182580953463634837991/500000000000000000000000000000", + "record_suffix": "25518183080953463634837991/500025518182580953463634837991", + "row_product_gap": "6548/25", + "short_record_fallback": "499974480514563711027641740160491885440816916081/500025518182580953463634837991000000000000000000", + "small_field_exposure": "1/1000000000000" + }, + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "margins": { + "g1": "25518183080953463634837991/500025518182580953463634837991", + "g2": "51036365162009/1000000000000000000", + "g3": "25518182580927945452257037536365162009/500025518182580953463634837991000000000000", + "g4": "51036365162009/1000000000000000000", + "g5": "40829092429500023633159832136365162009/800040829092129525541815740785600000000000", + "g6": "204145464147602190896122974536365162009/4000204145460647627709078703928000000000000", + "g7": "499999999999500000000000000000/500025518182580953463634837991" + }, + "minimum_margin": "25518182580927945452257037536365162009/500025518182580953463634837991000000000000", + "parameters": { + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": "1", + "a_bit": "51036365162009/1000000000000000000", + "a_complex": "717/10000000", + "alpha_squared_power": "51036365661881409087095028536365162009/1000051036365161906927269675982000000000000", + "beta": "1/20", + "c": "25518182705953463634837991/500000000000000000000000000000", + "delta": "1/8000000000000", + "epsilon": "499999999999500000000000000000/500025518182580953463634837991", + "h": "1/1000000000000", + "kappa": "10206752116843/200000000000000000", + "lambda_": "999948963634838042036365162009/1000000000000000000000000000000", + "lambda_prime": "499974481817419046536365162009/500000000000000000000000000000", + "q": "25518182580953463634837991/500000000000000000000000000000", + "sigma": "9999283/10000000", + "tau": "999948963634837991/1000000000000000000" + }, + "recurrence": { + "internal": "999948963634837991/1000000000000000000", + "leaf": "199986377/200000000", + "reservations": "499974481817294046536365162009/500000000000000000000000000000" + }, + "scoped_limit": "51036365162009/1000051036365162009" + }, + "eventual_bounds": { + "additional_eventual_conditions": [ + "BHP prime threshold and distinct-prime packing", + "Fixed rational basis, eligible common prime and native table setup", + "Catalogue/descriptor domination, logarithm absorption, exact recovery" + ], + "all_interval_argument": "For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). Successive intervals double LHS; the positive affine RHS grows at most linearly, so 2^j >= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956143, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + "exponent": 5333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5715743812, + "rhs": 1792000000313576, + "rhs_bits": 51 + }, + "rows": { + "exponent": 5715743812, + "rhs": 896000000156824000, + "rhs_bits": 60 + } + } + }, + { + "log2_input": 224000000000000, + "powers": { + "alpha": { + "exponent": 11431487624, + "rhs": 1792000000156824, + "rhs_bits": 51 + }, + "compact": { + "exponent": 11431487624, + "rhs": 7168000000627232, + "rhs_bits": 53 + }, + "leaf": { + "exponent": 10666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11431487624, + "rhs": 3584000000313576, + "rhs_bits": 52 + }, + "rows": { + "exponent": 11431487624, + "rhs": 1792000000156824000, + "rhs_bits": 61 + } + } + }, + { + "log2_input": 448000000000000, + "powers": { + "alpha": { + "exponent": 22862975248, + "rhs": 3584000000156824, + "rhs_bits": 52 + }, + "compact": { + "exponent": 22862975248, + "rhs": 14336000000627232, + "rhs_bits": 54 + }, + "leaf": { + "exponent": 21333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 22862975248, + "rhs": 7168000000313576, + "rhs_bits": 53 + }, + "rows": { + "exponent": 22862975248, + "rhs": 3584000000156824000, + "rhs_bits": 62 + } + } + } + ], + "practical_runtime_claim": false + }, + "kappa": "10206752116843/200000000000000000", + "next_kappa": "6379220073027/125000000000000000", + "next_kappa_rejection": "{'g3_above_kappa': '-54404741498227752163082843757/62503189772822619182954354748875000000000000000'}" + }, + "profile_path": "research/slot-cost-rank-pair/paired-candidate.json", + "profile_sha256": "be0322ad60f73923953f242eaffaf114ff12438e8617dae38888b77fa03184cc", + "proof_limits": [ + "The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.", + 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a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) ++ slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();pending={};stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): +@@ -149,7 +151,8 @@ + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 +- return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) ++ endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 ++ return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} +@@ -161,6 +164,9 @@ + old,e=bb[p];row^=old;expr^=e + return expr + for s in anchors:ins(s) ++ for s,target in pending.items(): ++ if contains(blocks[frames[s]]['frame'],blocks[g]['frame']) and contains(blocks[g]['frame'],blocks[target]['frame']): ++ ins(s);stats['live_anchor_candidates']+=1 + best=None + # Inspect every eligible dependent candidate across all retired ranks. + # Rank the actual fixed-basis growth/cleanup profiles by an integer entropy score. +@@ -176,7 +182,9 @@ + if best is None or key= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and kappa > previous_kappa + bridge = json.loads((OLD/'certificate.json').read_text())['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/split-pair/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr67_commit='b3745601e947a94316bf25c2c6263d93c06e3364', + pr67_kappa=previous_kappa, ratio_pr67=kappa/previous_kappa, + absolute_gain_pr67=kappa-previous_kappa, + pr67_complete_profile_exclusion_lower=prior65_lower, + full_pr67_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected split-pair partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'split-pair-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py new file mode 100644 index 0000000000..1290ef2eb8 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py @@ -0,0 +1,275 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py new file mode 100644 index 0000000000..7908c963a4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py @@ -0,0 +1,78 @@ +#!/usr/bin/env python3 +"""Replay the aligned split-pair/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from split_pair_compose import compose, check_sources +from split_pair_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'split-pair-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='split-pair-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + 'c++', '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'split-pair-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'split-pair-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'split-pair-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'split-pair-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'split-pair-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/tests/test_split_pair.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/tests/test_split_pair.py new file mode 100644 index 0000000000..5088cff133 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/tests/test_split_pair.py @@ -0,0 +1,238 @@ +"""Physical and exact-arithmetic controls for the aligned split/pair witness.""" +from copy import deepcopy +from fractions import Fraction +from itertools import combinations +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile +import unittest +from unittest.mock import patch + +ROOT = Path(__file__).resolve().parents[1] +EXPERIMENTS = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXPERIMENTS)) +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from binary_frame_math import moment + + +class SplitPairControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.words = {h: json.loads(gzip.decompress((ROOT/f'certificates/split-pair-word-{h}.json.gz').read_bytes())) + for h in (23,25)} + + def reject_mutation(self, mutate, checker='both'): + for h, original in self.words.items(): + with self.subTest(h=h), tempfile.TemporaryDirectory() as directory: + changed = deepcopy(original) + mutate(changed) + path = Path(directory)/'word.json' + path.write_text(json.dumps(changed, separators=(',', ':'))+'\n') + with self.assertRaises((AssertionError, ValueError, IndexError, KeyError)): + if checker != 'transitions': + replay(path) + if checker != 'replay': + prepare(path, Path(directory)/'transitions.bin') + + def test_selected_words_pass_independent_replay(self): + recorded = json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + actual = replay(ROOT/f'certificates/split-pair-word-{h}.json.gz') + self.assertEqual(json.loads(json.dumps(actual)), recorded['axes'][str(h)]['replay']) + + def test_omitted_literal_xor_is_rejected(self): + self.reject_mutation(lambda word: word['ops'].pop(0)) + + def test_self_xor_is_rejected(self): + def mutate(word): + word['ops'][0][1] = word['ops'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_non_nested_operation_frame_is_rejected(self): + def mutate(word): + narrow = next(i for i,(core,cover) in enumerate(word['frames']) if core == cover) + operation = next(op for op in word['ops'] if word['frames'][op[2]][0] != word['frames'][op[2]][1]) + operation[2] = narrow + self.reject_mutation(mutate) + + def test_aliased_terminal_role_is_rejected(self): + def mutate(word): + word['outputs'][1][0] = word['outputs'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_missing_copied_center_is_rejected(self): + def mutate(word): + index = next(i for i,(_,_,_,target) in enumerate(word['outputs']) if len(target) == 1) + word['outputs'].pop(index) + self.reject_mutation(mutate) + + def test_omitted_transition_cannot_reduce_paid_profile(self): + self.reject_mutation(lambda word: word['events'].pop(0), 'transitions') + + def test_understated_physical_width_is_rejected(self): + def mutate(word): + word['R'] -= 1 + self.reject_mutation(mutate) + + def test_complete_pr67_profile_fails_new_bit_saving(self): + from split_pair_arithmetic import refine + previous = json.loads((ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/paired-candidate.json').read_text())['bit'] + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + result = refine.exact_moment(previous['m'], previous['W'], {int(t): n for t,n in previous['child_multiplicities'].items()}, Fraction(current['bit_saving'])) + self.assertGreater(result['lower'], 1) + self.assertGreater(Fraction(current['kappa']), Fraction(current['comparison']['pr67_kappa'])) + + def test_private_import_preserves_path_and_arithmetic_module(self): + import split_pair_graph as provider + import split_pair_arithmetic as arithmetic + sentinel = object() + existing = sys.modules.get('refine', sentinel) + previous_path = sys.path[:] + graph, schedule = provider._private_modules() + refine, audit = arithmetic.private_arithmetic() + self.assertIs(audit.refine, refine) + self.assertIs(sys.modules.get('refine', sentinel), existing) + self.assertEqual(sys.path, previous_path) + + def test_failed_graph_build_restores_original_providers(self): + import split_pair_graph as provider + previous_class, previous_points = provider._graph.circuit_class, provider._graph.alternating_points + with patch.object(provider._graph, 'graph', side_effect=RuntimeError('deliberate graph failure')): + with self.assertRaises(RuntimeError): + provider.graph(23) + self.assertIs(provider._graph.circuit_class, previous_class) + self.assertIs(provider._graph.alternating_points, previous_points) + + def test_failed_compilation_restores_engine_graph_and_schedule(self): + import split_pair_compiler as producer + previous_graph, previous_build = producer.compiler.graph, producer.compiler.build + missing = object() + runtime = {name:getattr(producer.compiler,name,missing) for name in ('PENDING_COST','ORACLE_EXE','ORACLE_INPUT','oracles')} + with patch.object(producer.compiler, 'compile_', side_effect=RuntimeError('deliberate compiler failure')): + with self.assertRaises(RuntimeError): + producer.compile_axis(23) + self.assertIs(producer.compiler.graph, previous_graph) + self.assertIs(producer.compiler.build, previous_build) + for name,value in runtime.items(): + self.assertIs(getattr(producer.compiler,name,missing),value) + + def test_uncertified_configurations_are_rejected(self): + import split_pair_graph as provider + wrong_anchor = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_anchor['anchor'] = False + boolean_group = deepcopy(provider.EXPECTED_CONFIGS[23]); boolean_group['groups'][0] = True + changed_schedule = deepcopy(provider.EXPECTED_CONFIGS[23]); changed_schedule['schedule'] = 'reverse-node' + for changed in (wrong_anchor, boolean_group, changed_schedule): + with self.subTest(configuration=changed), patch.object(provider.json, 'loads', return_value=changed): + with self.assertRaises(ValueError): + provider.configuration(23) + for dimension in (True, 22, 24, '23'): + with self.subTest(dimension=dimension), self.assertRaises(ValueError): + provider.configuration(dimension) + + def test_recursive_weighted_exclusions_and_contraction(self): + import split_pair_graph as provider + for h in (23,25): + block_sizes = [] + parent = provider._graph.circuit_class(h) + selected = provider.split_class(parent, provider.configuration(h)['groups']) + case = self + class Audited(selected): + def grouping(self, points): + groups = super().grouping(points) + case.assertEqual([x for group in groups for x in group], list(points)) + case.assertLess(len(groups), len(points)) + return groups + + def _block(self, points, edges, weights, level): + def expected(omitted): + values = [value for pair,value in edges.items() if not set(pair) & omitted] + values += [value for point,value in weights.items() if point not in omitted] + support = 0 + for value in values: + case.assertEqual(support & self.support[value], 0) + support |= self.support[value] + return support + total, single, pairs = super()._block(points, edges, weights, level) + case.assertEqual(self.support[total], expected(set())) + case.assertEqual(set(single), set(points)) + for a in points: + case.assertEqual(self.support[single[a]], expected({a})) + case.assertEqual(set(pairs), set(combinations(points,2))) + for a,b in combinations(points,2): + case.assertEqual(self.support[pairs[a,b]], expected({a,b})) + block_sizes.append(len(points)) + return total, single, pairs + local = Audited(h-1) + block_sizes.clear() + local.pair(list(range(h-1))) + self.assertEqual(sorted(block_sizes, reverse=True), [h-1, 12 if h==23 else 13, 7 if h==23 else 8, 5, 3, 2]) + + def test_next_fine_grid_points_and_old_assembly_controls_reject(self): + from split_pair_arithmetic import refine + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + bit = current['bit']; saving = Fraction(current['bit_saving']); kappa = Fraction(current['kappa']) + grid = Fraction(1,10**18) + rows = {int(t): n for t,n in bit['child_multiplicities'].items()} + self.assertLess(refine.exact_moment(bit['m'],bit['W'],rows,saving)['upper'], 1) + self.assertGreater(refine.exact_moment(bit['m'],bit['W'],rows,saving+grid)['lower'], 1) + for label, variant in ( + ('next_kappa', dict(kappa=kappa+grid)), + ('zero_backoff', dict(h=Fraction())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))): + call = dict(a_bit=saving, kappa=kappa, h=Fraction(1,10**12));call.update(variant) + with self.subTest(control=label), self.assertRaises(refine.balanced.InvalidAssembly): + refine.balanced.assembly(current['finite_bridge'], **call) + + def test_mass_preserving_profile_mutation_is_rejected(self): + from split_pair_compose import check_sources + profile_path = ROOT/'certificates/split-pair-profiles-23.json' + changed = json.loads(profile_path.read_text()) + before = sum(t*n for t,n in enumerate(changed['blocks'])) + changed['blocks'][2] += 3; changed['blocks'][3] -= 2 + self.assertTrue(all(n >= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'split-pair-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from split_pair_compose import check_sources + manifest_path = ROOT/'research/split-pair/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/split-pair-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import split_pair_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('split_pair_graph.py', 'split_pair_engine.py', 'split_pair_compiler.py', 'split_pair_arithmetic.py', 'split_pair_compose.py', 'verify_split_pair.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/tests/test_split_pair_pending.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/tests/test_split_pair_pending.py new file mode 100644 index 0000000000..e6d63f72a4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr71/tests/test_split_pair_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/split_pair_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/FETCH.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/FETCH.json new file mode 100644 index 0000000000..92196075e8 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/FETCH.json @@ -0,0 +1,72 @@ +{ + "pr": 74, + "commit": "3f78d8967c009153f2df5c6a6577b6ab1d37e2ca", + "files": [ + { + "path": "research/balanced-split-frames/producer.py", + "blob_sha": 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/NOTICE b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/NOTICE new file mode 100644 index 0000000000..e5c5688e6c --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/NOTICE @@ -0,0 +1,336 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Rank-first reclamation on interval-strip pair assembly, 8 October 2026 +Composition and exact profile witness: Dominik Scholz, with substantial OpenAI +GPT-6 Astra / Codex assistance. The PR #60 descending-frame-rank compiler by +Chafik Boukhalfa is reused unchanged on Avi Eisenberg's PR #62 scalar graph. +The joint frame compiler and paid reclamation are eumemic's PR #57, developed +with OpenAI Codex assistance. PR #62 records Anthropic Claude assistance. +This composition improves actual fixed-basis block profiles with unchanged +role counts; no new slot-priority rule or scalar graph is claimed. All prior +contributors, licenses, compiler arguments and conditional analytic/tape +interfaces remain credited. See research/rank-pair/PROOF.md. + +Ordered scalar frames, minimum-raise reclamation and coordinate relabeling +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. +The new finite construction and exact arithmetic certificates are in +research/ordered-frames, with an earlier parameter refinement in +research/rank-pair-refinement. These build on Dominik Scholz's PR #63 +composition, Chafik Boukhalfa's PR #60 reclamation compiler, Avi Eisenberg's +PR #62 scalar graph and eumemic's PR #57 reversible frame compiler. +Concurrent PR #65/#67 work is acknowledged in the proof. All inherited +licenses, author notices and conditional proof boundaries remain in force. + +Balanced split frames with core node ordering and coordinate relabeling +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. +This composition combines eumemic's PR69 coarse column sums, Chafik Boukhalfa's +PR71 anchored split/next-use-live compiler, and the earlier PR74 node ordering +and coordinate relabeling. Rohan Garg's PR59 split operation, Avi Eisenberg's +PR62 scalar graph, Rohan Arun's PR65/67 schedules and profile-cost selection, +Dominik Scholz's PR63/68 composition and pending controls, and eumemic's PR57 +compiler remain credited. Original source closures and notices are preserved +under references/frame-compiler/pr69 and pr71; all preceding licenses apply. +See research/balanced-split-frames/PROOF.md for the finite conditional scope. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/SOURCE.json new file mode 100644 index 0000000000..87bd75428a --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/SOURCE.json @@ -0,0 +1,19 @@ +{ + "commit": "3f78d8967c009153f2df5c6a6577b6ab1d37e2ca", + "files": { + "FETCH.json": "4aee950c461d4b46ca42d323d7a7041118ba2b1002d7a867616f3c7ea4d66c1c", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "c087c747998243c96db63203920affd28cec880b702c36017c40a3eb29947fa9", + "research/balanced-split-frames/PROOF.md": "f7a908eea56fdab2f2e8f4ce694a0132c37844ae1cb657962b6549f585bfcdfb", + "research/balanced-split-frames/README.md": "f620b1a18df2b6c0f5d179ebf50f90e630270bba90e14c0d4bff189e3056ee49", + "research/balanced-split-frames/SOURCE.json": "c933a96c636f1e22e02be6fb775a9da2cd14c11fa2d07ba75af17c7e99f00049", + "research/balanced-split-frames/certificate.json": "cec62c4ca612e458b638982056c80be8741ed634904077a5c220427e23cc3edd", + "research/balanced-split-frames/check.py": "45fb95cb2a6b0573efbe37938c149936f4aa4fff1a88425380af7bc59239b4ae", + "research/balanced-split-frames/producer.py": "ec94e4b7af370f7e921fffa3679e80d081a672dbd3ff198043edfb0dc7a9cc9d", + "research/balanced-split-frames/profile-23.json": "7f61525499f56ccc3a183a2741ef823cce30423475fa586ba7d36610b5b66844", + "research/balanced-split-frames/profile-25.json": "9b4d0647e3667af963c164c048c6ea750d90397b046336ede5a5b6902a9f6473", + "research/balanced-split-frames/selection.json": "cbc616540af0ff5b63a90a920c70acd660fbb67052e4dc19889fe0443f2129f4" + }, + "pr": 74, + "scope": "Exact attributed contributor inputs and reported comparison certificate, not a new audit of the entire foreign claim." +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/PROOF.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/PROOF.md new file mode 100644 index 0000000000..7244811413 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/PROOF.md @@ -0,0 +1,145 @@ +# A paid composition of balanced coarse sums, split recursion and frame order + +## Statement and boundary + +The complete finite profile below certifies + +`kappa = 10366199626713/200000000000000000` + +for the inherited conditional bound `T(n)=O(n(log n)^(1-kappa))`. +The all-size compiler, analytic transfer, fixed-alphabet tape simulation, +precision, routing, prime selection and exact recovery hypotheses are inherited. +Finite source checks and arithmetic do not establish those general hypotheses. + +## 1. Pinned ingredients + +PR #71 is frozen at `1bef94fd40a746452548c84a4a8f8834670a3113` in +`references/frame-compiler/pr71/`, including its complete consumed source +closure, selected words, data interfaces, licenses, notices and root documents. +Its own source manifest is preserved without re-pinning. PR #69's original +coarse-sum compiler and notices are frozen at +`91aa1f17e6e3fc063241686a41a34ddd0dc24c50` in the adjacent `pr69/` archive. + +The new producer reads PR #69's literal BEFORE/AFTER replacement, applies it +exactly once to the archived PR #62 scalar graph consumed by PR #71, and keeps +PR #71's `[1,1,2]` split choices and lowest-intact-pair anchoring. The original +source files are unchanged. After reordering, it uses the archived PR #71 +compiler and its next-use profile-cost selection unchanged. + +## 2. Shared intermediate sums preserve the scalar map + +For two disjoint groups A and B, replace the chain forming +`sum_{a in A,b in B} e(a,b)` by +`sum_{b in B} (sum_{a in A} e(a,b))`. +Each operand support occurs exactly once. The nested sums are disjoint, +so this is an equality over the inherited scalar field. Existing node +interning shares the column intermediates with later strip computations. +The singleton cases and strictly decreasing recursive partitions retain the +same identity. No negative coefficient or cancellation is introduced. + +`graph_audit.py` reconstructs dense global triple-coordinate supports using +its own recurrence. For each dimension it checks every input, addition, +core, cover and prescribed output, and compares the complete output support +inventory with original PR #71. This checks 67,460 / 94,993 additions and +5,336 / 6,925 outputs. Original PR #71 has 68,771 / 96,718 additions. + +## 3. Legal node order and fully charged live reclamation + +Keep source IDs fixed. Group remaining active nodes by their original +(core, cover), retaining their original order within each group. Sort groups +lexicographically by + +`(popcount(cover)-popcount(core), -core, cover, first_original_node)`. + +Remap every operand and output ID, clear support caches indexed by old IDs, +and verify again. The independent audit proves that each literal edge and +output is preserved, every operand precedes its consumer, every envelope is +unchanged, and this is exactly the selected renumbering. Matching is recomputed +on the resulting graph and the compiler uses its natural region order. + +PR #71's unchanged pending live controls enter a clearing basis only when +their current frame is contained in the present frame and that frame is +contained in their next-use frame. Controls retain their values. The complete +word contains every chosen clearing XOR and every required frame raise. +The discovery score is never substituted for the actual charged profile. + +Both complete words are regenerated with dirty-basis checks enabled. A +separate serialized-word checker replays every input and arbitrary dirty +basis column in both orientations. The final roles are 27,136 / 35,744. + +## 4. Coordinate relabeling and the data family + +Apply each selected permutation to the frame core/cover masks, source-triple +indices, scatter target-triple indices, output common points and output +triples. Literal XORs, scratch IDs and frame IDs remain unchanged. The complete +permutations are frozen in `selection.json`; both relabeled words are replayed. + +For permutation matrix P, both fixed bases `I+J` and the inverse metric +`I-J/9` commute with P. Envelope projectors therefore transform by conjugation. +Containment and every legal incidence remain valid. Ordered contiguous child +profiles can change, and every one is regenerated from the literal word +using the inherited exact bounded-minor/CRT profiler, with zero disagreements. + +Each coordinate permutation induces a bijection on the complete triple set. +Consequently the complete two-axis data-block family is only reindexed: its +aggregate inherited profile and rational recovery cases remain valid. Copied +centers, endpoints and data growth remain explicitly charged. + +## 5. Complete recurrence and assembly + +Let `N=4073300`, `m=575`, and let `R_h` and `b_{h,t}` be the verified role count +and exact internal profile. The physical width is + +`W = 2N + (N/1771)R_23 + (N/2300)R_25 = 133862024`. + +The complete child multiset includes: + +- data: `18N` children of size 1 and `2N` each of sizes 21, 17 and 481; +- paid endpoint copies: `N` additional size-1 children; +- internal axis h: `(N/binom(h,3))*b_{h,t}` children of size t; +- exterior axis h: `(N/binom(h,3))*R_h` each of sizes h and `m-2h`; +- data growth per axis: `2N` each of sizes 1 and `h-2`. + +The total rank is `76968816900 = mW-1846900`; maximum child size is 529. +The exact characteristic is +`M(a)=sum_t (t*n_t/(mW))*exp(a*log(m/t))`. +At `a=25916842362591/500000000000000000`, a rigorous upper bound is below 1. +At `a+10^-18`, a rigorous lower bound is above 1. Positive logarithms make +the characteristic increasing. The complete original PR #71 profile is +separately excluded at the new accepted saving. + +Production arithmetic uses the retained rational logarithm/exponential +helper. The independent checker derives the complete paid multiset and uses +40 exact atanh terms for logarithms and Taylor degree 10 with a geometric +exponential tail. It imports no production arithmetic and checks each of the +47 assembly slacks and seven margins independently. The next kappa grid value +is rejected. Negative controls reject omitted paid children, fabricated slacks +and incorrect source hashes. + +Use positive backoff `10^-18`. Since W is below `2^27`, its `bit_length()` is +27. The product-row coefficient becomes `9*27+20*30=843`. Keeping degree 2000 +and suffix slope 8000 gives degree gap `2000-(51/25)*843=7007/25`. +These values are derived and checked; no stale predecessor constants remain. +Arithmetic cutoff bounds are not complete operational runtime thresholds. + +## Credits + +The composition, core-order continuation, coordinate choices, packaging and +independent audits were prepared for Thomas DiFiore with substantial OpenAI +Codex assistance. Coarse-sum reassociation is eumemic's PR #69. Anchored split +frames and next-use-aware live selection are Chafik Boukhalfa's PR #71. +Rohan Garg supplied the split operation (#59); Avi Eisenberg supplied interval +strips and core-aware pair assembly (#62); Rohan Arun supplied region schedules +and profile-cost selection (#65/#67); Dominik Scholz supplied ranked composition +and pending live controls (#63/#68); eumemic supplied the reversible compiler +and physical/profile checking interfaces (#57). Our earlier PR #74 supplied the +core node ordering and coordinate-relabeling continuation used here. + +The preserved archives retain all earlier credits, including RaD/hipotures, +icekylinx, James Chang, Zhihao Chen, Aurel Prosz, Swapnil Jain, Alejandro Zarzuelo +Urdiales, Douglas Colkitt, OpenAI and Harvey–van der Hoeven, and predecessor +AI-assistance disclosures. No predecessor authorship or endorsement of this +composition is implied. Existing licenses and notices remain in force. + +Concurrent PR #75–#79 contributions, including carry exchanges, balanced split +constructions and coordinate flags, are acknowledged. No priority claim is made. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/README.md new file mode 100644 index 0000000000..5784b8b928 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/README.md @@ -0,0 +1,70 @@ +# Balanced split frames with shared sums and reusable live controls + +**κ = 10366199626713 / 200000000000000000 = 0.000051830998133565** + +The conditional bound is `T(n) = O(n (log n)^(1-kappa))`. +This is **0.9788258% above our original PR #74 result**, **0.8097927% above +pinned PR #71**, and **0.8082664% above PR #75's claim observed on 8 October +2026**. The later PR #79 claim `5.1745625472866e-5`, observed at 19:55 UTC on the same +date, is also below this result by **0.1649853%**. These compare asymptotic exponent savings; they are not measured +multiplication speedups. + +| Quantity | Original PR #74 | Pinned PR #71 | This composition | +| --- | ---: | ---: | ---: | +| h23 auxiliary roles | 27,698 | 27,455 | 27,136 | +| h25 auxiliary roles | 36,310 | 36,015 | 35,744 | +| Physical width | 136,157,010 | 135,075,665 | 133,862,024 | +| Conditional κ | 5.132858076595e-5 | 5.1414646104039e-5 | 5.1830998133565e-5 | + +## Construction + +Compose eumemic's PR #69 column-balanced coarse sums with Chafik Boukhalfa's +PR #71 anchored split recursion and next-use-aware live reclamation. Apply +our original-envelope node order before carrier matching, then relabel the +geometric coordinates and recompute the actual fixed-basis profiles. + +The balanced graph has 67,460 / 94,993 active additions, compared with +PR #71's 68,771 / 96,718. Every prescribed output is unchanged. The complete +physical words pay for all XORs, frame raises, copied centers and data blocks. +The width now lies below `2^27`; its role-logarithm and product-row constants +are recomputed in the exact certificate. + +## Evidence and reproduction + +- [Proof, scope and contributor credits](PROOF.md) +- [Exact certificate](certificate.json) +- [Selected graph and coordinate choices](selection.json) +- [Immutable source manifest](SOURCE.json) +- [Independent dense scalar audit](graph-audit.json) +- [Independent exact arithmetic audit](independent-audit.json) +- [Verification receipt](validation.json) and [raw log](verification.log) + +Use Python 3.11 or newer and a C++17 compiler with unsigned 128-bit support: + +```sh +make balanced-split-frames-verify +``` + +This regenerates both words from pinned sources, checks their selected raw +hashes, audits the complete scalar graph, independently replays every input +and dirty basis vector in both orientations, reconstructs every literal frame +transition and exact profile, and checks the full paid recurrence and assembly. +The two replay dimensions contain 30,678 / 40,344 basis coordinates. +Both profiles have zero CRT disagreements. Independent arithmetic verifies +all 47 strict inequalities, seven margins, adjacent-grid rejection, and +exclusion of the complete pinned PR #71 profile at the new bit saving. + +The earlier full-suite receipt in `../ordered-frames/validation.json` covers +that historical source state. Current upstream checks and formal packages +remain separate CI jobs. The new source archives retain original notices +and original root documentation so predecessor pins remain unchanged. + +All inherited analytic, all-size compiler, fixed-tape, precision, routing, +prime-selection and recovery hypotheses remain assumed. This is a verified +finite conditional witness, with no global-optimality or practical-speed claim. + +Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. Original +PR #74 remains available in `../ordered-frames/`; all predecessor credits and +licenses remain applicable. + +Concurrent PR #75–#79 work is acknowledged; no priority claim is made. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/SOURCE.json new file mode 100644 index 0000000000..06404d9283 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/SOURCE.json @@ -0,0 +1,21 @@ +{ + "files": { + "references/frame-compiler/pr69/SOURCE.json": "928fa8cce0964a6894af3f40cbde6d983aac395336e5277f751c9cbf1b07957f", + "references/frame-compiler/pr71/SOURCE.json": "1c79309362044dd386f72946ccb2e258e98d07d7239ea89d8a8646338d24228a", + "research/balanced-split-frames/check.py": "45fb95cb2a6b0573efbe37938c149936f4aa4fff1a88425380af7bc59239b4ae", + "research/balanced-split-frames/graph_audit.py": "b95cf9269fbcaf7f7b9732b28d7a8b790feefc262e86a36de33a92ab7906a8b3", + "research/balanced-split-frames/independent_check.py": "02dd998ebe68f111a42657e1591416b28b618a8d58bbd4fb0686d3afd929db1a", + "research/balanced-split-frames/producer.py": "ec94e4b7af370f7e921fffa3679e80d081a672dbd3ff198043edfb0dc7a9cc9d", + "research/balanced-split-frames/profile-23.json": "7f61525499f56ccc3a183a2741ef823cce30423475fa586ba7d36610b5b66844", + "research/balanced-split-frames/profile-25.json": "9b4d0647e3667af963c164c048c6ea750d90397b046336ede5a5b6902a9f6473", + "research/balanced-split-frames/selection.json": "cbc616540af0ff5b63a90a920c70acd660fbb67052e4dc19889fe0443f2129f4", + "research/balanced-split-frames/transitions-23.json": "0e9b6bbb1f9f08b34077bb93a60b39c2d61cf8f1329c884fd47326bf32bfac60", + "research/balanced-split-frames/transitions-25.json": "3bffd56836edefb309825f4ba303dc27ae88455aa7c8fc918af3ef24d82caee3", + "research/balanced-split-frames/word-23.json.gz": "956b886339ccbd3d599c5e0ec403b870958d052f3442067e8f12a56318e9525d", + "research/balanced-split-frames/word-25.json.gz": "ea090af1c4b56b7dae31d1f0d3fece4417677160f07c372e0455d7f8ac31c7b0", + "research/rank-pair-refinement/refine.py": "a19a79ea064fe66cb5f4e2971d6ab277cdfd452975c539e23066174533430691" + }, + "pr69_commit": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "pr71_commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "scope": "Selected sources and finite inputs. 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/check.py @@ -0,0 +1,104 @@ +#!/usr/bin/env python3 +"""Screen complete paid profiles from independently replayed axis constructions.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions required') +from pathlib import Path +from collections import Counter +from fractions import Fraction as Q +import importlib.util,argparse,json,subprocess,tempfile,hashlib,os,shlex +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +from producer import check_sources +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m +exact=load('candidate_exact',ROOT/'research/rank-pair-refinement/refine.py') +balanced=load('candidate_assembly',DEP/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') + +def profile(path): + v=json.loads(Path(path).read_text()) + return v['profile'] if 'profile' in v else v + +def calculate(first,second): + profiles=[profile(first),profile(second)] + N=4073300;m=575 + assert [p['h'] for p in profiles]==[23,25] + W=2*N+sum(N//p['v']*p['R'] for p in profiles) + parts={'data':Counter({1:18*N,21:2*N,17:2*N,481:2*N}),'endpoint_copy':Counter({1:N})} + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 + assert p['rank_sum']==h*p['R']+p['loss']==sum(t*n for t,n in enumerate(p['blocks'])) + assert p['loss']==h*(h-1) + parts[f'internal_{h}']=Counter({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + parts[f'exterior_{h}']=Counter({h:bank,m-2*h:bank}) + parts[f'growth_{h}']=Counter({1:2*N,h-2:2*N}) + rows=sum(parts.values(),Counter());assert sum(t*n for t,n in rows.items())==m*W-1846900 + lo,hi,grid=1,71700000000000,10**18 + while lo+11 + result.update(status='Verified finite conditional witness; inherited all-size transfer remains assumed', + source_manifest_sha256=hashlib.sha256((HERE/'SOURCE.json').read_bytes()).hexdigest(), + axes=axes,eventual_bounds=balanced.cutoffs(result['finite_bridge'],result['assembly']), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113',pr71_kappa=Q(previous['kappa']), + relative_gain_pr71=result['kappa']/Q(previous['kappa'])-1, + pr71_complete_profile_exclusion_lower=old_lower)) + result=arithmetic.js(result) + path=HERE/'certificate.json' + if record:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:assert result==json.loads(path.read_text()) + print('PASS exact moment, next-grid exclusions, 47 inequalities and seven margins',flush=True) + return result + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--record',action='store_true');args=parser.parse_args();generate(args.record) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/producer.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/producer.py new file mode 100644 index 0000000000..8d68303a3b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/producer.py @@ -0,0 +1,132 @@ +#!/usr/bin/env python3 +"""Balanced coarse sums + anchored split/live frames + core ordering and coordinates. + +Composition for Thomas DiFiore with OpenAI Codex assistance. Apache-2.0. +PR69 coarse sums: eumemic. PR71 split/live composition: Chafik Boukhalfa. +Graph: Avi Eisenberg PR62; split operation: Rohan Garg PR59; reclamation: +Rohan Arun PR65/67, Dominik Scholz PR63/68, eumemic PR57. Original notices +and exact sources are retained under references/frame-compiler/pr69 and pr71. +""" +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +from hashlib import sha256 +import argparse,ast,gzip,importlib.util,json,types +from concurrent.futures import ProcessPoolExecutor +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +DEP=ROOT/'references/frame-compiler/pr71' +sys.path.insert(0,str(DEP/'scripts/experiments')) +import split_pair_graph as provider +import split_pair_compiler as ancestor +from binary_frame_replay import replay + + +def check_sources(): + for folder in (DEP,ROOT/'references/frame-compiler/pr69'): + manifest=json.loads((folder/'SOURCE.json').read_text()) + for name,digest in manifest['files'].items(): + assert sha256((folder/name).read_bytes()).hexdigest()==digest,name + manifest=json.loads((HERE/'SOURCE.json').read_text()) + required={str((HERE/name).relative_to(ROOT)) for name in ('producer.py','check.py','graph_audit.py','independent_check.py','selection.json')} + assert required <= set(manifest['files']), 'Incomplete selected source closure' + for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + + +def reorder(c): + groups={} + for x in sorted(c.active): + if c.args[x]: groups.setdefault((c.core[x],c.union[x]),[]).append(x) + def key(item): + (core,cover),nodes=item + return cover.bit_count()-core.bit_count(),-core,cover,min(nodes) + ids=list(range(len(c.inputs)+1))+[x for _,nodes in sorted(groups.items(),key=key) for x in nodes] + mapping={x:i for i,x in enumerate(ids)} + args,core,cover,provenance=c.args,c.core,c.union,c.provenance + c.args=[tuple(mapping[y] for y in args[x]) if args[x] else None for x in ids] + c.core=[core[x] for x in ids];c.union=[cover[x] for x in ids] + c.provenance=[provenance[x] for x in ids] + c.active={mapping[x] for x in c.active};c.outputs={k:mapping[v] for k,v in c.outputs.items()} + c.support_in.cache_clear() + c.verify() + return c + + +def graph(h,ordered=True): + source=Path(provider._graph.__file__).read_text() + original=ROOT/'references/frame-compiler/pr69/scripts/experiments/balanced_coarse_compiler.py' + replacements={} + for node in ast.parse(original.read_text()).body: + if isinstance(node,ast.Assign): + for target in node.targets: + if isinstance(target,ast.Name) and target.id in ('BEFORE','AFTER'): + replacements[target.id]=ast.literal_eval(node.value) + assert source.count(replacements['BEFORE'])==1 + module=types.ModuleType('balanced_split_private_graph');module.__file__=provider._graph.__file__ + exec(compile(source.replace(replacements['BEFORE'],replacements['AFTER']),module.__file__+':balanced-coarse','exec'),module.__dict__) + previous=provider._graph + try: + provider._graph=module + c=provider.graph(h) + finally: + provider._graph=previous + return reorder(c) if ordered else c + + +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + +def compile_axis(h): + check_sources() + config=json.loads((HERE/'selection.json').read_text())['axes'][str(h)] + previous_graph,previous_order=provider.graph,provider.ordered_build + # graph() calls the original provider; keep that callable private while + # the inherited driver resolves the selected composed graph dynamically. + original_graph=previous_graph + def selected_graph(dimension): + provider.graph=original_graph + try:return graph(dimension) + finally:provider.graph=selected_graph + try: + provider.graph=selected_graph + provider.ordered_build=lambda original,dimension:original + compiled,word=ancestor.compile_axis(h) + finally: + provider.graph,provider.ordered_build=previous_graph,previous_order + compiled['graph_configuration']=config + word=relabel(word,config['coordinate_permutation']) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + path=HERE/f'word-{h}.json.gz' + with path.open('wb') as stream: + with gzip.GzipFile(filename='',fileobj=stream,mode='wb',mtime=0) as archive:archive.write(raw) + receipt=replay(path) + assert sha256(raw).hexdigest()==config['expected_word_sha256'] + axis=dict(configuration=config,compiled=compiled,replay=receipt, + word_sha256=sha256(raw).hexdigest(),gzip_sha256=sha256(path.read_bytes()).hexdigest()) + (HERE/f'axis-{h}.json').write_text(json.dumps(axis,indent=2)+'\n') + print(f'PASS fresh balanced/split/core word h={h}, roles={receipt["roles"]}',flush=True) + + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--h',type=int,choices=(23,25));args=parser.parse_args() + if args.h:compile_axis(args.h) + else: + with ProcessPoolExecutor(max_workers=2) as pool:list(pool.map(compile_axis,(23,25))) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/profile-23.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/profile-23.json new file mode 100644 index 0000000000..013f4e59c7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/profile-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27136,"loss":506,"rank_sum":624634,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38292,"crt_matrices":5488,"crt_disagreements":0,"blocks":[0,355721,21666,6948,6524,3093,4314,2400,3266,1501,2094,1008,1374,586,732,353,307,139,62,16,0,23,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/profile-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/profile-25.json new file mode 100644 index 0000000000..1e3b6b89aa --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/profile-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":35744,"loss":600,"rank_sum":894200,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52202,"crt_matrices":7623,"crt_disagreements":0,"blocks":[0,490052,26188,13531,7191,4637,5355,4229,3705,2610,2620,2080,1814,1357,1070,868,612,463,233,56,141,0,71,25,0,0]} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/selection.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/selection.json new file mode 100644 index 0000000000..57cf3b6b65 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr74/research/balanced-split-frames/selection.json @@ -0,0 +1,86 @@ +{ + "source_pr71": "1bef94fd40a746452548c84a4a8f8834670a3113", + "source_pr69": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50", + "axes": { + "23": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 22, + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 20, + 19, + 21 + ], + "expected_word_sha256": "8dc6696a274e70ca0af3fc49c4bdede362adaedc8dc322f335e3dab499f1ed48" + }, + "25": { + "groups": [ + 1, + 1, + 2 + ], + "anchor": true, + "coarse_sums": "columns", + "node_order": "rank, descending original core, ascending cover, first original node", + "execution_order": "natural after node renumbering", + "pending_live_controls": true, + "pending_cost_uses_next_use_frame": true, + "coordinate_permutation": [ + 2, + 1, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "expected_word_sha256": "2c923afe366219ee3fffc9db063c91e44cdf7cbbdb62246b8e6a297dc440b577" + } + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/FETCH.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/FETCH.json new file mode 100644 index 0000000000..4db82db4a1 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/FETCH.json @@ -0,0 +1,48 @@ +{ + "pr": 78, + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf", + "files": [ + { + "path": "research/coordinate-flags/verify.py", + "blob_sha": "216ccd3d58c1331fffdb008df7547982cb43d2ae", + "sha256": "b59a5345c8684bb67a5ea666d5de11422c45cdf19f2c13de1520623a71bae7e1", + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf" + }, + { + "path": "research/coordinate-flags/order-23.json", + "blob_sha": "035f01df59be3312e30ec692754d3a331a766799", + "sha256": "def92cd69f3fba2986c7a230ece45f9eb63fd38fef512d055bf0adffe9edfa82", + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf" + }, + { + "path": "research/coordinate-flags/order-25.json", + "blob_sha": "7c06a68e6e4a4ff0ad8a43cd240ec7a51892f328", + "sha256": "209dee5fac04fa91a5bf63ed0307a56e849cc6800fa543254590045e0c95d6a5", + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf" + }, + { + "path": "research/coordinate-flags/README.md", + "blob_sha": "950f4eaa2d83c75ec5b9fa4046dd5e663c804d79", + "sha256": "cbc4f20613e1dfafcce7c5f82c274fdd48898cc968d14fbea7bf9b1a47607e85", + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf" + }, + { + "path": "research/coordinate-flags/SOURCE.json", + "blob_sha": "24c30b45bb695a46e24da75333d2de827324e734", + "sha256": "c0ec88783c06431d95e1e8efabbb2928857f1d4ca8d0ada10206e99322ae78e2", + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf" + }, + { + "path": "LICENSE", + "blob_sha": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64", + "sha256": 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/NOTICE b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/NOTICE new file mode 100644 index 0000000000..defe0f27b6 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/NOTICE @@ -0,0 +1,326 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Coordinate-flag relabeling and finite verification: Rohan Arun with OpenAI Codex assistance. Based on Chafik Boukhalfa PR71 and the inherited contributions credited in research/coordinate-flags/README.md. Existing contributor originals are preserved. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/SOURCE.json new file mode 100644 index 0000000000..15f08e2813 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/SOURCE.json @@ -0,0 +1,15 @@ +{ + "commit": "1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf", + "files": { + "FETCH.json": "79d6b40af23f03d6737be9a072ebca4f96aa6a663895cffdee4052432b5d13b8", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "0a0e0314b9d1e23a193e92aa633fc50c432b6e3ea326f40d5cbb1ea538823149", + "research/coordinate-flags/README.md": "cbc4f20613e1dfafcce7c5f82c274fdd48898cc968d14fbea7bf9b1a47607e85", + "research/coordinate-flags/SOURCE.json": "c0ec88783c06431d95e1e8efabbb2928857f1d4ca8d0ada10206e99322ae78e2", + "research/coordinate-flags/order-23.json": "def92cd69f3fba2986c7a230ece45f9eb63fd38fef512d055bf0adffe9edfa82", + "research/coordinate-flags/order-25.json": "209dee5fac04fa91a5bf63ed0307a56e849cc6800fa543254590045e0c95d6a5", + "research/coordinate-flags/verify.py": "b59a5345c8684bb67a5ea666d5de11422c45cdf19f2c13de1520623a71bae7e1" + }, + "pr": 78, + "scope": "Exact attributed contributor inputs and reported comparison certificate, not a new audit of the entire foreign claim." +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/README.md new file mode 100644 index 0000000000..950f4eaa2d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/README.md @@ -0,0 +1,68 @@ +# Coordinate flags for the split-pair witness + +This finite conditional witness gives kappa = 12857195906507 / 250000000000000000 += 5.1428783626028e-5, about 0.02750% above PR71's 5.1414646104039e-5. +The bit saving is 25715714341 / 500000000000000. Roles, physical width, +recursive rank mass, scalar operations, paid clearing and copied endpoints +remain those of PR71. The changed object is the coordinate flag used to +decompose internal frame transitions into consecutive pivot blocks. + +## General relabeling argument + +Let P be a permutation matrix on the h coordinates. It commutes with J, +so P commutes with the fixed basis L = I+J and preserves the form I-J/9. +For a core/cover frame F(C,U), the relabeled projector is +P F(C,U) P^-1 = F(P C,P U). Consequently, every frame inclusion, rank, +nondegeneracy condition, projector denominator bound and elementary role +operation is preserved. The existing exact CRT bounds apply unchanged. + +Relabel each input triple T to P T, each output (c,T) to (P c,P T), +each frame mask by P, and each scatter row by the induced triple permutation. +The role slots and literal XOR operations do not change. This conjugates +the complete linear word by the input/output permutation and therefore +preserves its identity on every ordinary input and arbitrary dirty role. +The verifier independently replays that identity in both orientations. + +The data component sums over every pair of source triples. Independent +coordinate permutations on the two axes induce a bijection on that complete +Cartesian product. Hence its existing complete histogram, copied-center +costs and endpoint corrections are unchanged. This argument uses the full +case set; it would not justify retaining a selected subset's histogram. + +North-east corner rank profiles depend on the fixed coordinate order. +Conjugating by P can change which adjacent pivots form a recursive block, +even though total rank is unchanged. We regenerate these profiles from the +actual relabeled words rather than assuming their costs are invariant. +Both dimensions use the selected orders in order-23.json and order-25.json. + +## Verification and scope + +Run `make coordinate-flags-verify`. It checks source closure, regenerates +both words byte for byte, replays every ordinary and dirty basis vector in +both orientations, reconstructs physical transitions, and recomputes all +fixed-I+J profiles with the inherited exact CRT bounds. Six negative controls +reject inconsistent coordinates, missing source/output relabeling, missing +operations and aliased terminal roles. + +The complete paid child list is rebuilt independently. Directed rational +moment bounds, an independent logarithm/exponential computation, 47 strict +constraints, seven margins, both next-grid rejections and exclusion of +PR71's complete profile at the new saving are checked. + +The search used structured coordinate orders and bounded adjacent swaps. +No global optimum or practical speedup is claimed. This remains conditional +on the inherited all-size residual compiler, routing, recovery, prime +selection, fixed finite-alphabet multitape simulation and analytic transfer. +The full expanded repository rerun is pending; this package is a draft. + +## Credit + +Chafik Boukhalfa's PR71 supplies the split-pair graph and next-use scoring. +Rohan Garg introduced the split operation (PR59); Avi Eisenberg supplied +interval/pair assembly (PR62); Dominik Scholz supplied ranked frames and +pending controls (PR63/68); Rohan Arun supplied schedule and profile-cost +search (PR65/67); eumemic supplied the reversible compiler and physical +checkers (PR57). Credit also icekylinx, James Chang, Zhihao Chen, Aurel +Prosz/Paureel, Swapnil Jain, Alejandro Zarzuelo Urdiales, RaD/hipotures, +Douglas Colkitt, OpenAI and all inherited contributors. Existing sources, +licenses and notices are retained. Prepared by Rohan Arun with OpenAI Codex. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/SOURCE.json new file mode 100644 index 0000000000..24c30b45bb --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/SOURCE.json @@ -0,0 +1,130 @@ +{ + "baseline_pr71_commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "files": { + ".github/workflows/verify.yml": "896aa64122e04f0b366fa1994096109b079b05cdbaec95a75db479dd365b4891", + "Makefile": "33a6c2c1aeccea6bd08dbef99e514079e84ba82f1a86b2774a416f06db7b342d", + "NOTICE": "0a0e0314b9d1e23a193e92aa633fc50c432b6e3ea326f40d5cbb1ea538823149", + "README.md": "2487c2467357f176d8320c70cda9ad06618f338277bb27597657e73b60511a39", + 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diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/order-23.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/order-23.json new file mode 100644 index 0000000000..035f01df59 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/order-23.json @@ -0,0 +1,53 @@ +{ + "h": 23, + "order": [ + 1, + 3, + 2, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 21, + 20, + 22, + 0 + ], + "mapping": { + "1": 0, + "3": 1, + "2": 2, + "4": 3, + "5": 4, + "6": 5, + "7": 6, + "8": 7, + "9": 8, + "10": 9, + "11": 10, + "12": 11, + "13": 12, + "14": 13, + "15": 14, + "16": 15, + "17": 16, + "18": 17, + "19": 18, + "21": 19, + "20": 20, + "22": 21, + "0": 22 + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/order-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/order-25.json new file mode 100644 index 0000000000..7c06a68e6e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/order-25.json @@ -0,0 +1,57 @@ +{ + "h": 25, + "order": [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 23, + 22, + 24, + 0 + ], + "mapping": { + "1": 0, + "2": 1, + "3": 2, + "4": 3, + "5": 4, + "6": 5, + "7": 6, + "8": 7, + "9": 8, + "10": 9, + "11": 10, + "12": 11, + "13": 12, + "14": 13, + "15": 14, + "16": 15, + "17": 16, + "18": 17, + "19": 18, + "20": 19, + "21": 20, + "23": 21, + "22": 22, + "24": 23, + "0": 24 + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/verify.py new file mode 100644 index 0000000000..216ccd3d58 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr78/research/coordinate-flags/verify.py @@ -0,0 +1,89 @@ +"""Rebuild the coordinate-permuted PR71 words and their exact paid bound.""" +import sys +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2];HERE=Path(__file__).resolve().parent +sys.path.insert(0,str(ROOT/'scripts/experiments')) +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +from split_pair_arithmetic import refine,audit +import binary_frame_math as arithmetic +from pin_split_pair_sources import required_paths +from fractions import Fraction as Q +from collections import Counter +from itertools import combinations +from math import comb +from hashlib import sha256 +import gzip,json,subprocess,tempfile + +def required(): + names=required_paths()|{'research/split-pair/SOURCE.json','certificates/split-pair-kappa.json', + '.github/workflows/verify.yml'} + names.update(str(p.relative_to(ROOT)) for p in HERE.iterdir() if p.is_file() and p.name not in ('SOURCE.json','validation.json')) + return names + +def sources(): + manifest=json.loads((HERE/'SOURCE.json').read_text()) + assert required()<=set(manifest['files']),'Source closure incomplete' + for name,digest in manifest['files'].items():assert sha256((ROOT/name).read_bytes()).hexdigest()==digest,name + +def relabel(word,config): + h=word['h'];order=config['order'];assert sorted(order)==list(range(h)) + perm={old:new for new,old in enumerate(order)} + assert perm=={int(k):v for k,v in config['mapping'].items()} + triples=list(combinations(range(h),3));lookup={t:i for i,t in enumerate(triples)} + index={i:lookup[tuple(sorted(perm[x] for x in triple))] for i,triple in enumerate(triples)} + def mask(m):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(index[int(i)]):s for i,s in word['sources'].items()} + v=word['v'];word['scatter']=[[v+index[a-v],b] for a,b in word['scatter']] + word['outputs']=[[s,g,perm[c],sorted(perm[x] for x in triple)] for s,g,c,triple in word['outputs']] + return word + +def exact(profiles): + cert=json.loads((HERE/'certificate.json').read_text());baseline=json.loads((HERE/'baseline-pr71.json').read_text()) + N=comb(23,3)*comb(25,3);m=575;W=2*N+sum(N//p['v']*p['R'] for p in profiles) + L=sum(N//p['v']*p['loss'] for p in profiles) + rows=Counter({1:19*N,21:2*N,17:2*N,481:2*N}) + for p in profiles: + h=p['h'];rep=N//p['v'];bank=rep*p['R'] + assert p['crt_disagreements']==0 and p['v']==comb(h,3) + assert sum(t*n for t,n in enumerate(p['blocks']))==h*p['R']+h*(h-1)==p['rank_sum'] + rows.update({t:n*rep for t,n in enumerate(p['blocks']) if t and n}) + rows[h]+=bank;rows[m-2*h]+=bank;rows[1]+=2*N;rows[h-2]+=2*N + bit=dict(m=m,N=N,W=W,L=L,total_rank=sum(t*n for t,n in rows.items()),child_multiplicities=dict(sorted(rows.items()))) + assert bit['total_rank']==m*W-N+L + assert arithmetic.js(bit)==cert['bit'] + saving=Q(cert['bit_saving']);moment=refine.exact_moment(m,W,rows,saving) + rejected=refine.exact_moment(m,W,rows,saving+Q(1,10**18)) + assert moment['upper']<11 + print('PASS exact conditional kappa',result['kappa'],'47 constraints, seven margins, independent bounds and next-grid controls') + +def verify(): + sources();profiles=[] + with tempfile.TemporaryDirectory(prefix='coordinate-flags-') as directory: + work=Path(directory);exe=work/'profiles' + subprocess.run(['c++','-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'scripts/experiments/binary_frame_profiles.cpp'),'-o',str(exe)],check=True) + for h in (23,25): + original=json.loads(gzip.decompress((ROOT/f'certificates/split-pair-word-{h}.json.gz').read_bytes())) + config=json.loads((HERE/f'order-{h}.json').read_text());word=relabel(original,config) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + assert raw==gzip.decompress((HERE/f'word-{h}.json.gz').read_bytes()) + path=work/f'word-{h}.json';path.write_bytes(raw);checked=replay(path) + stored=json.loads((HERE/f'replay-{h}.json').read_text());assert arithmetic.js(checked)==stored['replay'] + trans=work/f'transitions-{h}.bin';receipt=prepare(path,trans);assert arithmetic.js(receipt)==stored['transitions'] + subprocess.run([str(exe),str(trans)],check=True) + profile=json.loads(Path(str(trans)+'.profiles.json').read_text());assert profile==json.loads((HERE/f'profiles-{h}.json').read_text()) + profiles.append(profile);print('PASS complete relabelled physical word and profile',h,flush=True) + exact(profiles) +if __name__=='__main__':verify() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/.gitattributes b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/.gitattributes new file mode 100644 index 0000000000..48ba61f217 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/.gitattributes @@ -0,0 +1,15 @@ +* text=auto eol=lf +*.pdf binary +# Unified diffs require a leading space on blank context lines. +*.patch -whitespace +# Preserve the exact upstream bytes, including original whitespace. +upstream/** -whitespace +# Preserve the exact pinned third-party proof snapshots and notices. +references/copied-centers/pr29/** -whitespace +references/copied-centers/pr33/** -whitespace +references/semantic-bulk/** -whitespace + +# Immutable contributor archives retain original CRLF and whitespace bytes. +references/frame-compiler/pr69/** -text -whitespace +references/frame-compiler/pr70/** -text -whitespace +references/frame-compiler/pr71/** -text -whitespace diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/.github/workflows/verify.yml b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/.github/workflows/verify.yml new file mode 100644 index 0000000000..33886a2cdf --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/.github/workflows/verify.yml @@ -0,0 +1,63 @@ +name: Verify research artifacts + +on: + push: + pull_request: + workflow_dispatch: + +permissions: + contents: read + +jobs: + verify: + runs-on: ubuntu-24.04 + timeout-minutes: 20 + strategy: + fail-fast: false + matrix: + python-version: ['3.11', '3.13', '3.14'] + group: [community, producers, certificates, ternary, research, tests, strips, clones, positive, joint, pair, balanced] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: ${{ matrix.python-version }} + - name: Install headers for the exact enlarged-frame profiler + if: matrix.group == 'positive' + run: | + if ! test -f /usr/include/boost/multiprecision/cpp_int.hpp; then + sudo apt-get update + sudo apt-get install -y libboost-dev + fi + - name: Check arithmetic, source hashes, finite identities, and patches + run: make verify-${{ matrix.group }} + - name: Require reproducible certificates and patches + run: git diff --exit-code + + formal: + runs-on: ubuntu-24.04 + timeout-minutes: 30 + strategy: + fail-fast: false + matrix: + package: [historical, gaussian, matrix] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: '3.13' + - name: Install elan; each project pins its Lean toolchain + run: | + curl --proto '=https' --tlsv1.2 -sSf https://raw.githubusercontent.com/leanprover/elan/0e36a07b9bbcc5381fa6250df109f9a4f94d7bac/elan-init.sh -o /tmp/elan-init.sh + sh /tmp/elan-init.sh -y --default-toolchain none + echo "$HOME/.elan/bin" >> "$GITHUB_PATH" + - name: Fetch pinned Mathlib build cache + if: matrix.package == 'historical' + working-directory: formal/lean + run: lake exe cache get + - name: Check formal package and theorem axiom dependencies + run: make formal-${{ matrix.package }}-verify diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/LICENSE b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Keep local verification sequential: +# different groups regenerate certificates that another group may read. +verify: + $(MAKE) verify-community + $(MAKE) verify-producers + $(MAKE) verify-certificates + $(MAKE) verify-ternary + $(MAKE) verify-research + $(MAKE) verify-strips + $(MAKE) verify-clones + $(MAKE) verify-positive + $(MAKE) verify-joint + $(MAKE) verify-pair + $(MAKE) verify-balanced + $(MAKE) verify-tests + +verify-community: community-audit-check community-followup-check copied-reversed-producer copied-reversed-check copied-fixed-reversed-producer copied-fixed-reversed-check + $(MAKE) copied-fixed-verify + $(MAKE) climbed-48-verify + +verify-producers: + $(MAKE) copied-centers-verify + $(MAKE) structured-bulk-verify + $(MAKE) endpoint-gauge-producer endpoint-gauge-certificate + $(MAKE) partial-swap-producer partial-swap-certificate + +verify-certificates: + python3 scripts/prime_field_network.py + python3 scripts/complex_network.py + python3 scripts/fast_gaussian.py + $(MAKE) batched-certificate batched-patch + python3 scripts/certify.py + python3 scripts/search_network.py + python3 scripts/make_patch.py + python3 scripts/nonadjacent.py + python3 scripts/make_nonadjacent_patch.py + python3 scripts/tune_routing.py + python3 scripts/research_networks.py + python3 scripts/search_network_variants.py + python3 scripts/block_label_targets.py + python3 scripts/audit_block_labels.py + python3 scripts/audit_additive_labels.py + python3 scripts/small_block_witness.py + python3 scripts/incidence_network.py + python3 scripts/make_incidence_patch.py + python3 scripts/search_incidence_partitions.py + python3 scripts/dag_network.py + python3 scripts/make_dag_patch.py + python3 scripts/shared_point_network.py + python3 scripts/make_shared_point_patch.py + python3 scripts/paired_network.py + python3 scripts/make_paired_patch.py + python3 scripts/prepare_layers.py + python3 scripts/audit_sparse_fusion.py + python3 scripts/audit_fused_block.py + python3 scripts/audit_short_guards.py + python3 scripts/audit_gather_schedules.py + python3 scripts/audit_coded_carries.py + python3 scripts/audit_cancellation.py + python3 scripts/audit_joint_frames.py + python3 scripts/audit_compact_controls.py + python3 scripts/compact_control_layer.py + python3 scripts/make_compact_control_patch.py + python3 scripts/audit_scratch_pooling.py + python3 scripts/reuse_network.py + python3 scripts/make_reuse_patch.py + +verify-ternary: + python3 scripts/complex_compression.py + python3 scripts/make_complex_compression_patch.py + python3 scripts/audit_ternary_side.py + python3 scripts/make_ternary_patch.py + +verify-tests: + python3 scripts/run_isolated_tests.py + git apply --check --directory=upstream patches/frozen-154.patch + git apply --check --directory=upstream patches/balanced-153.patch + git apply --check --directory=upstream patches/same-network-129.patch + git apply --check --directory=upstream patches/h46-111.patch + git apply --check --directory=upstream patches/h46-109.patch + git apply --check --directory=upstream patches/h46-108.patch + git apply --check --directory=upstream patches/h46-rational.patch + git apply --check --directory=upstream patches/nonadjacent-layout.patch + git apply --check --directory=upstream patches/frozen-nonadjacent-107.patch + git apply --check --directory=upstream patches/h46-nonadjacent-78.patch + git apply --check --directory=upstream patches/h46-nonadjacent-76.patch + git apply --check --directory=upstream patches/h46-shared-side-75.patch + git apply --check --directory=upstream patches/h46-incidence-67.patch + git apply --check --directory=upstream patches/h46-dag-63.patch + git apply --check --directory=upstream patches/h46-shared-point.patch + git apply --check --directory=upstream patches/h50-paired-59.patch + git apply --check --directory=upstream patches/compact-control-34.patch + git apply --check --directory=upstream patches/complex-compression-31.patch + git apply --check --directory=upstream patches/ternary-30.patch + git apply --check --directory=upstream patches/batched-23.patch + +note: + mkdir -p artifacts + tectonic --outdir artifacts notes/parameter-note.tex + +audit-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/nonadjacent-axis-note.tex + +tuned-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/routing-tuned-note.tex + +reuse-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/stage-reuse-note.tex + +incidence-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/incidence-note.tex + +dag-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/dag-note.tex + +shared-point-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/shared-point-note.tex + +paired-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/paired-note.tex + +compact-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/compact-control-note.tex + +complex-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/complex-compression-note.tex + +ternary-note: + mkdir -p artifacts + tectonic --outdir artifacts notes/ternary-note.tex + +fetch: + python3 scripts/fetch_upstream.py + +.PHONY: batched-certificate batched-patch batched-note +PDFLATEX ?= pdflatex +TEX_ENGINE ?= pdflatex +TECTONIC ?= tectonic + +batched-certificate: + python3 scripts/controlled_bit_rank_moment.py --output certificates/controlled-bit-rank-moment.json > /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify + +.PHONY: balanced-split-verify verify-balanced +balanced-split-verify: + python3 scripts/experiments/verify_balanced_split.py + python3 scripts/experiments/audit_balanced_split_completion.py + python3 scripts/experiments/audit_balanced_split_exchange.py + python3 -m unittest discover -s tests -p 'test_balanced_split*.py' -v + +verify-balanced: balanced-split-verify diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/NOTICE b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/NOTICE new file mode 100644 index 0000000000..8a6bef1613 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/NOTICE @@ -0,0 +1,337 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Balanced coarse split composition (2026-10-08) +--------------------------------------------- +Eumemic / @eumemic supplied PR69's balanced coarse sums, with OpenAI Codex +assistance. Alejandro Zarzuelo Urdiales / @alejandrozu supplied PR70's bounded +carry-exchange strategy with the AI disclosures retained in the source archive. +Chafik Boukhalfa / @chafreaky, with OpenAI Codex assistance, selected the row/ +half-plane coarse rules, future-compatible unit completion, exact integer-price +carry adaptation, composition and this certificate package. The PR71 anchored +split vector, schedules, arithmetic, pending controls and their contributor +chain are retained as credited above. Original PR69/70 sources, licenses and +notices and the complete published PR71 baseline are preserved under +references/frame-compiler. All earlier notices remain applicable. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/README.md new file mode 100644 index 0000000000..1bd7139657 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/README.md @@ -0,0 +1,184 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: balanced coarse split frames + +The [balanced-split proof and reproduction guide](research/balanced-split/README.md) +gives **κ=25872812736433/500000000000000000=5.1745625472866e-5**, approximately +**0.6437453019850683%** above the complete published PR71 witness. It composes +PR69 balanced coarse sums and a bounded PR70 carry exchange with PR71's +anchored split graph, future unit completion and profile-cost pending controls. +All actual words, dirty inputs, paid profiles and 47 strict assembly constraints +are checked by `make balanced-split-verify`. This finite conditional construction +retains the inherited all-size hypotheses and contributor notices. Chafik +Boukhalfa prepared the selected composition with OpenAI Codex assistance. + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/SOURCE.json new file mode 100644 index 0000000000..6ba76e935b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/SOURCE.json @@ -0,0 +1,257 @@ +{ + "commit": "9a58e62cf9e8954a4dde3c9b1372d733c276a6d1", + "files": { + ".gitattributes": "5f257f4e9e574ad5767f902242f519dad19cc455d6858f49234d0ccc345cabf1", + ".github/workflows/verify.yml": "1a9cccd742ba2a5aa5a5ac38c1b7559bc0dec46b23d3ce3ff3e26c3137e6c3a2", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "Makefile": 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"word_sha256": "ab2f5e9c8400bedccf45b53297942881384a33eba17f38f9137261c862577d6c", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-transitions-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-transitions-25.json new file mode 100644 index 0000000000..205a6d4311 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-transitions-25.json @@ -0,0 +1,37 @@ +{ + "h": 25, + "v": 2300, + "R": 35684, + "frames": 84845, + "distinct_transitions": 212253, + "singles": 20700, + "rank_mass": 892700, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 90841, + "2": 111317, + "3": 13314, + "4": 18459, + "5": 8388, + "6": 3215, + "7": 948, + 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composition certificate.", + "status": "PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly", + "strict_constraints": 47 +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-word-23.json.gz b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-word-23.json.gz new file mode 100644 index 0000000000..a0d30213a2 Binary files /dev/null and b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-word-23.json.gz differ diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-word-25.json.gz b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-word-25.json.gz new file mode 100644 index 0000000000..75ea580d2b Binary files /dev/null and b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/certificates/balanced-split-word-25.json.gz differ diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/SOURCE.json new file mode 100644 index 0000000000..4e38e34dc8 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/SOURCE.json @@ -0,0 +1,16 @@ +{ + "files": { + "research/copied-fixed/balanced_assembly.py": "4d27575dcad2b45a281a34054d311409ecd954f373c0c3a62c29bcc843f06a86", + "research/copied-fixed/certificate.json": "33b3373c04e18a7f4cee33ba68da6ed71934acc3e0179cca6197696be4befa22", + "research/copied-fixed/changed_graph.py": 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a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py new file mode 100644 index 0000000000..c7fd42867d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py @@ -0,0 +1,196 @@ +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit', 'complex'): + data = finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json 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"commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous 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Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + 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} + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json new file mode 100644 index 0000000000..42958fc74b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json @@ -0,0 +1,195 @@ +{ + "artifact_sha256": { + "frame-profiles-23.json": "fec377bcf1512a427674983256b900229d4133026445b6e680c6e1e6dde5af7d", + "frame-profiles-25.json": "28b4b911e26fbc02dde0d2e1458ed16227f756126ab8144d6d45e164d1165262", + "frame-transitions-23.json": "86646f1110595294cccc15603c552f0a153574a690b69c3b144d84a449891103", + "frame-transitions-25.json": "c333c348665d12b95e168ca4fac48bfdca335104edd0f29c81fe94bec292e774", + "frame-word-23.json.gz": "a44e038e1c548ea8ac31dd04acc2bba7951b22e17df7b7ad3464ea2b504a8da4", + "frame-word-25.json.gz": "ad8b299697f90b185b6b791313b505586be97965519052100d097df6199e00c5", + "paired-candidate.json": "34a500d739537235dfc5d24325c22856ca4567b9eac998a3bce9b13db5501940" + }, + "axes": { + "23": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 36432, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 31460, + "elementary_xors": 149137, + "h": 23, + "histogram": { + "0": 302057, + "1": 42694, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "2": 82722, + "21": 165, + "22": 23, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 642620, + "roles": 27918, + "stats": { + "augmentations": 220, + "clearing_xors": 1577, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "regions": 52473 + } + }, + "gzip_sha256": "a44e038e1c548ea8ac31dd04acc2bba7951b22e17df7b7ad3464ea2b504a8da4", + "replay": { + "elementary_xors": 149137, + "full_basis_vectors": 31460, + "h": 23, + "histogram": { + "0": 162914, + "1": 42694, + "10": 442, + "11": 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orientations PASS", + "word_length": 856108 + }, + "schedule": "reverse-node", + "word_sha256": "a54443429f47c486016771ce0436effda098e142afc52861c20957e9ff8e086b" + } + }, + "source_sha256": { + "research/pair-assembly/frame/frame_verify.py": "fafe25d57166a747eeb847444a2e02dd7eed19038b93a2c495014d147d04a8fb", + "research/pair-assembly/pair_graph.py": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "research/reordered-rank-pair/test_negative.py": "88832242e6f74e3fe08d109d4f21ff188a9ca0ae50c3e8f31da0243fe9501510", + "research/reordered-rank-pair/verify.py": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352", + "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3", + "scripts/experiments/binary_frame_profiles.cpp": 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "loss": 506, + "rank_sum": 642620, + "field_prime": 2305843009213693951, + "frames": 52475, + "distinct_matrices": 36399, + "crt_matrices": 6049, + "crt_disagreements": 0, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json new file mode 100644 index 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json new file mode 100644 index 0000000000..2883a5f7c9 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "frames": 52475, + "distinct_transitions": 138016, + "singles": 15939, + "rank_mass": 642620, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 53320, + "2": 77409, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "21": 165, + "22": 23 + }, + "word_sha256": 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + "exponent": 5333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5715743812, + "rhs": 1792000000313576, + "rhs_bits": 51 + }, + "rows": { + "exponent": 5715743812, + "rhs": 896000000156824000, + "rhs_bits": 60 + } + } + }, + { + "log2_input": 224000000000000, + "powers": { + "alpha": { + "exponent": 11431487624, + "rhs": 1792000000156824, + "rhs_bits": 51 + }, + "compact": { + "exponent": 11431487624, + "rhs": 7168000000627232, + "rhs_bits": 53 + }, + "leaf": { + "exponent": 10666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11431487624, + "rhs": 3584000000313576, + "rhs_bits": 52 + }, + "rows": { + "exponent": 11431487624, + "rhs": 1792000000156824000, + "rhs_bits": 61 + } + } + }, + { + "log2_input": 448000000000000, + "powers": { + "alpha": { + "exponent": 22862975248, + "rhs": 3584000000156824, + "rhs_bits": 52 + }, + "compact": { + "exponent": 22862975248, + "rhs": 14336000000627232, + "rhs_bits": 54 + }, + "leaf": { + "exponent": 21333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 22862975248, + "rhs": 7168000000313576, + "rhs_bits": 53 + }, + "rows": { + "exponent": 22862975248, + "rhs": 3584000000156824000, + "rhs_bits": 62 + } + } + } + ], + "practical_runtime_claim": false + }, + "kappa": "40827/800000000", + "next_kappa": "318961/6250000000", + "next_kappa_rejection": "{'g1_above_kappa': '-25408022593116799041/7102635201420453820506250000000', 'g3_above_kappa': '-5201705247125960457841/1136421632227272611281000000000000', 'g5_above_kappa': '-7640875416065173165777/1818274611563636178049600000000000', 'g6_above_kappa': '-33658690551416775383761/9091373057818180890248000000000000'}", + "original_enclosure_control": { + "accepted_upper": "427922022655051425592169455669348999419009338821677321501934579031509793316011927849852932699225587520480274623290826519124585131702799274967695430254567113650998884459986946222692530282749027853246814000572815342011972280832203653626757194588235745687874105909336892415629002940540277569675953192803096179140323199169875932058482212840371519373866332987776983981442275480629595879092440778438065834410270423292532877965451564571150969903518733283745770147929604915103094966966240445718551419238205360172260389165815355293860586787487668007987689744585745259297708409486845374929838902410526770296527117452860612190765279746966315757114757646249443956020657651637850471083396567352186238660458491615294604389003317389825219053116168473153626947262543915434579501546193988862612230828605213616950127673267971569642351835151332191639228898384399684069201926146521990048728093044781289653532998958679374426311189560250341590145887508815021337226982815008224357898461730107482372032845888428476273500999760300211786400006201411895378711403441679516543048925021677151249124774565210588951830515783148269750340702961227551/427922022656065148722015624802653702889498564421131911283499341667573520226931037010841800905471906532344178836996138043716400845851217866305783744362952178488692163617667760947934446961428764096857095662125776648371730944750850740376437391609342381012534311915175448066736517476339673099556706774420618964194148648273392198066357729130169733561134843302857240883248026154958104699812690626052696940220399106081385425042375485602542555097186568052507330835744941604979041042724146442866160606543845260686788873587136675704407457814823973491248098778928607362558510538701395621352496475077156310639504247824069338077266718928997258973439362819271794470658904562860362470215133491491305622841328989108583065554731667738937158958161399293136952726957825424616696098290625805073806865420810062253320746566043770582998650738545122821954094593047815197564256009823257422725379706679933315631514838786135447434356419391187561619401952168548631044553632502869921434523792993783307013326156305798890689568359302672301544894715282222433613932715358768884516049207059704442128612279932500000000000000000000000000000000000000000", + "next_bit_lower": "374050380000830479912607937870818083834173718615907103079616878943322706260497332605534066060136407627149268792108716494485294881071/374050380000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + } + }, + "comparison": { + "additional_precision_gain": "2116843/200000000000000000", + "difference": "1238116843/200000000000000000", + "difference_pr65": "59693903/12500000000000000", + "kappa": "10206752116843/200000000000000000", + "pr63_kappa": "5102757/100000000000", + "pr65_kappa": "2041159402879/40000000000000000", + "structural_gain_on_original_grid": "309/50000000000" + }, + "grid_denominator": 1000000000000000000, + "next_bit_saving": "5103636516201/100000000000000000", + "preferred": { + "assembly": { + "absorption_gap": "12957517239351787231794417587/100005103636516190692726967598200000000000000000", + "constraints": { + "K_dominates_log": "25518182705927945452132037536365162009/500025518182580953463634837991000000000000", + "K_geometry": "375025518182705953463634837991/500025518182580953463634837991000000000000", + "a_below_b": "20663634837991/1000000000000000000", + "a_positive": "51036365162009/1000000000000000000", + "alpha_below_one": "999999999999500025518182580953463634837991/1000051036365161906927269675982000000000000", + "alpha_below_one_fourth": "249961722725628595322730323966963634837991/1000051036365161906927269675982000000000000", + "alpha_positive": "51036365661881409087095028536365162009/1000051036365161906927269675982000000000000", + "artificial_boundary": "28001633163690681098227177374284390904513973/4000204145460647627709078703928000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "499974481817294046536365162009/500000000000000000000000000000", + "c_positive": "25518182705953463634837991/500000000000000000000000000000", + "cell_above_band": "999999999998499974481817419046536365162009/2000102072730323813854539351964000000000000", + "compact_leaf": "8539317419046536365162009/500000000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "25518183080953463634837991/500025518182580953463634837991", + "epsilon_positive": "499999999999500000000000000000/500025518182580953463634837991", + "g1_above_kappa": "100005116594033430044514199392617587/100005103636516190692726967598200000000000000000", + "g2_above_kappa": "1302288897/500000000000000000", + "g3_above_kappa": "12957517239351787231794417587/100005103636516190692726967598200000000000000000", + "g4_above_kappa": "1302288897/500000000000000000", + "g5_above_kappa": "37501926821210810861559844643742587/100005103636516190692726967598200000000000000000", + "g6_above_kappa": "87504478639468906207923328442842587/100005103636516190692726967598200000000000000000", + "g7_above_kappa": "99994896363383814423867065831844514199392617587/100005103636516190692726967598200000000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "25518183080953463634837991/500025518182580953463634837991", + "lambda_above_internal": "51036365162009/1000000000000000000000000000000", + "lambda_above_sigma": "20663634838042036365162009/1000000000000000000000000000000", + "lambda_above_tau": "51036365162009/1000000000000000000000000000000", + "lambda_prime_above_lambda": "51036365162009/1000000000000000000000000000000", + "lambda_prime_below_one": "25518182580953463634837991/500000000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "40829092429500023633159832136365162009/800040829092129525541815740785600000000000", + "phase_leaf_above_bit": "17078634837991/1000000000000000000", + "phase_local": "204145464147602190896122974536365162009/4000204145460647627709078703928000000000000", + "prime_interval_packing": "25518183080953463634837991/500025518182580953463634837991", + "q_below_internal": "51036365162009/500000000000000000000000000000", + "q_below_leaf": "8539317419046536365162009/500000000000000000000000000000", + "q_below_reservations": "1/4000000000000", + "q_positive": "25518182580953463634837991/500000000000000000000000000000", + "record_suffix": "25518183080953463634837991/500025518182580953463634837991", + "row_product_gap": "6548/25", + "short_record_fallback": "499974480514563711027641740160491885440816916081/500025518182580953463634837991000000000000000000", + "small_field_exposure": "1/1000000000000" + }, + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "margins": { + "g1": "25518183080953463634837991/500025518182580953463634837991", + "g2": "51036365162009/1000000000000000000", + "g3": "25518182580927945452257037536365162009/500025518182580953463634837991000000000000", + "g4": "51036365162009/1000000000000000000", + "g5": "40829092429500023633159832136365162009/800040829092129525541815740785600000000000", + "g6": "204145464147602190896122974536365162009/4000204145460647627709078703928000000000000", + "g7": "499999999999500000000000000000/500025518182580953463634837991" + }, + "minimum_margin": "25518182580927945452257037536365162009/500025518182580953463634837991000000000000", + "parameters": { + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": "1", + "a_bit": "51036365162009/1000000000000000000", + "a_complex": "717/10000000", + "alpha_squared_power": "51036365661881409087095028536365162009/1000051036365161906927269675982000000000000", + "beta": "1/20", + "c": "25518182705953463634837991/500000000000000000000000000000", + "delta": "1/8000000000000", + "epsilon": "499999999999500000000000000000/500025518182580953463634837991", + "h": "1/1000000000000", + "kappa": "10206752116843/200000000000000000", + "lambda_": "999948963634838042036365162009/1000000000000000000000000000000", + "lambda_prime": "499974481817419046536365162009/500000000000000000000000000000", + "q": "25518182580953463634837991/500000000000000000000000000000", + "sigma": "9999283/10000000", + "tau": "999948963634837991/1000000000000000000" + }, + "recurrence": { + "internal": "999948963634837991/1000000000000000000", + "leaf": "199986377/200000000", + "reservations": "499974481817294046536365162009/500000000000000000000000000000" + }, + "scoped_limit": "51036365162009/1000051036365162009" + }, + "eventual_bounds": { + "additional_eventual_conditions": [ + "BHP prime threshold and distinct-prime packing", + "Fixed rational basis, eligible common prime and native table setup", + "Catalogue/descriptor domination, logarithm absorption, exact recovery" + ], + "all_interval_argument": "For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). Successive intervals double LHS; the positive affine RHS grows at most linearly, so 2^j >= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956143, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + "exponent": 5333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5715743812, + "rhs": 1792000000313576, + "rhs_bits": 51 + }, + "rows": { + "exponent": 5715743812, + "rhs": 896000000156824000, + "rhs_bits": 60 + } + } + }, + { + "log2_input": 224000000000000, + "powers": { + "alpha": { + "exponent": 11431487624, + "rhs": 1792000000156824, + "rhs_bits": 51 + }, + "compact": { + "exponent": 11431487624, + "rhs": 7168000000627232, + "rhs_bits": 53 + }, + "leaf": { + "exponent": 10666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11431487624, + "rhs": 3584000000313576, + "rhs_bits": 52 + }, + "rows": { + "exponent": 11431487624, + "rhs": 1792000000156824000, + "rhs_bits": 61 + } + } + }, + { + "log2_input": 448000000000000, + "powers": { + "alpha": { + "exponent": 22862975248, + "rhs": 3584000000156824, + "rhs_bits": 52 + }, + "compact": { + "exponent": 22862975248, + "rhs": 14336000000627232, + "rhs_bits": 54 + }, + "leaf": { + "exponent": 21333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 22862975248, + "rhs": 7168000000313576, + "rhs_bits": 53 + }, + "rows": { + "exponent": 22862975248, + "rhs": 3584000000156824000, + "rhs_bits": 62 + } + } + } + ], + "practical_runtime_claim": false + }, + "kappa": "10206752116843/200000000000000000", + "next_kappa": "6379220073027/125000000000000000", + "next_kappa_rejection": "{'g3_above_kappa': '-54404741498227752163082843757/62503189772822619182954354748875000000000000000'}" + }, + "profile_path": "research/slot-cost-rank-pair/paired-candidate.json", + "profile_sha256": "be0322ad60f73923953f242eaffaf114ff12438e8617dae38888b77fa03184cc", + "proof_limits": [ + "The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.", + 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a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 at the new bit saving, +and the new complete profile has exact upper moment <1. All47 strict assembly +conditions and seven margins pass. **53 Lean endpoints** pass:34 new universal, +15 concrete,4 reused rational-helper lemmas. No omitted proof, project axiom or +native decision shortcut. The math scope includes dirty-word/complement safety, +coordinate conjugacy, fresh-kernel clearing, actual finite rounding and old-profile +rejection. It does not formalize the Python/C++ compiler or the all-size theorem. + +## Reproduce the accepted words + +Use an external checkout of frozen PR62 commit +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No newer sources are consumed. +See `verification/README.md` to compile its exact C++17 profiler, then run: + +``` +python verification/verify_words.py --upstream UPSTREAM --profiler PROFILER --word23 words/word-23.json.gz --word25 words/word-25.json.gz --output work/recheck +python verification/check_guards.py words/word-23.json.gz +python verification/check_guards.py words/word-25.json.gz +cd math +lake build Frozen62Research +``` + +The verifier checks immutable sources and its own adapter hashes, full input/dirty +bases in both orientations, exact source/scatter inventory, every literal frame +transition and all fixed-I+J profiles with bounded-minor and CRT checks. It rejects +optimized Python assertion mode. Use the supplied words for authoritative replay; +floating discovery prices propose candidates and have no trusted-proof role. +Discovery source snapshots, exact oracle fixtures (gzip-compressed) and matching +seeds retain original byte hashes. `discovery/SEARCH.md` explains the algorithms, +heuristic boundary and experimental commands. Historical workspace paths in the +source-generation receipts identify the original run; the accepted-word replay +uses the explicit upstream argument and needs no private directory layout. +Portable discovery regeneration: + +``` +python discovery/regenerate_portable.py --upstream UPSTREAM --work work/regenerate +``` + +This rewrites workspace paths only and checks both raw words and deterministic +gzip against the accepted words. Floating discovery is outside the trusted +certificate; the independent word/profile verifier establishes acceptance. + +The one-hour session froze information through #62. The unchanged data geometry +and its rational recovery are inherited; selected physical words/profile checks +are fresh. All-size analytic, compiler/frame transfer, finite-alphabet tape, +routing, prime selection/recovery and eventual-threshold contracts remain +conditional. No practical runtime or global-optimality claim is made. + +Alejandro Zarzuelo Urdiales is the human author/developer, following earlier +Archivara and personal July/October matrix/parity work developed with multiple +AI tools. This synthesis involved substantial OpenAI Codex assistance. Known +linear algebra, matroid exchange, dirty uncomputation and concavity principles +retain prior-work status. The finite construction credits Avi Eisenberg/ikeboy +(#62 interval/core-aware graph), eumemic (#57 frame compiler), Chafik Boukhalfa +(#60 ranking and earlier exact profiling), Rohan Arun and other retained notices. +The prior matrix/parity source is in `../matrix-exponent-synthesis/` and prior +Gaussian work in PR45. Its product counts retain their separate arithmetic scope. +The paper is supplied as LaTeX source; no newly compiled PDF is claimed. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md new file mode 100644 index 0000000000..b8dd669634 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md @@ -0,0 +1,136 @@ +# Local frame-compiler search, frozen through PR62 + +All experiments in this directory use the pinned PR62 pair graph at +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No later community source is consumed. +The original checkout is unchanged. Each emitted word and compiler copy has +a SHA256 recorded in its `compiled.json`; changed words are sent separately +to the independent literal replay and profile verifier. + +## New dependency-circuit choices + +The inherited compiler reduces retired fresh-signal rows against the current +live anchors and an echelon basis of compatible retired rows. Instead of +accepting the first dependent retired row, the new selectors collect the +available fundamental dependency circuits and choose a circuit by one of: + +- total charged target/provider rank growth (`all_growth`); +- number and rank growth of other retired providers (`all_collateral`); +- anchor-only dependence before general retired dependence (`anchor_first`); +- actual physical transition child-profile moment cost (`profile_cost*`). + +Every clearing XOR and every target/provider frame promotion is still emitted +and charged. A zero fresh-signal row can contain arbitrary physical dirty state; +its reuse is justified by the complete reversible word, not by claiming that +the physical register is initialized to zero. The compiler runs both complete +dirty-basis orientations, and the independent verifier repeats them. + +For the last selector let `C(A,B) = sum_t n_t(A,B) F_t`, where the `n_t` are +the exact inherited fixed-I+J pivot-run profile of the physical frame transition +and `F_t = t exp(a log(m/t))`. A candidate target `s` at old frame `A_s`, cleared +into frame `G` with providers `z`, is priced by + +``` +C(A_s,G) - C(A_s,I) + + sum_z [C(A_z,G) + C(G,I) - C(A_z,I)]. +``` + +This accounts for immediate promotions and the change in deferred cleanup, +assuming each other retired provider remains retired until cleanup. Future +reuse couples decisions, so this is a discovery heuristic, not an additive +global optimality certificate. Linear rank mass cancels between candidates; +`t*expm1(a*log(m/t))` avoids cancellation in floating discovery prices. +Missing transition profiles are recorded and collected for the next iteration. +Once a run has zero missing pairs, every local price uses an actual transition +profile. The final saving is accepted only through exact rational whole-profile +moment bounds and all assembly gates. + +`build_pair_oracle.py` is a local adaptation of the frozen C++ profiler that +additionally exports each transition histogram. It preserves the projector, +pivot, bounded-minor and three-prime CRT routines. Its synthetic transition-list +input is an oracle request, not a physical executable word. Each immutable +profile dump and the source/header hashes are recorded. + +## Moment-ordered carry selection + +The `--weighted` experiment orders the inherited linear/partition-matroid +candidate edges by their physical transition moment change before the original +greedy initialization and augmenting paths. For a value produced at `P`, +preserved through donor frame `G`, and carried to future target `T`, its +no-reclamation child-cost change is + +``` +C(G,T) - C(G,I) - C(0,P) - C(P,T). +``` + +At fixed cardinality, role and external-volume corrections are common to all +edge choices in the same axis. The inherited augmenting algorithm still seeks +maximum cardinality; it does not optimize the weights globally. Reclamation +adds coupling, so only the changed whole-word profile can establish an actual +improvement. This experiment makes no minimum-cost matroid claim. + +The `--exchange` variant starts from the frozen original maximum-cardinality +matching and tries bounded improving one-edge exchanges. A new edge may replace +the old donor of the same use when its donor block stays linearly independent; +or it may replace a selected edge in the same donor block and serve an unused +use. Both preserve cardinality and distinct-use constraints. The `--cycle` +variant additionally tests two-edge donor/use cycles, checking the independence +of both changed blocks. No improving two-edge cycle was found in the tested +native-price instance; this is not a proof that longer cycles cannot improve it. + +## Joint basis and schedule search + +`--basis shift1` profiles all candidate physical transitions after the point +permutation `i -> (i+1) mod h`, while preserving their original frame IDs. +Matching and reclamation are then priced in that basis. The emitted word is +renamed by `relabel_word.py`: all frame masks, canonical source/output triples, +common points and scatter port indices change together. Scratch slots and +literal XOR instructions are retained. The complete triple family and the +permutation-invariant `I+J` basis are inherited; every final renamed word still +gets fresh full-basis and actual physical-profile verification. + +This joint search differs from merely relabeling an already selected schedule: +the selected carries and clearing circuits are optimized under the new ordered +pivot-run prices. It remains a bounded discovery heuristic. + +## Regeneration + +The frozen graph/matching setup and a moment-cost exchange run are generated by: + +``` +python -S collect_matching_pairs.py --h 23 +python -S build_pair_oracle.py --h 23 --strategy matching_collect +python -S run_strategy.py --h 23 --strategy profile_cost --exchange +``` + +Repeat at `h=25`. For joint search, add `--basis shift1` to the oracle and +strategy commands. Reclamation may encounter transitions absent from the +initial carry-edge inventory. Run the oracle again on the emitted strategy +directory with `--incremental`, then run a new strategy label. The new label +must start with `profile_cost`; output directories are never overwritten. +`compiled.json` records the exact oracle dump hash, missing-pair count, word +hashes and source pin. Immutable earlier oracle dumps are retained by SHA256. +Use `--oracle path/to/the-immutable-dump.jsonl` to reproduce the prices of a +specific recorded run instead of consuming the subsequently enlarged cache. +The initial compiler matching cache is accepted only if its complete candidate +edge list matches the current frozen graph and every restored selected block +passes the same linear-independence check. + +The runner saves an immutable source copy and its hash for later runs. Floating +`expm1` prices at discovery saving `a=0.00005103` select proposals only. Neither +those prices nor their reported local gains are used as an arithmetic witness. + +## Acceptance boundary + +The independent verifier checks all input and dirty basis vectors in both +orientations, exact literal-scatter incidences, causal nested physical frames, +event equality reconstructed from the actual XOR word, rank mass, actual child +profiles and CRT agreement. It then computes the whole mixed-axis recurrence +and exact rational moment/assembly witnesses. Existing all-size geometry, +analytic envelopes, compiler/tape arguments and the surrounding reduction are +inherited from frozen PR62. A finite profile improvement does not by itself +formally prove those inherited hypotheses. + +Reduced XOR count alone is not accepted as an exponent improvement. In this +search `all_collateral` and `anchor_first` reduced clearing XORs but worsened +the certified characteristic. Actual child-size distributions decide the +saving, even when both physical-role counts and total rank mass are unchanged. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py new file mode 100644 index 0000000000..7c154b1a29 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py @@ -0,0 +1,275 @@ +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +import sys;sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'matrix-synthesis/bridge/pr62/references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s,add=True): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>s&1;e^=1<=prices[f]-1e-14:continue + if not can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:-prices[z])if prices[e] /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/NOTICE b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/NOTICE new file mode 100644 index 0000000000..8adab44ba3 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/NOTICE @@ -0,0 +1,324 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/README.md new file mode 100644 index 0000000000..4a9b481aa3 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/README.md @@ -0,0 +1,172 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/SOURCE.json new file mode 100644 index 0000000000..c8cc31f3d0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/SOURCE.json @@ -0,0 +1,120 @@ +{ + "commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "Makefile": "6e9e48a677b2f66643226840f574a6535e3564ffb0c72284b60302684a5dfbe4", + "NOTICE": 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"https://github.com/CrocSwap/integer-mult-bounds/pull/48" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py new file mode 100644 index 0000000000..c7fd42867d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py @@ -0,0 +1,196 @@ +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit', 'complex'): + data = finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": "41187950749917624099/1000000000000000000000000", + "cell_above_band": "666666666665666652937349833360791967/1333388250600666556832132000000000000", + "compact_leaf": "26927049500082375901/1000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "13729317166639208033/333347062650166639208033", + "epsilon_positive": "333333333333000000000000/333347062650166639208033", + "g1_above_kappa": "3408408254232349301008147/3333470626501666392080330000000000000", + "g2_above_kappa": "4241/2500000000000", + "g3_above_kappa": "74937627730682908927817/3333470626501666392080330000000000000", + "g4_above_kappa": "4241/2500000000000", + "g5_above_kappa": "5299956450675231223831763/13333882506006665568321320000000000000", + "g6_above_kappa": "11966897703678564007992423/13333882506006665568321320000000000000", + "g7_above_kappa": "3333196040161742016173902349301008147/3333470626501666392080330000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "13729317166639208033/333347062650166639208033", + "lambda_above_internal": "82375901/2000000000000000000000000", + "lambda_above_sigma": "61024099000082375901/2000000000000000000000000", + "lambda_above_tau": "82375901/2000000000000000000000000", + "lambda_prime_above_lambda": "82375901/2000000000000000000000000", + "lambda_prime_below_one": "41187950499917624099/1000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "21966907133275670202633360791967/533355300240266622732852800000000000", + "phase_leaf_above_bit": "53854099/2000000000000", + "phase_local": 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": 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Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + 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"1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json 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b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json new file mode 100644 index 0000000000..42958fc74b --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json @@ -0,0 +1,195 @@ +{ + "artifact_sha256": { + "frame-profiles-23.json": "fec377bcf1512a427674983256b900229d4133026445b6e680c6e1e6dde5af7d", + "frame-profiles-25.json": "28b4b911e26fbc02dde0d2e1458ed16227f756126ab8144d6d45e164d1165262", + "frame-transitions-23.json": 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a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json new file mode 100644 index 0000000000..3b648dbe21 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "loss": 506, + "rank_sum": 642620, + "field_prime": 2305843009213693951, + "frames": 52475, + "distinct_matrices": 36399, + "crt_matrices": 6049, + "crt_disagreements": 0, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 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a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + "exponent": 5333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5715743812, + "rhs": 1792000000313576, + "rhs_bits": 51 + }, + "rows": { + "exponent": 5715743812, + "rhs": 896000000156824000, + "rhs_bits": 60 + } + } + }, + { + "log2_input": 224000000000000, + "powers": { + "alpha": { + "exponent": 11431487624, + "rhs": 1792000000156824, + "rhs_bits": 51 + }, + "compact": { + "exponent": 11431487624, + "rhs": 7168000000627232, + "rhs_bits": 53 + }, + "leaf": { + "exponent": 10666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11431487624, + "rhs": 3584000000313576, + "rhs_bits": 52 + }, + "rows": { + "exponent": 11431487624, + "rhs": 1792000000156824000, + "rhs_bits": 61 + } + } + }, + { + "log2_input": 448000000000000, + "powers": { + "alpha": { + "exponent": 22862975248, + "rhs": 3584000000156824, + "rhs_bits": 52 + }, + "compact": { + "exponent": 22862975248, + "rhs": 14336000000627232, + "rhs_bits": 54 + }, + "leaf": { + "exponent": 21333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 22862975248, + "rhs": 7168000000313576, + "rhs_bits": 53 + }, + "rows": { + "exponent": 22862975248, + "rhs": 3584000000156824000, + "rhs_bits": 62 + } + } + } + ], + "practical_runtime_claim": false + }, + "kappa": "40827/800000000", + "next_kappa": "318961/6250000000", + "next_kappa_rejection": "{'g1_above_kappa': '-25408022593116799041/7102635201420453820506250000000', 'g3_above_kappa': '-5201705247125960457841/1136421632227272611281000000000000', 'g5_above_kappa': '-7640875416065173165777/1818274611563636178049600000000000', 'g6_above_kappa': '-33658690551416775383761/9091373057818180890248000000000000'}", + "original_enclosure_control": { + "accepted_upper": "427922022655051425592169455669348999419009338821677321501934579031509793316011927849852932699225587520480274623290826519124585131702799274967695430254567113650998884459986946222692530282749027853246814000572815342011972280832203653626757194588235745687874105909336892415629002940540277569675953192803096179140323199169875932058482212840371519373866332987776983981442275480629595879092440778438065834410270423292532877965451564571150969903518733283745770147929604915103094966966240445718551419238205360172260389165815355293860586787487668007987689744585745259297708409486845374929838902410526770296527117452860612190765279746966315757114757646249443956020657651637850471083396567352186238660458491615294604389003317389825219053116168473153626947262543915434579501546193988862612230828605213616950127673267971569642351835151332191639228898384399684069201926146521990048728093044781289653532998958679374426311189560250341590145887508815021337226982815008224357898461730107482372032845888428476273500999760300211786400006201411895378711403441679516543048925021677151249124774565210588951830515783148269750340702961227551/427922022656065148722015624802653702889498564421131911283499341667573520226931037010841800905471906532344178836996138043716400845851217866305783744362952178488692163617667760947934446961428764096857095662125776648371730944750850740376437391609342381012534311915175448066736517476339673099556706774420618964194148648273392198066357729130169733561134843302857240883248026154958104699812690626052696940220399106081385425042375485602542555097186568052507330835744941604979041042724146442866160606543845260686788873587136675704407457814823973491248098778928607362558510538701395621352496475077156310639504247824069338077266718928997258973439362819271794470658904562860362470215133491491305622841328989108583065554731667738937158958161399293136952726957825424616696098290625805073806865420810062253320746566043770582998650738545122821954094593047815197564256009823257422725379706679933315631514838786135447434356419391187561619401952168548631044553632502869921434523792993783307013326156305798890689568359302672301544894715282222433613932715358768884516049207059704442128612279932500000000000000000000000000000000000000000", + "next_bit_lower": "374050380000830479912607937870818083834173718615907103079616878943322706260497332605534066060136407627149268792108716494485294881071/374050380000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + } + }, + "comparison": { + "additional_precision_gain": "2116843/200000000000000000", + "difference": "1238116843/200000000000000000", + "difference_pr65": "59693903/12500000000000000", + "kappa": "10206752116843/200000000000000000", + "pr63_kappa": "5102757/100000000000", + "pr65_kappa": "2041159402879/40000000000000000", + "structural_gain_on_original_grid": "309/50000000000" + }, + "grid_denominator": 1000000000000000000, + "next_bit_saving": "5103636516201/100000000000000000", + "preferred": { + "assembly": { + "absorption_gap": "12957517239351787231794417587/100005103636516190692726967598200000000000000000", + "constraints": { + "K_dominates_log": "25518182705927945452132037536365162009/500025518182580953463634837991000000000000", + "K_geometry": "375025518182705953463634837991/500025518182580953463634837991000000000000", + "a_below_b": "20663634837991/1000000000000000000", + "a_positive": "51036365162009/1000000000000000000", + "alpha_below_one": "999999999999500025518182580953463634837991/1000051036365161906927269675982000000000000", + "alpha_below_one_fourth": "249961722725628595322730323966963634837991/1000051036365161906927269675982000000000000", + "alpha_positive": "51036365661881409087095028536365162009/1000051036365161906927269675982000000000000", + "artificial_boundary": "28001633163690681098227177374284390904513973/4000204145460647627709078703928000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "499974481817294046536365162009/500000000000000000000000000000", + "c_positive": "25518182705953463634837991/500000000000000000000000000000", + "cell_above_band": "999999999998499974481817419046536365162009/2000102072730323813854539351964000000000000", + "compact_leaf": "8539317419046536365162009/500000000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "25518183080953463634837991/500025518182580953463634837991", + "epsilon_positive": "499999999999500000000000000000/500025518182580953463634837991", + "g1_above_kappa": "100005116594033430044514199392617587/100005103636516190692726967598200000000000000000", + "g2_above_kappa": "1302288897/500000000000000000", + "g3_above_kappa": "12957517239351787231794417587/100005103636516190692726967598200000000000000000", + "g4_above_kappa": "1302288897/500000000000000000", + "g5_above_kappa": "37501926821210810861559844643742587/100005103636516190692726967598200000000000000000", + "g6_above_kappa": "87504478639468906207923328442842587/100005103636516190692726967598200000000000000000", + "g7_above_kappa": "99994896363383814423867065831844514199392617587/100005103636516190692726967598200000000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "25518183080953463634837991/500025518182580953463634837991", + "lambda_above_internal": "51036365162009/1000000000000000000000000000000", + "lambda_above_sigma": "20663634838042036365162009/1000000000000000000000000000000", + "lambda_above_tau": "51036365162009/1000000000000000000000000000000", + "lambda_prime_above_lambda": "51036365162009/1000000000000000000000000000000", + "lambda_prime_below_one": "25518182580953463634837991/500000000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "40829092429500023633159832136365162009/800040829092129525541815740785600000000000", + "phase_leaf_above_bit": "17078634837991/1000000000000000000", + "phase_local": "204145464147602190896122974536365162009/4000204145460647627709078703928000000000000", + "prime_interval_packing": "25518183080953463634837991/500025518182580953463634837991", + "q_below_internal": "51036365162009/500000000000000000000000000000", + "q_below_leaf": "8539317419046536365162009/500000000000000000000000000000", + "q_below_reservations": "1/4000000000000", + "q_positive": "25518182580953463634837991/500000000000000000000000000000", + "record_suffix": "25518183080953463634837991/500025518182580953463634837991", + "row_product_gap": "6548/25", + "short_record_fallback": "499974480514563711027641740160491885440816916081/500025518182580953463634837991000000000000000000", + "small_field_exposure": "1/1000000000000" + }, + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "margins": { + "g1": "25518183080953463634837991/500025518182580953463634837991", + "g2": "51036365162009/1000000000000000000", + "g3": "25518182580927945452257037536365162009/500025518182580953463634837991000000000000", + "g4": "51036365162009/1000000000000000000", + "g5": "40829092429500023633159832136365162009/800040829092129525541815740785600000000000", + "g6": "204145464147602190896122974536365162009/4000204145460647627709078703928000000000000", + "g7": "499999999999500000000000000000/500025518182580953463634837991" + }, + "minimum_margin": "25518182580927945452257037536365162009/500025518182580953463634837991000000000000", + "parameters": { + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": "1", + "a_bit": "51036365162009/1000000000000000000", + "a_complex": "717/10000000", + "alpha_squared_power": "51036365661881409087095028536365162009/1000051036365161906927269675982000000000000", + "beta": "1/20", + "c": "25518182705953463634837991/500000000000000000000000000000", + "delta": "1/8000000000000", + "epsilon": "499999999999500000000000000000/500025518182580953463634837991", + "h": "1/1000000000000", + "kappa": "10206752116843/200000000000000000", + "lambda_": "999948963634838042036365162009/1000000000000000000000000000000", + "lambda_prime": "499974481817419046536365162009/500000000000000000000000000000", + "q": "25518182580953463634837991/500000000000000000000000000000", + "sigma": "9999283/10000000", + "tau": "999948963634837991/1000000000000000000" + }, + "recurrence": { + "internal": "999948963634837991/1000000000000000000", + "leaf": "199986377/200000000", + "reservations": "499974481817294046536365162009/500000000000000000000000000000" + }, + "scoped_limit": "51036365162009/1000051036365162009" + }, + "eventual_bounds": { + "additional_eventual_conditions": [ + "BHP prime threshold and distinct-prime packing", + "Fixed rational basis, eligible common prime and native table setup", + "Catalogue/descriptor domination, logarithm absorption, exact recovery" + ], + "all_interval_argument": "For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). Successive intervals double LHS; the positive affine RHS grows at most linearly, so 2^j >= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956143, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + 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a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) ++ slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();pending={};stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): +@@ -149,7 +151,8 @@ + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 +- return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) ++ endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 ++ return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} +@@ -161,6 +164,9 @@ + old,e=bb[p];row^=old;expr^=e + return expr + for s in anchors:ins(s) ++ for s,target in pending.items(): ++ if contains(blocks[frames[s]]['frame'],blocks[g]['frame']) and contains(blocks[g]['frame'],blocks[target]['frame']): ++ ins(s);stats['live_anchor_candidates']+=1 + best=None + # Inspect every eligible dependent candidate across all retired ranks. + # Rank the actual fixed-basis growth/cleanup profiles by an integer entropy score. +@@ -176,7 +182,9 @@ + if best is None or key= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and kappa > previous_kappa + bridge = json.loads((OLD/'certificate.json').read_text())['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/split-pair/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr67_commit='b3745601e947a94316bf25c2c6263d93c06e3364', + pr67_kappa=previous_kappa, ratio_pr67=kappa/previous_kappa, + absolute_gain_pr67=kappa-previous_kappa, + pr67_complete_profile_exclusion_lower=prior65_lower, + full_pr67_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected split-pair partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'split-pair-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py new file mode 100644 index 0000000000..1290ef2eb8 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py @@ -0,0 +1,275 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py new file mode 100644 index 0000000000..7908c963a4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py @@ -0,0 +1,78 @@ +#!/usr/bin/env python3 +"""Replay the aligned split-pair/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from split_pair_compose import compose, check_sources +from split_pair_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'split-pair-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='split-pair-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + 'c++', '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'split-pair-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'split-pair-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'split-pair-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'split-pair-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'split-pair-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair.py new file mode 100644 index 0000000000..5088cff133 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair.py @@ -0,0 +1,238 @@ +"""Physical and exact-arithmetic controls for the aligned split/pair witness.""" +from copy import deepcopy +from fractions import Fraction +from itertools import combinations +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile +import unittest +from unittest.mock import patch + +ROOT = Path(__file__).resolve().parents[1] +EXPERIMENTS = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXPERIMENTS)) +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from binary_frame_math import moment + + +class SplitPairControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.words = {h: json.loads(gzip.decompress((ROOT/f'certificates/split-pair-word-{h}.json.gz').read_bytes())) + for h in (23,25)} + + def reject_mutation(self, mutate, checker='both'): + for h, original in self.words.items(): + with self.subTest(h=h), tempfile.TemporaryDirectory() as directory: + changed = deepcopy(original) + mutate(changed) + path = Path(directory)/'word.json' + path.write_text(json.dumps(changed, separators=(',', ':'))+'\n') + with self.assertRaises((AssertionError, ValueError, IndexError, KeyError)): + if checker != 'transitions': + replay(path) + if checker != 'replay': + prepare(path, Path(directory)/'transitions.bin') + + def test_selected_words_pass_independent_replay(self): + recorded = json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + actual = replay(ROOT/f'certificates/split-pair-word-{h}.json.gz') + self.assertEqual(json.loads(json.dumps(actual)), recorded['axes'][str(h)]['replay']) + + def test_omitted_literal_xor_is_rejected(self): + self.reject_mutation(lambda word: word['ops'].pop(0)) + + def test_self_xor_is_rejected(self): + def mutate(word): + word['ops'][0][1] = word['ops'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_non_nested_operation_frame_is_rejected(self): + def mutate(word): + narrow = next(i for i,(core,cover) in enumerate(word['frames']) if core == cover) + operation = next(op for op in word['ops'] if word['frames'][op[2]][0] != word['frames'][op[2]][1]) + operation[2] = narrow + self.reject_mutation(mutate) + + def test_aliased_terminal_role_is_rejected(self): + def mutate(word): + word['outputs'][1][0] = word['outputs'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_missing_copied_center_is_rejected(self): + def mutate(word): + index = next(i for i,(_,_,_,target) in enumerate(word['outputs']) if len(target) == 1) + word['outputs'].pop(index) + self.reject_mutation(mutate) + + def test_omitted_transition_cannot_reduce_paid_profile(self): + self.reject_mutation(lambda word: word['events'].pop(0), 'transitions') + + def test_understated_physical_width_is_rejected(self): + def mutate(word): + word['R'] -= 1 + self.reject_mutation(mutate) + + def test_complete_pr67_profile_fails_new_bit_saving(self): + from split_pair_arithmetic import refine + previous = json.loads((ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/paired-candidate.json').read_text())['bit'] + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + result = refine.exact_moment(previous['m'], previous['W'], {int(t): n for t,n in previous['child_multiplicities'].items()}, Fraction(current['bit_saving'])) + self.assertGreater(result['lower'], 1) + self.assertGreater(Fraction(current['kappa']), Fraction(current['comparison']['pr67_kappa'])) + + def test_private_import_preserves_path_and_arithmetic_module(self): + import split_pair_graph as provider + import split_pair_arithmetic as arithmetic + sentinel = object() + existing = sys.modules.get('refine', sentinel) + previous_path = sys.path[:] + graph, schedule = provider._private_modules() + refine, audit = arithmetic.private_arithmetic() + self.assertIs(audit.refine, refine) + self.assertIs(sys.modules.get('refine', sentinel), existing) + self.assertEqual(sys.path, previous_path) + + def test_failed_graph_build_restores_original_providers(self): + import split_pair_graph as provider + previous_class, previous_points = provider._graph.circuit_class, provider._graph.alternating_points + with patch.object(provider._graph, 'graph', side_effect=RuntimeError('deliberate graph failure')): + with self.assertRaises(RuntimeError): + provider.graph(23) + self.assertIs(provider._graph.circuit_class, previous_class) + self.assertIs(provider._graph.alternating_points, previous_points) + + def test_failed_compilation_restores_engine_graph_and_schedule(self): + import split_pair_compiler as producer + previous_graph, previous_build = producer.compiler.graph, producer.compiler.build + missing = object() + runtime = {name:getattr(producer.compiler,name,missing) for name in ('PENDING_COST','ORACLE_EXE','ORACLE_INPUT','oracles')} + with patch.object(producer.compiler, 'compile_', side_effect=RuntimeError('deliberate compiler failure')): + with self.assertRaises(RuntimeError): + producer.compile_axis(23) + self.assertIs(producer.compiler.graph, previous_graph) + self.assertIs(producer.compiler.build, previous_build) + for name,value in runtime.items(): + self.assertIs(getattr(producer.compiler,name,missing),value) + + def test_uncertified_configurations_are_rejected(self): + import split_pair_graph as provider + wrong_anchor = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_anchor['anchor'] = False + boolean_group = deepcopy(provider.EXPECTED_CONFIGS[23]); boolean_group['groups'][0] = True + changed_schedule = deepcopy(provider.EXPECTED_CONFIGS[23]); changed_schedule['schedule'] = 'reverse-node' + for changed in (wrong_anchor, boolean_group, changed_schedule): + with self.subTest(configuration=changed), patch.object(provider.json, 'loads', return_value=changed): + with self.assertRaises(ValueError): + provider.configuration(23) + for dimension in (True, 22, 24, '23'): + with self.subTest(dimension=dimension), self.assertRaises(ValueError): + provider.configuration(dimension) + + def test_recursive_weighted_exclusions_and_contraction(self): + import split_pair_graph as provider + for h in (23,25): + block_sizes = [] + parent = provider._graph.circuit_class(h) + selected = provider.split_class(parent, provider.configuration(h)['groups']) + case = self + class Audited(selected): + def grouping(self, points): + groups = super().grouping(points) + case.assertEqual([x for group in groups for x in group], list(points)) + case.assertLess(len(groups), len(points)) + return groups + + def _block(self, points, edges, weights, level): + def expected(omitted): + values = [value for pair,value in edges.items() if not set(pair) & omitted] + values += [value for point,value in weights.items() if point not in omitted] + support = 0 + for value in values: + case.assertEqual(support & self.support[value], 0) + support |= self.support[value] + return support + total, single, pairs = super()._block(points, edges, weights, level) + case.assertEqual(self.support[total], expected(set())) + case.assertEqual(set(single), set(points)) + for a in points: + case.assertEqual(self.support[single[a]], expected({a})) + case.assertEqual(set(pairs), set(combinations(points,2))) + for a,b in combinations(points,2): + case.assertEqual(self.support[pairs[a,b]], expected({a,b})) + block_sizes.append(len(points)) + return total, single, pairs + local = Audited(h-1) + block_sizes.clear() + local.pair(list(range(h-1))) + self.assertEqual(sorted(block_sizes, reverse=True), [h-1, 12 if h==23 else 13, 7 if h==23 else 8, 5, 3, 2]) + + def test_next_fine_grid_points_and_old_assembly_controls_reject(self): + from split_pair_arithmetic import refine + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + bit = current['bit']; saving = Fraction(current['bit_saving']); kappa = Fraction(current['kappa']) + grid = Fraction(1,10**18) + rows = {int(t): n for t,n in bit['child_multiplicities'].items()} + self.assertLess(refine.exact_moment(bit['m'],bit['W'],rows,saving)['upper'], 1) + self.assertGreater(refine.exact_moment(bit['m'],bit['W'],rows,saving+grid)['lower'], 1) + for label, variant in ( + ('next_kappa', dict(kappa=kappa+grid)), + ('zero_backoff', dict(h=Fraction())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))): + call = dict(a_bit=saving, kappa=kappa, h=Fraction(1,10**12));call.update(variant) + with self.subTest(control=label), self.assertRaises(refine.balanced.InvalidAssembly): + refine.balanced.assembly(current['finite_bridge'], **call) + + def test_mass_preserving_profile_mutation_is_rejected(self): + from split_pair_compose import check_sources + profile_path = ROOT/'certificates/split-pair-profiles-23.json' + changed = json.loads(profile_path.read_text()) + before = sum(t*n for t,n in enumerate(changed['blocks'])) + changed['blocks'][2] += 3; changed['blocks'][3] -= 2 + self.assertTrue(all(n >= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'split-pair-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from split_pair_compose import check_sources + manifest_path = ROOT/'research/split-pair/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/split-pair-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import split_pair_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('split_pair_graph.py', 'split_pair_engine.py', 'split_pair_compiler.py', 'split_pair_arithmetic.py', 'split_pair_compose.py', 'verify_split_pair.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair_pending.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair_pending.py new file mode 100644 index 0000000000..e6d63f72a4 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/references/frame-compiler/pr71/tests/test_split_pair_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/split_pair_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/research/balanced-split/PROOF.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/research/balanced-split/PROOF.md new file mode 100644 index 0000000000..c34f8542cc --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/research/balanced-split/PROOF.md @@ -0,0 +1,251 @@ +# Finite certificate and inherited scope + +## 1. Exact change and provenance + +This construction preserves PR71's anchored `[1,1,2]` split recursion, +PR65 region schedules, PR67 profile-cost reclamation and PR68 pending live +controls with next-use scoring. It composes three finite choices: PR69's +balanced coarse parenthesization, future-compatible unit completion, and a +bounded adaptation of PR70 carry exchanges. The contributor originals, +licenses and notices are retained in hash-checked archives. The published +PR71 source, words and complete arithmetic certificate are preserved at +`1bef94fd40a746452548c84a4a8f8834670a3113` for the full-profile comparison. +The new namespace is `balanced-split`. Two portable engines differ from the +independently audited discovery engines only in the repository-relative ROOT +constant; their relocation patches and SHA256s are recorded. + +The h23 coarse cell uses columns when `i+jstep and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority):''' +check(s.count(completion)==1 and s.count(changed_start)==1,'Changed source not uniquely recognized') +check(s.replace(changed_start,old_start).replace(completion,' for i in range(len(ins)):')==old,'Compiler changed beyond the claimed unit-completion priority') +tree=ast.parse(s) +helpers=[n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name in ('basis','independent')] +namespace={};exec(compile(ast.Module(body=helpers,type_ignores=[]),str(SOURCE),'exec'),namespace) +basis=namespace['basis'];independent=namespace['independent'] +future=next(n for n in ast.walk(tree) if isinstance(n,ast.FunctionDef) and n.name=='future_priority') +contains=lambda a,b:not(b[0]&~a[0]) and not(a[1]&~b[1]) +# Actual-use fixtures distinguish future compatible uses from backward or nonnested uses. +ns=dict(position={0:0,1:1,2:2,3:3},step=1,b={'frame':(1,3),'inputs':[10,11,12,13]},blocks=[{'frame':(1,3)},{'frame':(1,3)},{'frame':(1,7)},{'frame':(1,5)}],uses=[(10,2,None),(10,2,('terminal',)),(11,2,None),(11,0,None),(12,3,None),(13,3,None)],value_uses={10:[0,1],11:[2,3],12:[4],13:[5]},contains=contains,slots=[7,1,3,3],ins=[0,1,2,3]) +exec(compile(ast.Module(body=[future],type_ignores=[]),str(SOURCE),'exec'),ns) +check([ns['future_priority'](i) for i in range(4)]==[(-2,3,0),(-1,1,1),(0,2,2),(0,2,3)],'Priority does not use compatible actual future uses, symbolic support, index') +check(sorted(range(4),key=ns['future_priority'])==[0,1,2,3],'Priority is not deterministic') +# General span argument is below; these adversarial numerical fixtures check the actual helpers and literal synthesis. +rng=Random(20261008);cases=0;operations=0 +for n in range(1,10): + for trial in range(250): + rows=[] + for _ in range(rng.randrange(n+1)*3): + candidate=rng.randrange(1,1<>i&1) + if j!=i: + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];ops.append((a,z)) + for j in range(n): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];ops.append((j,i)) + check(rr==[1< 1 and kappa > previous_kappa + bridge = finite_bridge(p['W']) + validate_bridge(bridge, p['W']) + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/balanced-split/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113', + pr71_kappa=previous_kappa, ratio_pr71=kappa/previous_kappa, + absolute_gain_pr71=kappa-previous_kappa, + pr71_complete_profile_exclusion_lower=prior71_lower, + full_pr71_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected balanced-split partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring, PR69 balanced coarse sums, future unit completion and bounded PR70 carry exchanges; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'balanced-split-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/balanced_split_engine.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/balanced_split_engine.py new file mode 100644 index 0000000000..e1a9883726 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/balanced_split_engine.py @@ -0,0 +1,278 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + _graph = _graphs[h] + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_math.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_math.py new file mode 100644 index 0000000000..b87855e808 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_math.py @@ -0,0 +1,87 @@ +"""Exact rational helpers extracted without body changes from pinned PR48 verify.py. +Credits: icekylinx PR32/36, Dominik Scholz PR35, Zhihao Chen PR29/23, +Paureel/Aurel Prosz, Swapnil Jain, Rohan Arun PR25/31, RaD/hipotures, +Chafik Boukhalfa and inherited notices in references/frame-compiler/pr48. +Prepared with OpenAI Codex assistance; no formal theorem claim. +""" +from fractions import Fraction as Q +from functools import lru_cache +from math import comb, factorial, isqrt, prod + +def js(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):js(v)for k,v in x.items()} + if isinstance(x,(list,tuple)):return [js(v)for v in x] + return x + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def mersenne(exponent): + require(exponent >= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'balanced-split-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from balanced_split_compose import check_sources + manifest_path = ROOT/'research/balanced-split/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/balanced-split-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import balanced_split_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_all_threshold_dependent_bridge_fields_are_checked(self): + from balanced_split_compose import finite_bridge, validate_bridge + expected = finite_bridge(134126064) + self.assertTrue(validate_bridge(expected, 134126064)) + for section,key in (('bit','wire_bits'),('rows','coefficient'),('rows','degree'),('rows','degree_gap'),('rows','suffix_slope')): + changed = deepcopy(expected) + changed[section][key] = Fraction(changed[section][key])+1 + with self.subTest(field=section+'.'+key), self.assertRaisesRegex(AssertionError, 'Stale finite bridge'): + validate_bridge(changed, 134126064) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('balanced_split_graph.py', 'balanced_split_engine.py', 'balanced_split_compiler.py', 'split_pair_arithmetic.py', 'balanced_split_exchange_engine.py', 'balanced_split_compose.py', 'verify_balanced_split.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/tests/test_balanced_split_pending.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/tests/test_balanced_split_pending.py new file mode 100644 index 0000000000..cce267112e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/references/frame-compiler/pr79/tests/test_balanced_split_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/balanced_split_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/balanced-split-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/research/indexed-cycle/PROOF.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/research/indexed-cycle/PROOF.md new file mode 100644 index 0000000000..61621dd74e --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/research/indexed-cycle/PROOF.md @@ -0,0 +1,63 @@ +# Finite indexed-cycle certificate and inherited scope + +## 1. Frozen construction and general weighted recursion + +At level d, start with the inherited ordered groups of size one or two. The chosen vector requests first/middle pair splits: h23 `[4,1,1]`, h25 `[1,4,1]`, where 1 requests the first group and 4 requests first then middle. Requested indices are deduplicated, valid, and must contain two points. Before admitting the kth split require `number_of_groups + admitted_splits + 1 < number_of_points`. Apply admitted splits in decreasing index order so earlier indices keep their meaning. Each split replaces one pair by its two ordered singletons; the point partition and ordering are unchanged. + +The admission guard proves that the final number of groups is strictly less than the number of points, even for multiple requested splits and overlapping first/middle indices. Splits are disabled for n≤3; n=3 has two coarse groups and n≤2 uses the direct base case. Thus every recursive call strictly contracts, for every input size allowed by the grouping interface. + +Coarse vertex weights contain the original vertex weights in that group and its internal edges. Each coarse edge contains exactly the Cartesian-product edges between its two groups. These sets partition the original weighted total. Recursive total and single/pair exclusions therefore have the required support by induction on size. Row and column coarse parenthesizations partition the same Cartesian product into disjoint sets, so changing between them preserves every identity. The half-plane rule uses fixed indices only. The generic singleton/pair assembly and interval-strip identities are inherited; tests independently check weighted exclusions at each recursive call. + +At common coordinate c, choose the smallest intact fixed global pair disjoint from c and move it to the front of the inherited alternating order, preserving all other relative positions. This is a permutation of precisely the other coordinates and preserves scalar exclusions. Dense graph verification checks the full triple-input map and all disjoint additions in both selected dimensions. + +## 2. PR74 node order, synthesis, and completion + +Group active computed nodes by exact `(core,cover)` frame and sort groups by `(rank,-core,cover,min_node)`, where rank is cover size minus core size. Keep input IDs fixed and retain original node order inside each group. Remap every dependency, active ID, output ID and provenance entry, and clear support caches. This is a bijective graph renaming; the preserved within-frame order and rank order retain scalar dependencies. The graph verifier recomputes the dense supports, and the compiler recomputes fixed linear signals before accepting the natural region order `(rank,min_node)`. Candidate carriers target strictly later regions with containing frames. No PR65 schedule wrapper is applied. + +The output rows and selected carriers form an independent prefix. Scan every standard input unit vector in future-use priority order and retain it only if independent. Every rejected unit is already in the current span and remains there; after the scan every standard unit is in the span. The final rows therefore form a full basis and keep the chosen prefix. Gaussian elimination and its reversed literal XOR synthesis implement an invertible transformation on arbitrary inputs and dirty roles. Future-use priority depends only on fixed graph incidence, symbolic signal supports and indices. It never examines runtime input data. + +Retired roles are reclaimed only by a valid literal clearing expression in an eligible signal span. Pending live controls have current frame F and assigned future frame G. They may clear a retired role in frame E only when F⊆E⊆G. A control's value does not change; its literal frame raise is charged, and the future inclusion remains valid. Candidate comparison makes no physical mutation until a chosen expression is emitted. Exact integer profile scores only order legal candidates; they do not certify the final recurrence. + +## 3. Exact retired and pending indexes + +For frames `(core,cover)`, containment F⊆E means `core(E)⊆core(F)` and `cover(F)⊆cover(E)`. The retired index intersects active-role core bitmaps for each coordinate in core(E), and removes roles whose cover includes any coordinate outside cover(E). This selects exactly the eligible roles. Rank bitmaps partition that set; descending rank and ascending set-bit order exactly reproduce the original `(-rank,slot)` enumeration. + +The pending index first enforces F⊆E using the same lower-frame index. It then removes target cores containing coordinates outside core(E) and intersects target-cover bitmaps for coordinates in cover(E). The result is precisely F⊆E⊆G. Each insertion receives a serial; removal deletes it; frame moves keep it. Sorting eligible roles by serial reproduces pending dictionary insertion order, including removal/reinsertion of reused slots. + +Insertion, reclamation and incoming-use removal update both representations. Every frame raise updates a retired role's old/new rank/frame index, or a pending control's lower frame without changing serial order. Retired and pending lifecycles remain disjoint. Actual-source exhaustive and randomized audits compare ordered queries with the direct predicates and exercise actual frame-raise functions, not copies of those functions. These indexes preserve compiler semantics; no measured speedup is claimed. + +## 4. Carry exchanges, two-cycles, and output routing + +Candidate edges remain subject to inherited temporal/frame eligibility. A single exchange removes the selected owner of an occupied future use, or drops a carrier from the receiving region for an unoccupied future use. The full output/carrier basis of the receiving region is checked after the removal. A distinct donor region only loses a row, preserving independence. Thus cardinality, linear independence and unique future-use ownership remain valid. Each accepted exchange decreases a fixed integer score; at most three deterministic passes execute. + +A two-cycle swaps carriers between distinct regions and distinct already-owned future uses. For new edge e and its complementary edge other, `carry_can(e,z)` checks the receiving region after removing z and `carry_can(other,f)` checks the other region after removing f. Because the regions differ, these tests describe exactly the final two bases. Remove both old edges before inserting either new edge; the two freed future uses are distinct, so unique ownership and global cardinality are preserved. Both regions lose and gain one carrier. The `(region,use)` lookup is checked for uniqueness. Accept only a strictly positive decrease of the sum of the two fixed integer scores; execute at most three passes. The source audit instruments every accepted exchange in 1,204 cases, including adverse linear dependence, equal-price, missing-complement and duplicate-key cases. This is a bounded legal heuristic, not an optimality proof. + +For h25, outgoing non-carrier uses are visited by descending fixed future-region deadline, with original use ID as tie-breaker. Terminal uses keep the explicit terminal deadline. This permutes a fixed list of uses; each is still assigned exactly once to a physical role. It may affect later reclamation choices, but changes no scalar target or candidate legality. h23 retains baseline output order. Both final physical words are independently regenerated and checked, including every charged allocation, XOR, raise and copy. + +## 5. Coordinate bijection and physical evidence + +For a permutation π of h coordinates, map every triple input to its sorted π-image, every frame's core/cover bitmask by π, each source's triple index, scatter input row, output common coordinate and output triple. Physical role IDs, operation order, operation frame IDs and transition event IDs are unchanged. Coordinate permutation is a bijection on triples, preserves set inclusion, and conjugates the scalar linear map. The scatter mapping changes only designated data-bank target rows and leaves auxiliary control rows fixed. Therefore arbitrary-dirty reversibility and the scalar target identities transport to the new word. + +The fixed I+J geometry is preserved by coordinate permutations, but the ordered fixed-coordinate child profile need not be invariant. Consequently profiles are freshly computed from the relabeled word's actual transitions; parent profiles are not reused. Full-basis replay checks both orientations on every ordinary and dirty column. The transition checker reconstructs every raise from literal XORs, splits side growth into paid singletons and requires exact equality with the event list. The original bounded-minor/CRT profiler verifies sufficient modulus product and agreement. Missing XORs, frames, centers, transitions, aliased terminals and understated width fail adverse tests. + +## 6. Complete recursive multiset and exact inequalities + +Let a=23, b=25, m=575, and N=binom(23,3)binom(25,3)=4,073,300. With R23=26,834 and R25=35,348, + + W = 2N + (N/binom(23,3))R23 + (N/binom(25,3))R25 = 132,466,108. + +Include all 18N rank-one data children and 2N at each data rank 21,17,481; N endpoint-copy singletons; every axis profile block replicated N/binom(h,3) times; (N/binom(h,3))Rh exterior children at each rank h and m−2h; and 2N growth children at each rank 1 and h−2. Each axis has rank sum hRh+h(h−1). Thus total rank is 76,166,165,200, deficit from mW is 1,846,900, and every child lies between 1 and 5291. The exponential tail bound is `(v^9/9!)/(1-v/10)` for upper argument v<1. An independent atanh log expansion at base 3/2 with 60 terms and a degree-12 exponential bound confirms both signs. Complete pinned PR79 and reported PR74 child lists separately have lower moment greater than one at s. These are complete-profile historical comparisons; the foreign PR74 claim is an accepted working input, not an independent audit of its entire construction. + +The reconstructed bridge has bit wire bits 27, row coefficient 843, row degree 2000, gap `2000-(51/25)*843=7007/25`, and suffix slope 8000. Tests reject stale values. The complex saving stays 717/10^7 and the backoff stays 10^-12. All 47 strict assembly constraints and seven margins hold for κ=261356445457/5000000000000000. The next 10^-18 κ point violates a controlling strict margin; coarser-grid reassembly and original-prefix/old-guard/old-exposure negative controls also execute. Eventual arithmetic cutoffs are recomputed by the unchanged inherited routine. + +## 7. Provenance and proof boundary + +This proves the stated finite scalar, arbitrary-dirty physical, actual-frame/profile, complete-child and exact-inequality claims. The ordered affine residual compiler, all-size construction and recursion, finite scalar alphabet/overhead, routing, prime selection, exact recovery, fixed-tape simulation and analytic transfer remain inherited assumptions. Arithmetic cutoffs cover the recorded inequalities and do not establish every operational threshold. Existing Lean packages remain inherited checks, not a formalization of the complete multiplication theorem. + +The engine is byte-identical to the preserved R5 compiler; the graph wrapper implements its selected split/coarse branch; PR74 order/relabel functions are byte-identical extracts. PR79's complete published construction archive and PR74/78 original input archives are immutable. The full source closure binds the selected configs, wrapper, engine, tests, proof, words, transition profiles and integration files. Derived arithmetic and validation receipts are excluded to avoid circular pins. + +Source credits: @eumemic [#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57) and [#69](https://github.com/CrocSwap/integer-mult-bounds/pull/69), reversible compilation and balanced coarse sums; @rohangar1 [#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59), split recursion; @ikeboy [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62), interval strips and core-aware assembly; @DominikScholz [#63](https://github.com/CrocSwap/integer-mult-bounds/pull/63) and [#68](https://github.com/CrocSwap/integer-mult-bounds/pull/68), ranked composition and pending live controls; @rohanarun [#65](https://github.com/CrocSwap/integer-mult-bounds/pull/65), [#67](https://github.com/CrocSwap/integer-mult-bounds/pull/67) and [#78](https://github.com/CrocSwap/integer-mult-bounds/pull/78), exact refined assembly, profile-cost reclamation and coordinate-flag search; @alejandrozu [#70](https://github.com/CrocSwap/integer-mult-bounds/pull/70), carry exchanges; Thomas DiFiore (@tomdif) [#74](https://github.com/CrocSwap/integer-mult-bounds/pull/74), exact node order, coordinate relabeling and the selected h25 permutation; @chafreaky [#60](https://github.com/CrocSwap/integer-mult-bounds/pull/60), [#71](https://github.com/CrocSwap/integer-mult-bounds/pull/71), [#79](https://github.com/CrocSwap/integer-mult-bounds/pull/79) and this composition, ranked reclamation, anchored splits, future completion, integer scoring, exact indexes, two-cycles, output routing, search and certification. + +Chafik Boukhalfa prepared this package with OpenAI Codex assistance. Original contributor, OpenAI/manuscript, Apache-2.0, and AI-assistance notices remain attached. In particular Avi Eisenberg's Claude assistance and the original contributors' OpenAI disclosures are retained verbatim in the archives. PR78 inspires the coordinate search; its published selected permutations are not claimed as the selected permutations here. diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/research/indexed-cycle/README.md b/references/frame-compiler/pr88/references/frame-compiler/pr84/research/indexed-cycle/README.md new file mode 100644 index 0000000000..c6c59c54b6 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/research/indexed-cycle/README.md @@ -0,0 +1,32 @@ +# Indexed two-cycles with balanced multi-splits and coordinate flags + +The frozen finite conditional witness has **κ = 261356445457/5000000000000000 = 5.22712890914e-5**, with bit saving **408390793141/7812500000000000**. This is about **0.8494742%** above the reported PR74 value at `3f78d8967c009153f2df5c6a6577b6ab1d37e2ca`, observed 2026-10-08. This is a historical pinned comparison, not a claim about the current community frontier. The complete pinned PR74 and PR79 recursive profiles are strictly excluded at the new accepted bit saving. + +| Quantity | This witness | +|---|---:| +| h23 auxiliary roles | 26,834 | +| h25 auxiliary roles | 35,348 | +| Physical width W | 132,466,108 | +| Total recursive rank | 76,166,165,200 | +| Rank deficit | 1,846,900 | +| Largest child / parent dimension | 529 / 575 | +| Bit wire bits / row coefficient | 27 / 843 | + +Additional reported comparisons observed on 2026-10-08: PR81 at `acae4964aef41c69f3c57e72a45e76afc4d4934d` reports κ=5.1915547765237e-5; PR82 at `3410b940aa26e5876202152dfa7c4f66451ee22c` reports κ=5.203279888519e-5. This frozen witness is about 0.4583459% above the reported PR82 value. These are metadata comparisons only; their foreign producers were not replayed. Exact rational ratios and authors are recorded in `reported-comparisons.json`. + +Both axes use balanced coarse columns when `i+j>i&1) + if j!=i: + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];ops.append((a,z)) + for j in range(n): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];ops.append((j,i)) + check(rr==[1<0 and current==previous-gain,'Fixed integer price does not strictly improve') + previous=current;observed.append([e,other,f,z]) + invariant() + env=dict(blocks=blocks,edges=edges,chosen=chosen,right=right,prices=prices,priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])),basis=basis,independent=independent,stats=Counter(),sys=types.SimpleNamespace(stderr=io.StringIO()),audit_cycle=audit_cycle) + exec(code,env);invariant();check(env['stats']['carry_two_cycles']==len(observed),'Cycle count differs') + if expected is not None:check(len(observed)==expected,'Targeted cycle outcome differs') + cycles+=len(observed);cases+=1 + return observed + +# Each group is full (one outbasis row + one carrier). Neither cross-group +# single addition is independent, but simultaneous replacement is legal. +blocks=[{'outbasis':[3]},{'outbasis':[3]}] +edges=[(1,0,0),(0,1,0),(0,0,1),(1,1,1)] +run(blocks,edges,{0,1},[10,10,9,9],1) +run(blocks,edges,{0,1},[10,10,10,10],0) +# With the receiving group's unit vector already in its output span, reject. +run([{'outbasis':[2]},{'outbasis':[3]}],edges,{0,1},[10,10,9,9],0) +# Missing the complementary future-use edge also rejects. +run(blocks,edges[:3],{0,1},[10,10,9],0) +# Duplicate group/use lookup keys are explicitly rejected before iteration. +try:run(blocks,edges+[(0,0,0)],{0,1},[10,10,9,9,1]) +except AssertionError:duplicate_rejected=True +else:raise ValueError('Ambiguous group/use candidate key accepted') +rng=Random(231025) +for trial in range(1200): + ng=rng.randrange(2,6);nuses=rng.randrange(2,14);blocks=[];edges=[] + for g in range(ng): + width=rng.randrange(2,6);rows=[] + for _ in range(rng.randrange(width)*2): + v=rng.randrange(1,1<150 or choice<.34): + s=rng.choice(list(records));f,g=records.pop(s);idx.remove(s,f,g) + elif records and choice<.66: + s=rng.choice(list(records));f,g=records[s];new=between(f,g);check(contains(f,new) and contains(new,g),'Invalid random promotion') + before_order=dict(idx.order);idx.move(s,f,new);records[s]=(new,g);check(idx.order==before_order,'Frame move changes insertion order') + else: + s=rng.randrange(1200) + if s in records:continue + f=envelope();g=extend(f);idx.insert(s,f,g);records[s]=(f,g) + mutations+=1 + if iteration%4==0: + for target in (envelope(),(1,mask)): + check(idx.eligible(target)==query(records,target),'Random ordered pending query differs');queries+=1 + if iteration%100==0: + check(idx.lower.all==sum(1<>k&1),'Target core bitmap stale') + check(idx.cover[k]==sum(1<>k&1),'Target cover bitmap stale') +idx=Pending(4);idx.insert(1,(1,3),(1,5)) +check(idx.lower.eligible_mask((1,7))==2 and idx.eligible((1,7))==[],'Fixture does not reject missing future containment') +# Audit the actual integrated raise_ function on passive live controls. +compile_node=next(n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name=='compile_');raise_node=next(n for n in compile_node.body if isinstance(n,ast.FunctionDef) and n.name=='raise_') +blocks=[dict(frame=(3,3),rank=1),dict(frame=(1,7),rank=2),dict(frame=(1,15),rank=3)] +idx=Pending(4);idx.insert(0,blocks[0]['frame'],blocks[2]['frame']);idx.insert(1,blocks[0]['frame'],blocks[2]['frame']) +env=dict(frames=[0,0],blocks=blocks,contains=contains,retired=set(),retired_index=Retired(4),pending={0:2,1:2},pending_index=idx,hist=Counter(),events=[]) +exec(compile(ast.Module(body=[raise_node],type_ignores=[]),str(NEW),'exec'),env);env['raise_'](0,1) +check(idx.eligible(blocks[0]['frame'])==[1] and idx.eligible(blocks[1]['frame'])==[0,1],'Actual raise changes pending selection incorrectly') +check(idx.order=={0:0,1:1},'Actual raise changes pending order') +receipt=dict(status='PASS actual ordered two-envelope pending index and frame lifecycle',source_sha256=sha256(SOURCE.read_bytes()).hexdigest(),mutations=mutations,ordered_queries=queries,actual_raise_fixture=True,future_containment_negative_fixture=True) +(ROOT/'certificates/indexed-cycle-pending-index-validation.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/audit_indexed_cycle_retired.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/audit_indexed_cycle_retired.py new file mode 100644 index 0000000000..10fc7fe4b2 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/audit_indexed_cycle_retired.py @@ -0,0 +1,67 @@ +"""Focused actual-source audit. Chafik Boukhalfa with OpenAI Codex assistance; Apache-2.0.""" +from pathlib import Path +from hashlib import sha256 +from datetime import datetime,timezone +from random import Random +from collections import Counter +from copy import deepcopy +import ast,gzip,json,io,types,sys +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1] +SOURCE=HERE/'indexed_cycle_engine.py';NEW=SOURCE +source=SOURCE.read_text();tree=ast.parse(source) +def check(ok,why): + if not ok:raise ValueError(why) +klass=next(n for n in tree.body if isinstance(n,ast.ClassDef) and n.name=='RetiredIndex') +space={};exec(compile(ast.Module(body=[n for n in tree.body if isinstance(n,ast.ClassDef)],type_ignores=[]),str(SOURCE),'exec'),space);Index=space['RetiredIndex'] +contains=lambda f,g:not(g[0]&~f[0]) and not(f[1]&~g[1]) +def valid_frames(h): + return [(c,d) for d in range(1,1<150 or rng.random()<0.48): + s=rng.choice(list(records));f,r=records.pop(s);idx.remove(s,f,r) + else: + s=rng.randrange(1200) + if s in records:continue + f=frame();r=rng.randrange(h+1);idx.insert(s,f,r);records[s]=(f,r) + mutations+=1 + if iteration%4==0: + for target in (frame(),(1,full)): + check(list(idx.eligible(target))==order(records,target),'Random exact frame/order query differs');queries+=1 + if iteration%100==0: + check(idx.all==sum(1<>k&1),'Core bitmap stale') + check(idx.cover[k]==sum(1<>k&1),'Cover bitmap stale') +# The actual integrated raise function keeps already-retired controls indexed at their new frame. +compile_node=next(n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name=='compile_') +raise_node=next(n for n in compile_node.body if isinstance(n,ast.FunctionDef) and n.name=='raise_') +blocks=[dict(frame=(3,3),rank=1),dict(frame=(1,7),rank=2),dict(frame=(1,15),rank=3)] +idx=Index(4);idx.insert(0,blocks[0]['frame'],1) +env=dict(frames=[0,0],blocks=blocks,contains=contains,retired={0},retired_index=idx,pending={},pending_index=space['PendingIndex'](4),hist=Counter(),events=[]) +exec(compile(ast.Module(body=[raise_node],type_ignores=[]),str(NEW),'exec'),env) +env['raise_'](0,1) +check(list(idx.eligible(blocks[0]['frame']))==[] and list(idx.eligible(blocks[1]['frame']))==[0],'Actual retired control frame promotion not reflected') +env['raise_'](1,1) +check(idx.all==1 and env['frames']==[1,1],'Nonretired raise inserted an indexed role') +env['raise_'](0,2);idx.remove(0,blocks[2]['frame'],3) +check(idx.all==0 and not any(idx.ranks) and not any(idx.core) and not any(idx.cover),'Actual promoted role removal leaves stale bits') +receipt=dict(status='PASS actual ordered retired index and frame lifecycle',source_sha256=sha256(SOURCE.read_bytes()).hexdigest(),mutations=mutations,ordered_queries=queries,actual_raise_fixture=True) +(ROOT/'certificates/indexed-cycle-retired-index-validation.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/binary_frame_math.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/binary_frame_math.py new file mode 100644 index 0000000000..b87855e808 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/binary_frame_math.py @@ -0,0 +1,87 @@ +"""Exact rational helpers extracted without body changes from pinned PR48 verify.py. +Credits: icekylinx PR32/36, Dominik Scholz PR35, Zhihao Chen PR29/23, +Paureel/Aurel Prosz, Swapnil Jain, Rohan Arun PR25/31, RaD/hipotures, +Chafik Boukhalfa and inherited notices in references/frame-compiler/pr48. +Prepared with OpenAI Codex assistance; no formal theorem claim. +""" +from fractions import Fraction as Q +from functools import lru_cache +from math import comb, factorial, isqrt, prod + +def js(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):js(v)for k,v in x.items()} + if isinstance(x,(list,tuple)):return [js(v)for v in x] + return x + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def mersenne(exponent): + require(exponent >= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"< 1 and kappa > previous_kappa + prior74 = json.loads((ROOT/'references/frame-compiler/pr74/research/balanced-split-frames/certificate.json').read_text()) + rows74 = {int(t):n for t,n in prior74['child_multiplicities'].items()} + prior74_lower = refine.exact_moment(575, prior74['W'], rows74, bit_saving)['lower'] + reported74 = Q('10366199626713/200000000000000000') + assert prior74_lower > 1 and kappa > reported74 + bridge = finite_bridge(p['W']) + validate_bridge(bridge, p['W']) + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/indexed-cycle/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr79_commit='9a58e62cf9e8954a4dde3c9b1372d733c276a6d1', + pr74_commit='3f78d8967c009153f2df5c6a6577b6ab1d37e2ca', reported_pr74_kappa=reported74, + ratio_reported_pr74=kappa/reported74, pr74_complete_profile_exclusion_lower=prior74_lower, + pr79_kappa=previous_kappa, ratio_pr79=kappa/previous_kappa, + absolute_gain_pr79=kappa-previous_kappa, + pr79_complete_profile_exclusion_lower=prior71_lower, + full_pr79_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected indexed-cycle partition and point permutation, PR74 node order, natural execution, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring, PR69 balanced coarse sums, future unit completion and bounded PR70-derived single exchanges and two-cycles, exact frame indices, late-output routing and PR74/78-inspired coordinate relabeling; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'indexed-cycle-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/indexed_cycle_engine.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/indexed_cycle_engine.py new file mode 100644 index 0000000000..beb64af862 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/indexed_cycle_engine.py @@ -0,0 +1,407 @@ +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + first,mid,last = 0,(len(groups)-1)//2,len(groups)-1 + requested = {1:[first],2:[mid],3:[last],4:[first,mid],5:[first,last],6:[mid,last],7:[first,mid,last],8:[first,first+1],9:[last-1,last]}[choice] + chosen=[] + for k in requested: + if k not in chosen and 0<=k>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/joint_dual_reclaim_compiler.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/joint_dual_reclaim_compiler.py new file mode 100644 index 0000000000..1eb8dea9fa --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/scripts/experiments/joint_dual_reclaim_compiler.py @@ -0,0 +1,240 @@ +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'indexed-cycle-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from indexed_cycle_compose import check_sources + manifest_path = ROOT/'research/indexed-cycle/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/indexed-cycle-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_all_threshold_dependent_bridge_fields_are_checked(self): + from indexed_cycle_compose import finite_bridge, validate_bridge + expected = finite_bridge(132466108) + self.assertTrue(validate_bridge(expected, 132466108)) + for section,key in (('bit','wire_bits'),('rows','coefficient'),('rows','degree'),('rows','degree_gap'),('rows','suffix_slope')): + changed = deepcopy(expected) + changed[section][key] = Fraction(changed[section][key])+1 + with self.subTest(field=section+'.'+key), self.assertRaisesRegex(AssertionError, 'Stale finite bridge'): + validate_bridge(changed, 132466108) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('indexed_cycle_graph.py', 'indexed_cycle_engine.py', 'indexed_cycle_compiler.py', 'split_pair_arithmetic.py', 'indexed_cycle_compose.py', 'verify_indexed_cycle.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/references/frame-compiler/pr84/tests/test_indexed_cycle_coordinates.py b/references/frame-compiler/pr88/references/frame-compiler/pr84/tests/test_indexed_cycle_coordinates.py new file mode 100644 index 0000000000..12fedd3b90 --- /dev/null +++ b/references/frame-compiler/pr88/references/frame-compiler/pr84/tests/test_indexed_cycle_coordinates.py @@ -0,0 +1,49 @@ +"""Bijection and adverse-coordinate controls for the actual PR74 relabel functions.""" +from pathlib import Path +from itertools import combinations +from copy import deepcopy +from hashlib import sha256 +import gzip,json,sys,unittest +ROOT=Path(__file__).resolve().parents[1];sys.path.insert(0,str(ROOT/'scripts/experiments')) +from indexed_cycle_nodeops import relabel +from indexed_cycle_graph import configuration + +class CoordinateControls(unittest.TestCase): + def test_selected_permutations_are_exact_integer_bijections(self): + for h in (23,25): + perm=configuration(h)['coordinate_permutation'] + self.assertEqual(sorted(perm),list(range(h))) + self.assertTrue(all(type(x) is int for x in perm)) + self.assertEqual(configuration(23)['coordinate_permutation'],list(range(1,23))+[0]) + + def test_every_selected_word_roundtrips_full_coordinate_inverse(self): + for h in (23,25): + word=json.loads(gzip.decompress((ROOT/f'certificates/indexed-cycle-word-{h}.json.gz').read_bytes())) + perm=configuration(h)['coordinate_permutation'];inverse=[perm.index(i) for i in range(h)] + parent=relabel(deepcopy(word),inverse) + # Dict iteration and scatter order are deliberately retained by the actual function. + raw=(json.dumps(parent,separators=(',',':'))+'\n').encode() + selection=json.loads((ROOT/'research/indexed-cycle/discovery-selection.json').read_text())['axes'][str(h)] + self.assertEqual(sha256(raw).hexdigest(),selection['parent_word_sha256']) + self.assertEqual(relabel(parent,perm),word) + + def test_relabel_preserves_physical_operations_and_frame_inclusions(self): + h=5;triples=list(combinations(range(h),3));v=len(triples);perm=[4,0,2,1,3] + word=dict(h=h,v=v,frames=[[3,7],[1,31]],sources={str(i):i for i in range(v)}, + scatter=[[v+i,2*v+i] for i in reversed(range(v))],outputs=[[2*v+i,0,0,list(t)] for i,t in enumerate(triples)], + ops=[[2*v,2*v+1,0]],events=[[2*v,0,1]]) + changed=relabel(deepcopy(word),perm) + self.assertEqual(changed['ops'],word['ops']);self.assertEqual(changed['events'],word['events']) + self.assertEqual(set(map(int,changed['sources'])),set(range(v))) + self.assertEqual([b for a,b in changed['scatter']],[b for a,b in word['scatter']]) + self.assertEqual(set(a for a,b in changed['scatter']),set(range(v,2*v))) + (a,b),(c,d)=changed['frames'];self.assertEqual(c&~a,0);self.assertEqual(b&~d,0) + + def test_invalid_permutation_and_scatter_source_are_rejected(self): + word=dict(h=3,v=1,frames=[[1,7]],sources={'0':0},scatter=[[1,2]],outputs=[[2,0,0,[0,1,2]]]) + for permutation in ([0,1,1],[0,1],[0,1,3]): + with self.subTest(permutation=permutation),self.assertRaises(AssertionError):relabel(deepcopy(word),permutation) + word['scatter'][0][0]=0 + with self.assertRaises(AssertionError):relabel(word,[0,1,2]) + +if __name__=='__main__':unittest.main() diff --git a/references/frame-compiler/pr88/research/final-frame/PROOF.md b/references/frame-compiler/pr88/research/final-frame/PROOF.md new file mode 100644 index 0000000000..c6144c419c --- /dev/null +++ b/references/frame-compiler/pr88/research/final-frame/PROOF.md @@ -0,0 +1,71 @@ +# Finite final-frame certificate and inherited scope + +## 1. Frozen construction and general weighted recursion + +At level d, start with the inherited ordered groups of size one or two. The chosen vector requests first/middle pair splits: h23 `[4,4,4]`, h25 `[4,4,1]`, where 1 requests the first group and 4 requests first then middle. Requested indices are deduplicated, valid, and must contain two points. Before admitting the kth split require `number_of_groups + admitted_splits + 1 < number_of_points`. Apply admitted splits in decreasing index order so earlier indices keep their meaning. Each split replaces one pair by its two ordered singletons; the point partition and ordering are unchanged. + +The admission guard proves that the final number of groups is strictly less than the number of points, even for multiple requested splits and overlapping first/middle indices. Splits are disabled for n≤3; n=3 has two coarse groups and n≤2 uses the direct base case. Thus every recursive call strictly contracts, for every input size allowed by the grouping interface. + +Coarse vertex weights contain the original vertex weights in that group and its internal edges. Each coarse edge contains exactly the Cartesian-product edges between its two groups. These sets partition the original weighted total. Recursive total and single/pair exclusions therefore have the required support by induction on size. Row and column coarse parenthesizations partition the same Cartesian product into disjoint sets, so changing between them preserves every identity. The half-plane rule uses fixed indices only. The generic singleton/pair assembly and interval-strip identities are inherited; tests independently check weighted exclusions at each recursive call. + +At common coordinate c, choose the smallest intact fixed global pair disjoint from c and move it to the front of the inherited alternating order, preserving all other relative positions. This is a permutation of precisely the other coordinates and preserves scalar exclusions. Dense graph verification checks the full triple-input map and all disjoint additions in both selected dimensions. + +## 2. PR74 node order, synthesis, and completion + +Group active computed nodes by exact `(core,cover)` frame. Every scalar edge u→v has `core(v)⊆core(u)` and `cover(u)⊆cover(v)`. If the two envelopes differ, `|cover(v)|−|core(v)|` strictly exceeds `|cover(u)|−|core(u)|`: at least one set containment is strict. Thus rank-first group order is topological between distinct envelopes. Original node order is retained inside every group. h23 uses `(rank,-cover,-core,min_node)`; h25 retains PR74's `(rank,-core,cover,min_node)`. Input IDs stay fixed. Remapping every dependency, active ID, output ID and provenance entry is a bijection; support caches are cleared. The verifier separately reconstructs all global triple-input supports, disjoint additions, exact envelopes and every target output, without relying on provenance records. The compiler then recomputes signals, region order and carrier eligibility from the renamed graph. No PR65 schedule wrapper is applied. + +The output rows and selected carriers form an independent prefix. Scan every standard input unit vector in future-use priority order and retain it only if independent. Every rejected unit is already in the current span and remains there; after the scan every standard unit is in the span. The final rows therefore form a full basis and keep the chosen prefix. Gaussian elimination and its reversed literal XOR synthesis implement an invertible transformation on arbitrary inputs and dirty roles. Future-use priority depends only on fixed graph incidence, symbolic signal supports and indices. It never examines runtime input data. + +Retired roles are reclaimed only by a valid literal clearing expression in an eligible signal span. Pending live controls have current frame F and assigned future frame G. They may clear a retired role in frame E only when F⊆E⊆G. A control's value does not change; its literal frame raise is charged, and the future inclusion remains valid. Candidate comparison makes no physical mutation until a chosen expression is emitted. Exact integer profile scores only order legal candidates; they do not certify the final recurrence. + +## 3. Exact retired and pending indexes + +For frames `(core,cover)`, containment F⊆E means `core(E)⊆core(F)` and `cover(F)⊆cover(E)`. The retired index intersects active-role core bitmaps for each coordinate in core(E), and removes roles whose cover includes any coordinate outside cover(E). This selects exactly the eligible roles. Rank bitmaps partition that set; descending rank and ascending set-bit order exactly reproduce the original `(-rank,slot)` enumeration. + +The pending index first enforces F⊆E using the same lower-frame index. It then removes target cores containing coordinates outside core(E) and intersects target-cover bitmaps for coordinates in cover(E). The result is precisely F⊆E⊆G. Each insertion receives a serial; removal deletes it; frame moves keep it. Sorting eligible roles by serial reproduces pending dictionary insertion order, including removal/reinsertion of reused slots. + +Insertion, reclamation and incoming-use removal update both representations. Every frame raise updates a retired role's old/new rank/frame index, or a pending control's lower frame without changing serial order. Retired and pending lifecycles remain disjoint. Actual-source exhaustive and randomized audits compare ordered queries with the direct predicates and exercise actual frame-raise functions, not copies of those functions. These indexes preserve compiler semantics; no measured speedup is claimed. + +## 4. Carry exchanges, two-cycles, and output routing + +Candidate edges remain subject to inherited temporal/frame eligibility. A single exchange removes the selected owner of an occupied future use, or drops a carrier from the receiving region for an unoccupied future use. The full output/carrier basis of the receiving region is checked after the removal. A distinct donor region only loses a row, preserving independence. Thus cardinality, linear independence and unique future-use ownership remain valid. Each accepted exchange decreases a fixed integer score; at most three deterministic passes execute. + +A two-cycle swaps carriers between distinct regions and distinct already-owned future uses. For new edge e and its complementary edge other, `carry_can(e,z)` checks the receiving region after removing z and `carry_can(other,f)` checks the other region after removing f. Because the regions differ, these tests describe exactly the final two bases. Remove both old edges before inserting either new edge; the two freed future uses are distinct, so unique ownership and global cardinality are preserved. Both regions lose and gain one carrier. The `(region,use)` lookup is checked for uniqueness. Accept only a strictly positive decrease of the sum of the two fixed integer scores; execute at most three passes. The source audit instruments every accepted exchange in 1,204 cases, including adverse linear dependence, equal-price, missing-complement and duplicate-key cases. This is a bounded legal heuristic, not an optimality proof. + +Three-donor exchanges generalize the two-cycle argument to three distinct regions. Each region loses one selected vector and gains a candidate checked by `carry_can` against its full final output/carrier basis. The three distinct already-owned use IDs are cyclically reassigned, so their set and global cardinality stay fixed. All three old edges are removed before any new edge is inserted. Distinct-region and distinct-edge assertions prevent overlapping local replacements. Acceptance requires a strict decrease of the sum of fixed integer prices; deterministic candidate keys choose the best available cycle for that step. h23 uses zero passes; h25 uses at most three, with two accepted cycles in this frozen witness. The actual-source audit covers 1,604 cases, including a strict three-cycle with no legal single/two-cycle alternative, equal/worsening costs, dependent replacements and randomized independent bases. This establishes legality, not global cost optimality. + +For h25, outgoing non-carrier uses are visited by descending fixed future-region deadline, with original use ID as tie-breaker. Terminal uses keep the explicit terminal deadline. This permutes a fixed list of uses; each is still assigned exactly once to a physical role. It may affect later reclamation choices, but changes no scalar target or candidate legality. h23 retains baseline output order. Both final physical words are independently regenerated and checked, including every charged allocation, XOR, raise and copy. + +## Coordinate-aware discovery prices + +Rohan Arun's PR82 coordinate-aware pricing is active only on h25. Before the oracle input is serialized, each frame mask is mapped by the same coordinate permutation used for the final word. Block indices and ranks are unchanged. This modifies only the binary oracle frame table: all in-memory graph frames, scalar signals, frame-containment tests, temporal eligibility and basis tests stay unchanged. Identity pricing on h23 is byte-identical to the original writer. An actual-source control checks 400 arbitrary frame/map cases, in-memory immutability, identity equality and invalid-map rejection. + +Oracle answers enter only fixed integer carry scores and comparison among already legal reclamation candidates. The accepted physical operations still satisfy every original containment and linear-independence guard. Heuristic score quality is not a correctness assumption. All final profiles are recomputed from the selected physical words after actual coordinate relabeling. + +## 5. Coordinate bijection and physical evidence + +For a permutation π of h coordinates, map every triple input to its sorted π-image, every frame's core/cover bitmask by π, each source's triple index, scatter input row, output common coordinate and output triple. Physical role IDs, operation order, operation frame IDs and transition event IDs are unchanged. Coordinate permutation is a bijection on triples, preserves set inclusion, and conjugates the scalar linear map. The scatter mapping changes only designated data-bank target rows and leaves auxiliary control rows fixed. Therefore arbitrary-dirty reversibility and the scalar target identities transport to the new word. + +The fixed I+J geometry is preserved by coordinate permutations, but the ordered fixed-coordinate child profile need not be invariant. Consequently profiles are freshly computed from the relabeled word's actual transitions; parent profiles are not reused. Full-basis replay checks both orientations on every ordinary and dirty column. The transition checker reconstructs every raise from literal XORs, splits side growth into paid singletons and requires exact equality with the event list. The original bounded-minor/CRT profiler verifies sufficient modulus product and agreement. Missing XORs, frames, centers, transitions, aliased terminals and understated width fail adverse tests. + +## 6. Complete recursive multiset and exact inequalities + +Let a=23, b=25, m=575, and N=binom(23,3)binom(25,3)=4,073,300. With R23=26,581 and R25=35,133, + + W = 2N + (N/binom(23,3))R23 + (N/binom(25,3))R25 = 131,503,443. + +Include all 18N rank-one data children and 2N at each data rank 21,17,481; N endpoint-copy singletons; every axis profile block replicated N/binom(h,3) times; (N/binom(h,3))Rh exterior children at each rank h and m−2h; and 2N growth children at each rank 1 and h−2. Each axis has rank sum hRh+h(h−1). Thus total rank is 75,612,632,825, deficit from mW is 1,846,900, and every child lies between 1 and 5291. The exponential tail bound is `(v^9/9!)/(1-v/10)` for upper argument v<1. An independent atanh log expansion at base 3/2 with 60 terms and a degree-12 exponential bound confirms both signs. Complete pinned PR84 and reported PR74 child lists separately have lower moment greater than one at s. These are complete-profile historical comparisons; the foreign PR74 claim is an accepted working input, not an independent audit of its entire construction. + +The reconstructed bridge has bit wire bits 27, row coefficient 843, row degree 2000, gap `2000-(51/25)*843=7007/25`, and suffix slope 8000. Tests reject stale values. The complex saving stays 717/10^7 and the backoff stays 10^-12. All 47 strict assembly constraints and seven margins hold for κ=52514124198891/1000000000000000000. The next 10^-18 κ point violates a controlling strict margin; coarser-grid reassembly and original-prefix/old-guard/old-exposure negative controls also execute. Eventual arithmetic cutoffs are recomputed by the unchanged inherited routine. + +## 7. Provenance and proof boundary + +This proves the stated finite scalar, arbitrary-dirty physical, actual-frame/profile, complete-child and exact-inequality claims. The ordered affine residual compiler, all-size construction and recursion, finite scalar alphabet/overhead, routing, prime selection, exact recovery, fixed-tape simulation and analytic transfer remain inherited assumptions. Arithmetic cutoffs cover the recorded inequalities and do not establish every operational threshold. Existing Lean packages remain inherited checks, not a formalization of the complete multiplication theorem. + +The portable engine and node helper are byte-identical to the independently audited 90-pin final R10 discovery runtime. Relative to the archived R5 engine, the only AST changes are the coordinate-aware oracle writer and the audited three-donor helper/call. The graph provider preserves the frozen split/coarse construction and passes the selected order explicitly. The complete 590-file PR84 construction archive preserves all original source/finite inputs and construction certificates. Original PR74/78/82 contributor inputs and all older archives remain immutable. The local source closure binds selected configurations, wrappers, engine, tests, proof, physical words, transition profiles and additive integration files. Derived arithmetic and validation receipts are excluded to avoid circular pins. + +Source credits: @eumemic [#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57) and [#69](https://github.com/CrocSwap/integer-mult-bounds/pull/69), reversible compilation and balanced coarse sums; @rohangar1 [#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59), split recursion; @ikeboy [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62), interval strips and core-aware assembly; @DominikScholz [#63](https://github.com/CrocSwap/integer-mult-bounds/pull/63) and [#68](https://github.com/CrocSwap/integer-mult-bounds/pull/68), ranked composition and pending live controls; @rohanarun [#65](https://github.com/CrocSwap/integer-mult-bounds/pull/65), [#67](https://github.com/CrocSwap/integer-mult-bounds/pull/67) [#78](https://github.com/CrocSwap/integer-mult-bounds/pull/78) and [#82](https://github.com/CrocSwap/integer-mult-bounds/pull/82), exact refined assembly, profile-cost reclamation, coordinate-flag search and coordinate-aware pricing; @alejandrozu [#70](https://github.com/CrocSwap/integer-mult-bounds/pull/70), carry exchanges; Thomas DiFiore (@tomdif) [#74](https://github.com/CrocSwap/integer-mult-bounds/pull/74), original rank-first node order and exact coordinate relabeling; @chafreaky [#60](https://github.com/CrocSwap/integer-mult-bounds/pull/60), [#71](https://github.com/CrocSwap/integer-mult-bounds/pull/71), [#79](https://github.com/CrocSwap/integer-mult-bounds/pull/79) [#84](https://github.com/CrocSwap/integer-mult-bounds/pull/84) and this composition, rank-preserving tie orders, three-donor cycles, ranked reclamation, anchored splits, future completion, integer scoring, exact indexes, two-cycles, output routing, search and certification. + +Chafik Boukhalfa prepared this package with OpenAI Codex assistance. Original contributor, OpenAI/manuscript, Apache-2.0, and AI-assistance notices remain attached. In particular Avi Eisenberg's Claude assistance and the original contributors' OpenAI disclosures are retained verbatim in the archives. PR78 inspires the coordinate search; its published selected permutations are not claimed as the selected permutations here. diff --git a/references/frame-compiler/pr88/research/final-frame/README.md b/references/frame-compiler/pr88/research/final-frame/README.md new file mode 100644 index 0000000000..b0d77bdd00 --- /dev/null +++ b/references/frame-compiler/pr88/research/final-frame/README.md @@ -0,0 +1,31 @@ +# Final frame composition + +The frozen finite conditional witness has **κ = 52514124198891/1000000000000000000 = 5.2514124198891e-5**, with bit saving **52516882077117/1000000000000000000**. It is **0.4645669003% above the pinned PR84 construction** `88ca39571907343a49e97f328971ec7bcd26fbfd`. This is a historical pinned comparison, not a claim about the current global frontier. Complete PR84 and reported PR74 paid child profiles are strictly excluded at the accepted bit saving. + +| Quantity | This witness | +|---|---:| +| h23 / h25 auxiliary roles | 26,581 / 35,133 | +| Physical width W | 131,503,443 | +| Total recursive rank | 75,612,632,825 | +| Rank deficit | 1,846,900 | +| Largest child / parent dimension | 529 / 575 | +| Bit wire bits / row coefficient | 27 / 843 | + +Both axes use anchored point order, balanced half-plane coarse sums, exact retired/pending indexes, future-compatible unit completion, pending next-use prices and up to three single/two-cycle passes. The h23 split vector is `[4,4,4]`, with descending cover/core rank ties, baseline output order, identity oracle pricing and no three-cycles. The h25 split vector is `[4,4,1]`, with PR74 node order, late output order, coordinate-aware oracle pricing and up to three three-cycle passes (two accepted). Explicit coordinate maps are in the certified configs; they come from our bounded R6 search. + +```sh +make final-frame-verify +make verify +``` + +The focused gate regenerates original and relabeled words byte-for-byte, reconstructs dense scalar supports, replays every ordinary and arbitrary-dirty basis column in both orientations, and computes fresh literal frame/CRT profiles. Every copied center, endpoint, data-growth block, cleanup and complex cost remains charged. Exact assembly checks two independent rational moment enclosures, neighboring 10^-18 grid rejection, all 47 inequalities and seven margins. Actual-source audits cover both indexes, completion, single/two/three-cycle exchanges and coordinate-aware oracle serialization. Mutation controls reject invalid words, sources, configurations and bridge fields. + +The selected words, paid profiles and source are immutable. The 51,525-pair discovery portfolio has two equivalent best pairs, differing only in an inactive h23 three-cycle setting; the freeze selects zero passes. That finite portfolio result is not a global optimality theorem. Discovery paths are retained only as provenance; executable verification uses repository-relative inputs. + +The [proof](PROOF.md) separates general compatibility arguments from finite evidence. Ordered residual compilation, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery, fixed-tape simulation and analytic transfer remain inherited assumptions. Arithmetic cutoffs are not full operational thresholds. No measured practical speedup or complete formal multiplication theorem is asserted. + +The complete PR84 construction and original contributor archives are preserved byte-for-byte. `reported-comparisons.json` records external reported values and pinned heads without replaying foreign producers. The actual coordinate-aware pricing source is PR82. + +Source credits: @eumemic [#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57) and [#69](https://github.com/CrocSwap/integer-mult-bounds/pull/69), reversible compilation and balanced coarse sums; @rohangar1 [#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59), split recursion; @ikeboy [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62), interval strips and core-aware assembly; @DominikScholz [#63](https://github.com/CrocSwap/integer-mult-bounds/pull/63) and [#68](https://github.com/CrocSwap/integer-mult-bounds/pull/68), ranked composition and pending live controls; @rohanarun [#65](https://github.com/CrocSwap/integer-mult-bounds/pull/65), [#67](https://github.com/CrocSwap/integer-mult-bounds/pull/67) [#78](https://github.com/CrocSwap/integer-mult-bounds/pull/78) and [#82](https://github.com/CrocSwap/integer-mult-bounds/pull/82), exact refined assembly, profile-cost reclamation, coordinate-flag search and coordinate-aware pricing; @alejandrozu [#70](https://github.com/CrocSwap/integer-mult-bounds/pull/70), carry exchanges; Thomas DiFiore (@tomdif) [#74](https://github.com/CrocSwap/integer-mult-bounds/pull/74), original rank-first node order and exact coordinate relabeling; @chafreaky [#60](https://github.com/CrocSwap/integer-mult-bounds/pull/60), [#71](https://github.com/CrocSwap/integer-mult-bounds/pull/71), [#79](https://github.com/CrocSwap/integer-mult-bounds/pull/79) [#84](https://github.com/CrocSwap/integer-mult-bounds/pull/84) and this composition, rank-preserving tie orders, three-donor cycles, ranked reclamation, anchored splits, future completion, integer scoring, exact indexes, two-cycles, output routing, search and certification. + +Chafik Boukhalfa prepared this package with OpenAI Codex assistance. Original contributor, OpenAI/manuscript, Apache-2.0, and AI-assistance notices remain attached. In particular Avi Eisenberg's Claude assistance and the original contributors' OpenAI disclosures are retained verbatim in the archives. 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selected physical/arithmetic clearance" +} diff --git a/references/frame-compiler/pr88/research/final-frame/discovery-source-audit.json b/references/frame-compiler/pr88/research/final-frame/discovery-source-audit.json new file mode 100644 index 0000000000..67f7f40b77 --- /dev/null +++ b/references/frame-compiler/pr88/research/final-frame/discovery-source-audit.json @@ -0,0 +1,123 @@ +{ + "actual_oracle_writer_cases": 400, + "engine_sha256": "e349c2b5837812398441601306d916c9fdb7d0ec548d0c68e19580fd3d4524c2", + "graph_wrapper_sha256": "fdd58de71596d1eaa85026ded59dfcff453be76165aaee1575decf924ae23159", + "invalid_oracle_permutation_rejected": true, + "nodeops_sha256": "dce113a25da77065a920d21b12047410fde09d0016690b30ecd00e976e323913", + "order_graphs": [ + { + "all_literal_edges_and_frames_preserved": true, + "dense_check": { + "nodes": 77199, + "outputs": 5336, + "sha256": "5f17f40fcaeaaa0034756a5bc8af75ac156454e360385bb621569d072bdcdc37", + "status": "PASS all global supports, exact 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If the envelopes differ, cover-size minus core-size strictly increases. Consequently any ordering whose first key is that rank is topological between different frames; retaining original node order inside each frame preserves the remaining dependencies. Both actual keys preserve every scalar edge, envelope, source prefix, output and provenance record.", + "Node renumbering happens before compiler build and carrier eligibility are reconstructed. Each generate call creates a fresh compiler module; order mode is passed explicitly, and price coordinate map and three-cycle pass count are assigned on that module before compilation. Thus workers or successive cases cannot inherit those settings implicitly.", + "The new coordinate writer changes only serialized oracle core/cover masks, leaving block indices, ranks, all in-memory graph frames, scalar signals and candidate eligibility untouched. Identity pricing is byte-identical to the previous writer. Bijective coordinate maps preserve frame inclusion and dimension, and the oracle queries address the same permuted frames later used by physical relabeling.", + "Oracle answers enter only fixed integer carry prices and legal retired-slot candidate comparison. Each emitted candidate still satisfies the unchanged frame containment, temporal edge, linear-independence, unique-future-use and literal clearing checks. Pricing quality is not a correctness assumption; actual final word profiles must still be regenerated after selection.", + "Three-donor source is byte-identical to the independently audited helper and parent integration. After any order/pricing choice, its proof applies to the newly constructed eligible edges with arbitrary fixed integer prices. All three affected bases, use ownership and global cardinality are preserved by each strictly improving atomic cycle.", + "The exact pinned batch covers two order modes times two pricing settings times zero/three cycle passes per axis, with the default combination supplied as the exact parent canary. The wrapper adds only those settings, explicit order dispatch, dense verification and receipt fields to the previously audited R7 construction." + ], + "scope": "General composition/source guards only. No final selected physical-word or arithmetic clearance, no numerical frontier/global-optimality claim, and no foreign PR82 producer replay. Final selected literal physical operations, fresh profiles and complete exact assembly remain separate gates. PR84 freeze remains unchanged.", + "source_manifest_sha256": "45c1f1e6da14472859d89b3247ad6591a596f0729eff369e21c7581d3794859e", + "source_pins": 90, + "status": "PASS general final-composition ordering, coordinate-pricing and three-cycle source guards", + "verified_utc": "2026-10-08T20:52:35.452881+00:00" +} diff --git a/references/frame-compiler/pr88/research/final-frame/engine-provenance.json b/references/frame-compiler/pr88/research/final-frame/engine-provenance.json new file mode 100644 index 0000000000..cf4245da1a --- /dev/null +++ b/references/frame-compiler/pr88/research/final-frame/engine-provenance.json @@ -0,0 +1,16 @@ +{ + "engine": { + "original": "references/frame-compiler/final-r10/scripts/experiments/compiler.py", + "original_source_manifest_sha256": "45c1f1e6da14472859d89b3247ad6591a596f0729eff369e21c7581d3794859e", + "portable_engine": "final_frame_engine.py", + "portable_engine_sha256": "e349c2b5837812398441601306d916c9fdb7d0ec548d0c68e19580fd3d4524c2", + "relation": 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649, + "19": 908, + "20": 3476, + "21": 7248, + "24": 25, + "23": 453 + }, + "rank_mass": 878925, + "elementary_xors": 247312, + "stats": { + "augmentations": 166, + "regions": 93828, + "matched": 70124, + "multi_node_regions": 11375, + "carry_exchanges": 1815, + "carry_two_cycles": 201, + "carry_three_cycles": 2, + "live_anchor_candidates": 97647, + "live_anchor_xors": 865, + "reclaimed": 3496, + "clearing_xors": 7154 + }, + "dirty_basis_vectors": 39733, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 74.67173290252686 +} diff --git a/references/frame-compiler/pr88/research/final-frame/reported-comparisons.json b/references/frame-compiler/pr88/research/final-frame/reported-comparisons.json new file mode 100644 index 0000000000..fc64a324b9 --- /dev/null +++ b/references/frame-compiler/pr88/research/final-frame/reported-comparisons.json @@ -0,0 +1,21 @@ +{ + "comparisons": { + "85": { + "author": "rohanarun", + "commit": 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Supplied open-PR baseline numerical claims remain accepted working inputs. Inherited all-size residual compiler, tape, prime selection, recovery and analytic transfer hypotheses remain. No global optimum or practical running-time claim. PR84 freeze is unchanged; this is a separate stronger result.", + "selected_exact_constraints": 47, + "selected_files_sha256": { + "spark-results/spark/final-composition-r10/results/23-444-envelope-half-baseline-cover-minus-core-minus-pricing0-cycles0/compiler-result.json": "7943956321b71ff22ef2beabd13370f66e38c447d6b374ee8dda050dff78f9fc", + "spark-results/spark/final-composition-r10/results/23-444-envelope-half-baseline-cover-minus-core-minus-pricing0-cycles0/exact-result.json": "b0a56281ebb137be54acb5e86debf05f7b28bd2a2ee753eed82c33fc727a08ac", + "spark-results/spark/final-composition-r10/results/23-444-envelope-half-baseline-cover-minus-core-minus-pricing0-cycles0/oracle-input.bin": "7817a61c9a43b96a18005ad3844531d980471743a1f1aad84dffed2cfa301315", + "spark-results/spark/final-composition-r10/results/23-444-envelope-half-baseline-cover-minus-core-minus-pricing0-cycles0/profiles.json": "45708723716dded9bb2688fc9e576de4550b31ff4762a41d533c486374ac8664", + 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"selected_strict_margins": 7, + "selection_sha256": "c05715807ad48d2c292f6e3431c338c39d4e7ae80b9758a8c3f8ace520178e23", + "source_manifest_sha256": "45c1f1e6da14472859d89b3247ad6591a596f0729eff369e21c7581d3794859e", + "source_pins": 90, + "status": "PASS final frozen R10 composition cleared for portable packaging", + "strictly_excluded_other_complete_profiles": 51523, + "verified_utc": "2026-10-08T21:00:47.956803+00:00", + "wire_bits": 27 +} diff --git a/references/frame-compiler/pr88/research/final-frame/word-bindings.json b/references/frame-compiler/pr88/research/final-frame/word-bindings.json new file mode 100644 index 0000000000..27df9e8540 --- /dev/null +++ b/references/frame-compiler/pr88/research/final-frame/word-bindings.json @@ -0,0 +1,12 @@ +{ + "23": { + "parent_word_sha256": "a6702539987f29202e6aef9559eef854df59313195423cc62f69f32173fc7541", + "profiles_sha256": "45708723716dded9bb2688fc9e576de4550b31ff4762a41d533c486374ac8664", + "word_sha256": "3b6aac37d3e39d60381fa05250a4c0a88ed665cc2dccca7242e8c1ad5f9b3a66" + }, + "25": { + "parent_word_sha256": "cf2783c6566ff3ff7537cc30b89a37485bc6b76e932cbbd89fcf847d67cb6996", + "profiles_sha256": "1ca57426564eb285f0d092dac5433531505f08f53ea169c3f12df9a2d47e1659", + "word_sha256": "81accb74c4697f5fb7569636023cd212b6995de44fe2ba862f89b80316cb3756" + } +} diff --git a/references/frame-compiler/pr88/scripts/experiments/audit_final_frame_completion.py b/references/frame-compiler/pr88/scripts/experiments/audit_final_frame_completion.py new file mode 100644 index 0000000000..2097e5a725 --- /dev/null +++ b/references/frame-compiler/pr88/scripts/experiments/audit_final_frame_completion.py @@ -0,0 +1,53 @@ +"""Focused actual-source audit. Chafik Boukhalfa with OpenAI Codex assistance; Apache-2.0.""" +from pathlib import Path +from hashlib import sha256 +from datetime import datetime,timezone +from random import Random +from collections import Counter +from copy import deepcopy +import ast,gzip,json,io,types,sys +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1] +SOURCE=HERE/'final_frame_engine.py';NEW=SOURCE +source=SOURCE.read_text();tree=ast.parse(source) +def check(ok,why): + if not ok:raise ValueError(why) +s=source +tree=ast.parse(s) +helpers=[n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name in ('basis','independent')] +namespace={};exec(compile(ast.Module(body=helpers,type_ignores=[]),str(SOURCE),'exec'),namespace) +basis=namespace['basis'];independent=namespace['independent'] +future=next(n for n in ast.walk(tree) if isinstance(n,ast.FunctionDef) and n.name=='future_priority') +contains=lambda a,b:not(b[0]&~a[0]) and not(a[1]&~b[1]) +# Actual-use fixtures distinguish future compatible uses from backward or nonnested uses. +ns=dict(position={0:0,1:1,2:2,3:3},step=1,b={'frame':(1,3),'inputs':[10,11,12,13]},blocks=[{'frame':(1,3)},{'frame':(1,3)},{'frame':(1,7)},{'frame':(1,5)}],uses=[(10,2,None),(10,2,('terminal',)),(11,2,None),(11,0,None),(12,3,None),(13,3,None)],value_uses={10:[0,1],11:[2,3],12:[4],13:[5]},contains=contains,slots=[7,1,3,3],ins=[0,1,2,3]) +exec(compile(ast.Module(body=[future],type_ignores=[]),str(SOURCE),'exec'),ns) +check([ns['future_priority'](i) for i in range(4)]==[(-2,3,0),(-1,1,1),(0,2,2),(0,2,3)],'Priority does not use compatible actual future uses, symbolic support, index') +check(sorted(range(4),key=ns['future_priority'])==[0,1,2,3],'Priority is not deterministic') +# General span argument is below; these adversarial numerical fixtures check the actual helpers and literal synthesis. +rng=Random(20261008);cases=0;operations=0 +for n in range(1,10): + for trial in range(250): + rows=[] + for _ in range(rng.randrange(n+1)*3): + candidate=rng.randrange(1,1<>i&1) + if j!=i: + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];ops.append((a,z)) + for j in range(n): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];ops.append((j,i)) + check(rr==[1<0 and current==previous-gain,'Fixed integer price does not strictly improve') + previous=current;observed.append([e,other,f,z]) + invariant() + env=dict(blocks=blocks,edges=edges,chosen=chosen,right=right,prices=prices,priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])),basis=basis,independent=independent,stats=Counter(),sys=types.SimpleNamespace(stderr=io.StringIO()),audit_cycle=audit_cycle) + exec(code,env);invariant();check(env['stats']['carry_two_cycles']==len(observed),'Cycle count differs') + if expected is not None:check(len(observed)==expected,'Targeted cycle outcome differs') + cycles+=len(observed);cases+=1 + return observed + +# Each group is full (one outbasis row + one carrier). Neither cross-group +# single addition is independent, but simultaneous replacement is legal. +blocks=[{'outbasis':[3]},{'outbasis':[3]}] +edges=[(1,0,0),(0,1,0),(0,0,1),(1,1,1)] +run(blocks,edges,{0,1},[10,10,9,9],1) +run(blocks,edges,{0,1},[10,10,10,10],0) +# With the receiving group's unit vector already in its output span, reject. +run([{'outbasis':[2]},{'outbasis':[3]}],edges,{0,1},[10,10,9,9],0) +# Missing the complementary future-use edge also rejects. +run(blocks,edges[:3],{0,1},[10,10,9],0) +# Duplicate group/use lookup keys are explicitly rejected before iteration. +try:run(blocks,edges+[(0,0,0)],{0,1},[10,10,9,9,1]) +except AssertionError:duplicate_rejected=True +else:raise ValueError('Ambiguous group/use candidate key accepted') +rng=Random(231025) +for trial in range(1200): + ng=rng.randrange(2,6);nuses=rng.randrange(2,14);blocks=[];edges=[] + for g in range(ng): + width=rng.randrange(2,6);rows=[] + for _ in range(rng.randrange(width)*2): + v=rng.randrange(1,1<150 or choice<.34): + s=rng.choice(list(records));f,g=records.pop(s);idx.remove(s,f,g) + elif records and choice<.66: + s=rng.choice(list(records));f,g=records[s];new=between(f,g);check(contains(f,new) and contains(new,g),'Invalid random promotion') + before_order=dict(idx.order);idx.move(s,f,new);records[s]=(new,g);check(idx.order==before_order,'Frame move changes insertion order') + else: + s=rng.randrange(1200) + if s in records:continue + f=envelope();g=extend(f);idx.insert(s,f,g);records[s]=(f,g) + mutations+=1 + if iteration%4==0: + for target in (envelope(),(1,mask)): + check(idx.eligible(target)==query(records,target),'Random ordered pending query differs');queries+=1 + if iteration%100==0: + check(idx.lower.all==sum(1<>k&1),'Target core bitmap stale') + check(idx.cover[k]==sum(1<>k&1),'Target cover bitmap stale') +idx=Pending(4);idx.insert(1,(1,3),(1,5)) +check(idx.lower.eligible_mask((1,7))==2 and idx.eligible((1,7))==[],'Fixture does not reject missing future containment') +# Audit the actual integrated raise_ function on passive live controls. +compile_node=next(n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name=='compile_');raise_node=next(n for n in compile_node.body if isinstance(n,ast.FunctionDef) and n.name=='raise_') +blocks=[dict(frame=(3,3),rank=1),dict(frame=(1,7),rank=2),dict(frame=(1,15),rank=3)] +idx=Pending(4);idx.insert(0,blocks[0]['frame'],blocks[2]['frame']);idx.insert(1,blocks[0]['frame'],blocks[2]['frame']) +env=dict(frames=[0,0],blocks=blocks,contains=contains,retired=set(),retired_index=Retired(4),pending={0:2,1:2},pending_index=idx,hist=Counter(),events=[]) +exec(compile(ast.Module(body=[raise_node],type_ignores=[]),str(NEW),'exec'),env);env['raise_'](0,1) +check(idx.eligible(blocks[0]['frame'])==[1] and idx.eligible(blocks[1]['frame'])==[0,1],'Actual raise changes pending selection incorrectly') +check(idx.order=={0:0,1:1},'Actual raise changes pending order') +receipt=dict(status='PASS actual ordered two-envelope pending index and frame lifecycle',source_sha256=sha256(SOURCE.read_bytes()).hexdigest(),mutations=mutations,ordered_queries=queries,actual_raise_fixture=True,future_containment_negative_fixture=True) +(ROOT/'certificates/final-frame-pending-index-validation.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt)) diff --git a/references/frame-compiler/pr88/scripts/experiments/audit_final_frame_pricing.py b/references/frame-compiler/pr88/scripts/experiments/audit_final_frame_pricing.py new file mode 100644 index 0000000000..13f3b1abea --- /dev/null +++ b/references/frame-compiler/pr88/scripts/experiments/audit_final_frame_pricing.py @@ -0,0 +1,43 @@ +"""Audit the actual coordinate-pricing writer and whole-engine delta. Apache-2.0.""" +from pathlib import Path +from hashlib import sha256 +from copy import deepcopy +from itertools import combinations +from random import Random +import ast,io,json,struct,sys +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +ROOT=Path(__file__).resolve().parents[2] +def check(ok,why): + if not ok:raise ValueError(why) +# At source level, restore only the oracle writer and remove the audited helper/call. +engine=ast.parse((ROOT/'scripts/experiments/final_frame_engine.py').read_text());base=ast.parse((ROOT/'references/frame-compiler/indexed-r5/scripts/experiments/compiler.py').read_text());new_compile=next(n for n in engine.body if isinstance(n,ast.FunctionDef) and n.name=='compile_');base_compile=next(n for n in base.body if isinstance(n,ast.FunctionDef) and n.name=='compile_') +writer=next(n for n in new_compile.body if isinstance(n,ast.With) and 'oracle_input.open' in ast.unparse(n.items[0].context_expr));base_writer=next(n for n in base_compile.body if isinstance(n,ast.With) and 'oracle_input.open' in ast.unparse(n.items[0].context_expr)) +trim=deepcopy(engine);trim.body=[n for n in trim.body if not(isinstance(n,ast.FunctionDef) and n.name=='improve_three_cycles')];fn=next(n for n in trim.body if isinstance(n,ast.FunctionDef) and n.name=='compile_');fn.body=[deepcopy(base_writer) if isinstance(n,ast.With) and 'oracle_input.open' in ast.unparse(n.items[0].context_expr) else n for n in fn.body];fn.body=[n for n in fn.body if not(isinstance(n,ast.For) and 'THREE_CYCLE_PASSES' in ast.unparse(n.iter))];check(ast.dump(trim,include_attributes=False)==ast.dump(base,include_attributes=False),'Whole engine changes exceed pricing writer plus cleared three-cycle helper/call') +# Exercise the ACTUAL binary oracle writer in memory. The block objects must stay +# untouched; only serialized core/cover masks are conjugated, while IDs/ranks stay. +class Capture: + def __init__(self):self.stream=None;self.bytes=None + def open(self,mode):check(mode=='wb','Unexpected oracle file mode');self.stream=io.BytesIO();return self + def __enter__(self):return self.stream + def __exit__(self,*args):self.bytes=self.stream.getvalue();return False +writer_code=compile(ast.Module(body=[deepcopy(writer)],type_ignores=[]),'actual_coordinate_oracle_writer','exec');base_code=compile(ast.Module(body=[deepcopy(base_writer)],type_ignores=[]),'original_oracle_writer','exec') +rng=Random(202610092046);writer_cases=0 +for h in (3,5,23,25): + for trial in range(100): + blocks=[] + for _ in range(rng.randrange(1,30)): + cover=rng.randrange(1,1<150 or rng.random()<0.48): + s=rng.choice(list(records));f,r=records.pop(s);idx.remove(s,f,r) + else: + s=rng.randrange(1200) + if s in records:continue + f=frame();r=rng.randrange(h+1);idx.insert(s,f,r);records[s]=(f,r) + mutations+=1 + if iteration%4==0: + for target in (frame(),(1,full)): + check(list(idx.eligible(target))==order(records,target),'Random exact frame/order query differs');queries+=1 + if iteration%100==0: + check(idx.all==sum(1<>k&1),'Core bitmap stale') + check(idx.cover[k]==sum(1<>k&1),'Cover bitmap stale') +# The actual integrated raise function keeps already-retired controls indexed at their new frame. +compile_node=next(n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name=='compile_') +raise_node=next(n for n in compile_node.body if isinstance(n,ast.FunctionDef) and n.name=='raise_') +blocks=[dict(frame=(3,3),rank=1),dict(frame=(1,7),rank=2),dict(frame=(1,15),rank=3)] +idx=Index(4);idx.insert(0,blocks[0]['frame'],1) +env=dict(frames=[0,0],blocks=blocks,contains=contains,retired={0},retired_index=idx,pending={},pending_index=space['PendingIndex'](4),hist=Counter(),events=[]) +exec(compile(ast.Module(body=[raise_node],type_ignores=[]),str(NEW),'exec'),env) +env['raise_'](0,1) +check(list(idx.eligible(blocks[0]['frame']))==[] and list(idx.eligible(blocks[1]['frame']))==[0],'Actual retired control frame promotion not reflected') +env['raise_'](1,1) +check(idx.all==1 and env['frames']==[1,1],'Nonretired raise inserted an indexed role') +env['raise_'](0,2);idx.remove(0,blocks[2]['frame'],3) +check(idx.all==0 and not any(idx.ranks) and not any(idx.core) and not any(idx.cover),'Actual promoted role removal leaves stale bits') +receipt=dict(status='PASS actual ordered retired index and frame lifecycle',source_sha256=sha256(SOURCE.read_bytes()).hexdigest(),mutations=mutations,ordered_queries=queries,actual_raise_fixture=True) +(ROOT/'certificates/final-frame-retired-index-validation.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt)) diff --git a/references/frame-compiler/pr88/scripts/experiments/audit_final_frame_three_cycles.py b/references/frame-compiler/pr88/scripts/experiments/audit_final_frame_three_cycles.py new file mode 100644 index 0000000000..f16e5e8555 --- /dev/null +++ b/references/frame-compiler/pr88/scripts/experiments/audit_final_frame_three_cycles.py @@ -0,0 +1,54 @@ +"""Actual-source exchange tests: cardinality, matroid feasibility, integer descent.""" +import ast,copy,random,json +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2] +source=ast.parse((ROOT/'scripts/experiments/final_frame_engine.py').read_text());fn=next(n for n in source.body if isinstance(n,ast.FunctionDef) and n.name=='improve_three_cycles');ns={};exec(compile(ast.Module(body=[fn],type_ignores=[]),'actual-source-three-cycle','exec'),ns);improve=ns[fn.name] +def rank(rows): + pivots={} + for row in rows: + while row: + bit=row.bit_length()-1 + if bit not in pivots:pivots[bit]=row;break + row^=pivots[bit] + return len(pivots) +def exercise(blocks,edges,chosen,prices,passes=3): + chosen=set(chosen);blocks=copy.deepcopy(blocks);right={edges[e][1]:e for e in chosen};assert len(right)==len(chosen) + count=len(chosen);initial=sum(prices[e] for e in chosen);priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e]));changes=0 + def can(e,drop): + g,u,i=edges[e];rows=blocks[g]['outbasis']+[1<=3 or result[0]==0 +assert accepted>0 +print(json.dumps({'status':'PASS','actual_source':str(ROOT/'scripts/experiments/final_frame_engine.py'),'fixtures':1604,'accepted_three_cycles':accepted,'checks':['strict-cycle-only fixture','equal and worsening cost rejected','dependent replacement rejected','cardinality','one use per choice','local vector independence','exact integer descent','determinism','distinct block requirement']})) diff --git a/references/frame-compiler/pr88/scripts/experiments/binary_frame_math.py b/references/frame-compiler/pr88/scripts/experiments/binary_frame_math.py new file mode 100644 index 0000000000..b87855e808 --- /dev/null +++ b/references/frame-compiler/pr88/scripts/experiments/binary_frame_math.py @@ -0,0 +1,87 @@ +"""Exact rational helpers extracted without body changes from pinned PR48 verify.py. +Credits: icekylinx PR32/36, Dominik Scholz PR35, Zhihao Chen PR29/23, +Paureel/Aurel Prosz, Swapnil Jain, Rohan Arun PR25/31, RaD/hipotures, +Chafik Boukhalfa and inherited notices in references/frame-compiler/pr48. +Prepared with OpenAI Codex assistance; no formal theorem claim. +""" +from fractions import Fraction as Q +from functools import lru_cache +from math import comb, factorial, isqrt, prod + +def js(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):js(v)for k,v in x.items()} + if isinstance(x,(list,tuple)):return [js(v)for v in x] + return x + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def mersenne(exponent): + require(exponent >= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr88/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr88/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr88/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr88/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr88/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr88/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"< 1 and kappa > previous_kappa + prior74 = json.loads((ROOT/'references/frame-compiler/pr74/research/balanced-split-frames/certificate.json').read_text()) + rows74 = {int(t):n for t,n in prior74['child_multiplicities'].items()} + prior74_lower = refine.exact_moment(575, prior74['W'], rows74, bit_saving)['lower'] + reported74 = Q('10366199626713/200000000000000000') + assert prior74_lower > 1 and kappa > reported74 + bridge = finite_bridge(p['W']) + validate_bridge(bridge, p['W']) + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/final-frame/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr84_commit='88ca39571907343a49e97f328971ec7bcd26fbfd', + pr74_commit='3f78d8967c009153f2df5c6a6577b6ab1d37e2ca', reported_pr74_kappa=reported74, + ratio_reported_pr74=kappa/reported74, pr74_complete_profile_exclusion_lower=prior74_lower, + pr84_kappa=previous_kappa, ratio_pr84=kappa/previous_kappa, + absolute_gain_pr84=kappa-previous_kappa, + pr84_complete_profile_exclusion_lower=prior71_lower, + full_pr84_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected final-frame partition and point permutation, rank-preserving selected node order, natural execution, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring, PR69 balanced coarse sums, future unit completion and bounded PR70-derived single exchanges, two-cycles and selected three-donor cycles, PR82 coordinate-aware heuristic pricing, exact frame indices, late-output routing and PR74/78-inspired coordinate relabeling; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'final-frame-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr88/scripts/experiments/final_frame_engine.py b/references/frame-compiler/pr88/scripts/experiments/final_frame_engine.py new file mode 100644 index 0000000000..5c82d20ab0 --- /dev/null +++ b/references/frame-compiler/pr88/scripts/experiments/final_frame_engine.py @@ -0,0 +1,462 @@ +# Coordinate-conjugated oracle pricing adapted from Rohan Arun PR82, with OpenAI Codex assistance. +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<0 and carry_can(x,f) and carry_can(other,y): + options.append((-gain,z,x,y,other)) + if not options:continue + _,z,x,y,other=min(options) + old=(f,z,y);new=(e,x,other) + assert len(set(old))==len(set(new))==3 and not set(old)&set(new) + assert {edges[t][1] for t in old}=={edges[t][1] for t in new} + assert len({edges[t][0] for t in old})==len({edges[t][0] for t in new})==3 + for t in old: + tg,tu,ti=edges[t];chosen.remove(t);blocks[tg]['selected'].remove(t);del right[tu] + for t in new: + tg,tu,ti=edges[t];assert tu not in right;chosen.add(t);blocks[tg]['selected'].add(t);right[tu]=t + changes+=1 + return changes + + +def compile_(h,matching=True,reclaim=False,dirty=True): + t0=time.time();c,blocks,uses,value_uses,owner,signal,order,contains=build(h);v=len(c.inputs);position={g:i for i,g in enumerate(order)} + print('built',h,len(blocks),'regions',flush=True,file=sys.stderr) + mode=globals().get('OUTPUT_MODE','baseline') + edges,chosen,right,stats=match(blocks,uses,matching) + print('matched',len(chosen),'seconds',time.time()-t0,flush=True,file=sys.stderr) + slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();retired_index=RetiredIndex(h);pending={};pending_index=PendingIndex(h);stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + oracle_map=globals().get('ORACLE_COORDINATES',list(range(h))) + assert sorted(oracle_map)==list(range(h)), 'Invalid oracle coordinate permutation' + for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + for phase in range(globals().get('THREE_CYCLE_PASSES',0)): + changes=improve_three_cycles(blocks,edges,chosen,right,prices,priority,carry_can) + stats['carry_three_cycles']+=changes + print('carry three-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + first,mid,last = 0,(len(groups)-1)//2,len(groups)-1 + requested = {1:[first],2:[mid],3:[last],4:[first,mid],5:[first,last],6:[mid,last],7:[first,mid,last],8:[first,first+1],9:[last-1,last]}[choice] + chosen=[] + for k in requested: + if k not in chosen and 0<=k>common&1 and not(mask&forbidden)) + assert support[x]==expected + return {'status':'PASS all global supports, exact envelopes, disjoint additions and target outputs','nodes':len(c.active),'outputs':len(c.outputs),'sha256':digest.hexdigest()} + +# Coordinate action preserves the literal physical word under a global input relabel. +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word diff --git a/references/frame-compiler/pr88/scripts/experiments/joint_dual_reclaim_compiler.py b/references/frame-compiler/pr88/scripts/experiments/joint_dual_reclaim_compiler.py new file mode 100644 index 0000000000..1eb8dea9fa --- /dev/null +++ b/references/frame-compiler/pr88/scripts/experiments/joint_dual_reclaim_compiler.py @@ -0,0 +1,240 @@ +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'final-frame-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from final_frame_compose import check_sources + manifest_path = ROOT/'research/final-frame/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/final-frame-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_all_threshold_dependent_bridge_fields_are_checked(self): + from final_frame_compose import finite_bridge, validate_bridge + expected = finite_bridge(131503443) + self.assertTrue(validate_bridge(expected, 131503443)) + for section,key in (('bit','wire_bits'),('rows','coefficient'),('rows','degree'),('rows','degree_gap'),('rows','suffix_slope')): + changed = deepcopy(expected) + changed[section][key] = Fraction(changed[section][key])+1 + with self.subTest(field=section+'.'+key), self.assertRaisesRegex(AssertionError, 'Stale finite bridge'): + validate_bridge(changed, 131503443) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('final_frame_graph.py', 'final_frame_engine.py', 'final_frame_compiler.py', 'split_pair_arithmetic.py', 'final_frame_compose.py', 'verify_final_frame.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr88/tests/test_final_frame_coordinates.py b/references/frame-compiler/pr88/tests/test_final_frame_coordinates.py new file mode 100644 index 0000000000..ef68ff7675 --- /dev/null +++ b/references/frame-compiler/pr88/tests/test_final_frame_coordinates.py @@ -0,0 +1,49 @@ +"""Bijection and adverse-coordinate controls for the actual PR74 relabel functions.""" +from pathlib import Path +from itertools import combinations +from copy import deepcopy +from hashlib import sha256 +import gzip,json,sys,unittest +ROOT=Path(__file__).resolve().parents[1];sys.path.insert(0,str(ROOT/'scripts/experiments')) +from final_frame_nodeops import relabel +from final_frame_graph import configuration + +class CoordinateControls(unittest.TestCase): + def test_selected_permutations_are_exact_integer_bijections(self): + for h in (23,25): + perm=configuration(h)['coordinate_permutation'] + self.assertEqual(sorted(perm),list(range(h))) + self.assertTrue(all(type(x) is int for x in perm)) + self.assertEqual(configuration(23)['coordinate_permutation'],[1, 2, 4, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 19, 21, 22, 0]) + + def test_every_selected_word_roundtrips_full_coordinate_inverse(self): + for h in (23,25): + word=json.loads(gzip.decompress((ROOT/f'certificates/final-frame-word-{h}.json.gz').read_bytes())) + perm=configuration(h)['coordinate_permutation'];inverse=[perm.index(i) for i in range(h)] + parent=relabel(deepcopy(word),inverse) + # Dict iteration and scatter order are deliberately retained by the actual function. + raw=(json.dumps(parent,separators=(',',':'))+'\n').encode() + selection=json.loads((ROOT/'research/final-frame/word-bindings.json').read_text())[str(h)] + self.assertEqual(sha256(raw).hexdigest(),selection['parent_word_sha256']) + self.assertEqual(relabel(parent,perm),word) + + def test_relabel_preserves_physical_operations_and_frame_inclusions(self): + h=5;triples=list(combinations(range(h),3));v=len(triples);perm=[4,0,2,1,3] + word=dict(h=h,v=v,frames=[[3,7],[1,31]],sources={str(i):i for i in range(v)}, + scatter=[[v+i,2*v+i] for i in reversed(range(v))],outputs=[[2*v+i,0,0,list(t)] for i,t in enumerate(triples)], + ops=[[2*v,2*v+1,0]],events=[[2*v,0,1]]) + changed=relabel(deepcopy(word),perm) + self.assertEqual(changed['ops'],word['ops']);self.assertEqual(changed['events'],word['events']) + self.assertEqual(set(map(int,changed['sources'])),set(range(v))) + self.assertEqual([b for a,b in changed['scatter']],[b for a,b in word['scatter']]) + self.assertEqual(set(a for a,b in changed['scatter']),set(range(v,2*v))) + (a,b),(c,d)=changed['frames'];self.assertEqual(c&~a,0);self.assertEqual(b&~d,0) + + def test_invalid_permutation_and_scatter_source_are_rejected(self): + word=dict(h=3,v=1,frames=[[1,7]],sources={'0':0},scatter=[[1,2]],outputs=[[2,0,0,[0,1,2]]]) + for permutation in ([0,1,1],[0,1],[0,1,3]): + with self.subTest(permutation=permutation),self.assertRaises(AssertionError):relabel(deepcopy(word),permutation) + word['scatter'][0][0]=0 + with self.assertRaises(AssertionError):relabel(word,[0,1,2]) + +if __name__=='__main__':unittest.main() diff --git a/references/frame-compiler/pr88/tests/test_final_frame_order.py b/references/frame-compiler/pr88/tests/test_final_frame_order.py new file mode 100644 index 0000000000..43e0832103 --- /dev/null +++ b/references/frame-compiler/pr88/tests/test_final_frame_order.py @@ -0,0 +1,45 @@ +from pathlib import Path +from itertools import combinations +from copy import deepcopy +import importlib.util,json,unittest +import sys +sys.path.insert(0,str(Path(__file__).resolve().parents[1]/'scripts/experiments')) +from final_frame_nodeops import order_key,reorder,verify_dense,relabel +ROOT=Path(__file__).resolve().parents[1] +spec=importlib.util.spec_from_file_location('original',ROOT/'scripts/experiments/indexed_cycle_nodeops.py');original=importlib.util.module_from_spec(spec);spec.loader.exec_module(original) +KEYS=['pr74','cover-minus-core-minus'] +class Fake: + def __init__(self): + self.h=5;self.inputs=list(combinations(range(5),3));self.args=[None]*11;self.core=[0]+[sum(1<1. The exponential tail bound is `(v^9/9!)/(1-v/10)` for upper argument v<1. An independent atanh log expansion at base 3/2 with 60 terms and a degree-12 exponential bound confirms both signs. Complete pinned PR88 and reported PR74 child lists separately have lower moment greater than one at s. These are complete-profile historical comparisons; the foreign PR74 claim is an accepted working input, not an independent audit of its entire construction. + +The reconstructed bridge has bit wire bits 27, row coefficient 843, row degree 2000, gap `2000-(51/25)*843=7007/25`, and suffix slope 8000. Tests reject stale values. The complex saving stays 717/10^7 and the backoff stays 10^-12. All 47 strict assembly constraints and seven margins hold for κ=52789616935221/1000000000000000000. The next 10^-18 κ point violates a controlling strict margin; coarser-grid reassembly and original-prefix/old-guard/old-exposure negative controls also execute. Eventual arithmetic cutoffs are recomputed by the unchanged inherited routine. + +## 7. Provenance and proof boundary + +This proves the stated finite scalar, arbitrary-dirty physical, actual-frame/profile, complete-child and exact-inequality claims. The ordered affine residual compiler, all-size construction and recursion, finite scalar alphabet/overhead, routing, prime selection, exact recovery, fixed-tape simulation and analytic transfer remain inherited assumptions. Arithmetic cutoffs cover the recorded inequalities and do not establish every operational threshold. The additive Lean companion proves 197 rational arithmetic theorems for this exact finite witness; the limits below remain explicit. + +The portable engine and node helper are byte-identical to the independently audited 109-pin R11 discovery runtime and unchanged from R10. The graph provider composes only the independently proved firstK/anchoring/depth-coarse hooks with the existing order, physical compiler and final relabeling. The complete 1,290-file PR88 construction archive preserves all original source/finite inputs and construction certificates. The 17 updated PR74 files, fetch provenance, Apache license and notices are separately retained byte-for-byte; older PR74/78/82 archives remain unchanged. The source closure binds selected configurations, wrappers, engine, tests, proof, physical words, transition profiles, Lean module/input/generator and additive integration files. Derived arithmetic and validation receipts are excluded to avoid circular pins. + +## 8. Lean arithmetic companion and review boundary + +`formal/lean/KappaCheck/AlignedFrameComposition.lean` is unchanged from the independently reviewed module compiled with Lean/mathlib 4.21.0. It proves the complete 27-rank positive child counts, total width/rank/deficit, 54 Taylor domains and 54 rational Taylor bounds across accepted/rejected moments, the moment inequalities computed from the supplied counts, 47 strict assembly slacks, seven strict margins, and neighboring grid rejection. All 197 theorem dependencies are audited against `propext`, `Classical.choice`, and `Quot.sound`; there are no added axioms, `sorry`, or `native_decide`. + +The generator regenerates the exact module from the pinned `lean/input.json` without workspace dependencies. The Python companion checks that the input profiles, counts, moment bounds, parameters and slacks match the freshly recomposed certificate. The historical PR26 source table and axiom audit are extended additively; existing entries and checks remain. + +This formalizes rational arithmetic, not the validity of real logarithm/exponential enclosures, the physical derivation of the supplied arrays, or the all-size multiplication theorem. Expert review should concentrate on: + +- The inherited all-size framed/residual compiler and fixed-tape implementation. +- Analytic transfer, prime/precision selection and exact recovery. +- Interpretation of the finite-profile interface and Lean's external real-log/exp hypotheses. + +The exact saving is κ=52789616935221/10^18. Its approximate display is 2^(-14.2093862772), a 37.2695587404% increase over the original PR36 κ=384569/10^10. The increase over reported PR74 at `428b5c167686b42a83f1abf7003c6d17aec561ea` is about 0.01415763596%; reported comparison and complete paid-profile arithmetic do not assert an independent replay of its foreign producer. The frozen 59,045-pair portfolio has two equivalent best pairs (differing only in an inactive h23 cycle setting), with every other paid pair excluded at the selected saving. This is not a global optimum claim. + +Source credits: @eumemic [#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57) and [#69](https://github.com/CrocSwap/integer-mult-bounds/pull/69), reversible compilation and balanced coarse sums; @rohangar1 [#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59), split recursion; @ikeboy [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62), interval strips and core-aware assembly; @DominikScholz [#63](https://github.com/CrocSwap/integer-mult-bounds/pull/63) and [#68](https://github.com/CrocSwap/integer-mult-bounds/pull/68), ranked composition and pending live controls; @rohanarun [#65](https://github.com/CrocSwap/integer-mult-bounds/pull/65), [#67](https://github.com/CrocSwap/integer-mult-bounds/pull/67) [#78](https://github.com/CrocSwap/integer-mult-bounds/pull/78) and [#82](https://github.com/CrocSwap/integer-mult-bounds/pull/82), exact refined assembly, profile-cost reclamation, coordinate-flag search and coordinate-aware pricing; @alejandrozu [#70](https://github.com/CrocSwap/integer-mult-bounds/pull/70), carry exchanges; Thomas DiFiore (@tomdif) [#74](https://github.com/CrocSwap/integer-mult-bounds/pull/74), aligned firstK partition, multi-pair anchoring, depth-dependent coarse sums, original rank-first order and coordinate relabeling; @chafreaky [#60](https://github.com/CrocSwap/integer-mult-bounds/pull/60), [#71](https://github.com/CrocSwap/integer-mult-bounds/pull/71), [#79](https://github.com/CrocSwap/integer-mult-bounds/pull/79) [#84](https://github.com/CrocSwap/integer-mult-bounds/pull/84), [#88](https://github.com/CrocSwap/integer-mult-bounds/pull/88) and this composition, rank-preserving tie orders, three-donor cycles, ranked reclamation, anchored splits, future completion, integer scoring, exact indexes, two-cycles, output routing, search and certification. + +Chafik Boukhalfa prepared this package with OpenAI Codex assistance. Original contributor, OpenAI/manuscript, Apache-2.0, and AI-assistance notices remain attached. In particular Avi Eisenberg's Claude assistance and the original contributors' OpenAI disclosures are retained verbatim in the archives. PR78 inspires coordinate-flag search; the selected maps here come from the pinned updated PR74 source. diff --git a/research/aligned-composition/README.md b/research/aligned-composition/README.md new file mode 100644 index 0000000000..b59cc14696 --- /dev/null +++ b/research/aligned-composition/README.md @@ -0,0 +1,30 @@ +# Aligned frame composition + +The frozen conditional finite witness certifies **κ = 52789616935221/1000000000000000000 = 5.2789616935221e-5**, with bit saving **10558480765231/200000000000000000**. This is about **2^(-14.2093862772)** and **37.2695587404% above the original PR36 κ=384569/10^10**. Exact fractions are authoritative; decimals and percentages are displays. It is approximately **0.01415763596% above reported PR74** at `428b5c167686b42a83f1abf7003c6d17aec561ea`. The reported external construction is a working baseline, not independently producer-replayed here. + +| Quantity | This witness | +|---|---:| +| h23 / h25 auxiliary roles | 26,387 / 34,772 | +| Physical width W | 130,417,912 | +| Total recursive rank | 74,988,452,500 | +| Rank deficit | 1,846,900 | +| Largest child / parent dimension | 529 / 575 | +| Bit wire bits / row coefficient | 27 / 843 | + +The selected vectors `['first6',1,1]` and `['first9',1,1,2]` use six/nine anchored pairs, depth-coarse word `hhh`, PR74 node order and its updated coordinate maps. h23 uses baseline output order, identity oracle pricing and zero three-cycle passes. h25 uses late output order, coordinate-aware prices and three passes (60 accepted three-cycles). Future-compatible completion, exact retired/pending indexes and next-use prices remain enabled; bounded single/two-cycle exchange passes remain three. + +```sh +make aligned-composition-verify +make verify +make formal-historical-verify +``` + +The focused gate regenerates both pre-permutation and final words byte-for-byte, reconstructs dense scalar supports, replays all ordinary and arbitrary-dirty basis columns in both orientations, computes fresh actual-frame CRT profiles and checks the complete paid child list. Two independent rational moment enclosures, 47 strict inequalities, seven margins, next-grid rejection and adverse controls are retained. The additive Lean module proves 197 rational arithmetic theorems and exposes its external physical/analytic/all-size hypotheses. + +The [proof](PROOF.md) supplies general compatibility arguments, finite evidence and exact scope. Expert review should focus on the inherited all-size framed/residual compiler and fixed-tape implementation; analytic/prime/precision/recovery transfer; and the finite-profile interface plus Lean's external real-log/exp hypotheses. Arithmetic cutoffs are not full operational thresholds and no practical speedup is asserted. + +The complete immutable PR88 construction and original contributor archives are retained. The 59,045-pair finite search has two equivalent winners and does not prove global optimality. Discovery paths are provenance only; executable verification uses repository-relative inputs. + +Source credits: @eumemic [#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57) and [#69](https://github.com/CrocSwap/integer-mult-bounds/pull/69), reversible compilation and balanced coarse sums; @rohangar1 [#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59), split recursion; @ikeboy [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62), interval strips and core-aware assembly; @DominikScholz [#63](https://github.com/CrocSwap/integer-mult-bounds/pull/63) and [#68](https://github.com/CrocSwap/integer-mult-bounds/pull/68), ranked composition and pending live controls; @rohanarun [#65](https://github.com/CrocSwap/integer-mult-bounds/pull/65), [#67](https://github.com/CrocSwap/integer-mult-bounds/pull/67) [#78](https://github.com/CrocSwap/integer-mult-bounds/pull/78) and [#82](https://github.com/CrocSwap/integer-mult-bounds/pull/82), exact refined assembly, profile-cost reclamation, coordinate-flag search and coordinate-aware pricing; @alejandrozu [#70](https://github.com/CrocSwap/integer-mult-bounds/pull/70), carry exchanges; Thomas DiFiore (@tomdif) [#74](https://github.com/CrocSwap/integer-mult-bounds/pull/74), aligned firstK partition, multi-pair anchoring, depth-dependent coarse sums, original rank-first order and coordinate relabeling; @chafreaky [#60](https://github.com/CrocSwap/integer-mult-bounds/pull/60), [#71](https://github.com/CrocSwap/integer-mult-bounds/pull/71), [#79](https://github.com/CrocSwap/integer-mult-bounds/pull/79) [#84](https://github.com/CrocSwap/integer-mult-bounds/pull/84), [#88](https://github.com/CrocSwap/integer-mult-bounds/pull/88) and this composition, rank-preserving tie orders, three-donor cycles, ranked reclamation, anchored splits, future completion, integer scoring, exact indexes, two-cycles, output routing, search and certification. + +Chafik Boukhalfa prepared this package with OpenAI Codex assistance. Original contributor, OpenAI/manuscript, Apache-2.0, and AI-assistance notices remain attached. In particular Avi Eisenberg's Claude assistance and the original contributors' OpenAI disclosures are retained verbatim in the archives. 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The unchanged sequential admission inequality g+s+1 (t, Nat.choose 25 3 * c)) ++ + (blocks25.zipIdx.map fun (c,t) => (t, Nat.choose 23 3 * c)) +def count (t : ℕ) : ℕ := + (counts.map fun p => if p.1 = t then p.2 else 0).sum +def mass : ℕ := (counts.map fun p => p.1*p.2).sum +''') +proof('network_counts', 'm = 575 ∧ n = 4073300 ∧ width = 130417912', + 'm, n, width, roles23, roles25, Nat.choose') +proof('rank_mass', 'mass = 74988452500 ∧ m*width-mass = 1846900', + 'mass, counts, blocks23, blocks25, n, m, width, roles23, roles25, Nat.choose') +for t,c in sorted(best['bit']['child_multiplicities'].items(), key=lambda x:int(x[0])): + proof(f'count_{t}', f'count {t} = {c}', 'count, counts, blocks23, blocks25, n, roles23, roles25, Nat.choose') +sizes = sorted(map(int,best['bit']['child_multiplicities'])) +emit(f'def childSizes : List ℕ := {sizes}') +proof('complete_child_support','∀ p ∈ counts, p.2 ≠ 0 → p.1 ∈ childSizes','counts, blocks23, blocks25, n, roles23, roles25, Nat.choose, childSizes') +proof('strict_child_contraction','∀ t ∈ childSizes, 0 < t ∧ t < m','childSizes, m') +emit('''def a : ℚ := 52792403826155 / 1000000000000000000 +def b : ℚ := 717 / 10000000 +def kappa : ℚ := 52789616935221 / 1000000000000000000 +def eta : ℚ := 1 / 1000000000000 +def beta : ℚ := 1 / 20 +def tau : ℚ := 1-a +def sigma : ℚ := 1-b +def qParam : ℚ := a*(1-2*eta) +def lp : ℚ := 1-qParam +def c : ℚ := qParam+eta/4 +def epsilon : ℚ := (1-eta)/(1+qParam) +def lam : ℚ := (tau+lp)/2 +def g : ℚ := epsilon*qParam +def r : ℚ := (g+1-epsilon)/2 +def delta : ℚ := eta/8 +def internal : ℚ := tau+(1-beta)*max (sigma-tau) 0 +def leaf : ℚ := sigma+beta*(1-sigma) +def complexWidth : ℕ := 537696432 +def complexRank : ℕ := 421548223824 +def scalar : ℕ := 4793351472 +def guardE : ℕ := 64*(complexWidth+784+scalar+1)^3 +def guardB : ℕ := complexRank+guardE +def literal : ℕ := 2*scalar*complexWidth^2+8*complexRank+4*complexWidth+4+32*784 +def guardC : ℕ := 32*784*guardB^2 +def literalGap : ℚ := (guardE : ℚ)-literal +def rowGap : ℚ := 2000-(51/25)*(9*27+20*30) +def margins : List ℚ := [1-epsilon,a,g,a,min (1-epsilon-delta) (r-delta),1-epsilon-delta,epsilon] +''') +defs='a, b, kappa, eta, beta, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, guardE, guardB, guardC, literal, complexWidth, complexRank, scalar' +slacks = { + 'a_positive':'a','a_below_b':'b-a','b_below_one_over32':'1/32-b', + 'beta_positive':'beta','beta_below_one':'1-beta','phase_leaf_above_bit':'(1-beta)*b-a', + 'q_positive':'qParam','q_below_internal':'1-internal-qParam','q_below_leaf':'1-leaf-qParam', + 'c_positive':'c','c_below_one':'1-c','q_below_reservations':'c-qParam', + 'lambda_above_tau':'lam-tau','lambda_above_sigma':'lam-sigma','lambda_above_internal':'lam-internal', + 'lambda_prime_above_lambda':'lp-lam','compact_leaf':'lp-leaf','compact_reservations':'lp-(1-c)', + 'lambda_prime_below_one':'qParam','epsilon_positive':'epsilon','epsilon_below_one':'1-epsilon', + 'guard_width':'1-epsilon','K_geometry':'1-epsilon*(1+c)','K_dominates_log':'epsilon*c', + 'record_suffix':'1-epsilon','phase_local':'1-epsilon-delta','phase_boundary':'r-delta', + 'gamma_sublinear':'1-epsilon-r','cell_above_band':'epsilon-(1-r)/2','prime_interval_packing':'1-epsilon', + 'alpha_positive':'r','alpha_below_one':'1-r','alpha_below_one_fourth':'1/4-r','delta_positive':'delta', + 'delta_below_one_eighth':'1/8-delta','short_record_fallback':'epsilon-a','small_field_exposure':'1-epsilon-g', + 'artificial_boundary':'8-epsilon+r-delta-g','literal_scalar_guard':'literalGap','row_product_gap':'rowGap'} +margin_expr = ['1-epsilon','a','g','a','min (1-epsilon-delta) (r-delta)','1-epsilon-delta','epsilon'] +for i,x in enumerate(margin_expr,1): slacks[f'g{i}_above_kappa']=f'({x})-kappa' +assert set(slacks)==set(best['assembly']['assembly']['constraints']) +for name,expr in slacks.items(): + value=best['assembly']['assembly']['constraints'][name] + proof('slack_'+name, f'({expr}) = ({q(value)} : ℚ) ∧ (0 : ℚ) < ({expr})', defs) +proof('margins_strict', '∀ x ∈ margins, kappa < x', 'margins, '+defs) +proof('balanced_identities', '1-epsilon-g = eta ∧ 1-epsilon-r = eta/2 ∧ 1-epsilon*(1+c) = eta-epsilon*eta/4',defs) +proof('controlling_margin', 'g < kappa+1/1000000000000000000 ∧ kappa < g',defs) +proof('gain_over_original', 'kappa > (384569/10000000000 : ℚ) ∧ kappa > (409953/10000000000 : ℚ) ∧ (1/2^15 : ℚ) < kappa ∧ kappa < (1/2^14 : ℚ)',defs) +proof('finite_bridge', '575^9 > (2:ℕ)*529^9 ∧ 575^8 ≤ (2:ℕ)*529^8 ∧ 784^20 > (2:ℕ)*756^20 ∧ 784^19 ≤ (2:ℕ)*756^19 ∧ (2:ℕ)^26 ≤ width ∧ width < (2:ℕ)^27 ∧ (2:ℕ)^29 ≤ complexWidth ∧ complexWidth < (2:ℕ)^30 ∧ guardE > literal ∧ 2*guardB*(784-756) ≥ complexRank+guardE ∧ guardC > 2*guardB+18','width, n, roles23, roles25, Nat.choose, '+defs) +emit('''-- Rounded exponential bounds are supplied here. Their weighted sums and +-- their domination of the degree-eight Taylor arithmetic are checked below. +-- Analytic connections to real log/exp remain external to this supplement. +def taylor8 (x : ℚ) : ℚ := 1+x+x^2/2+x^3/6+x^4/24+x^5/120+x^6/720+x^7/5040+x^8/40320 +def expUpper (x : ℚ) : ℚ := taylor8 x+x^9/362880/(1-x/10) +''') +moment_names=[] +for typ, side, saving in [('accepted','upper','a'),('rejected','lower','(a+1/1000000000000000000)')]: + terms=best[typ+'_moment']['terms'] + moment=[] + recomputed=[] + for t,item in sorted(terms.items(),key=lambda z:int(z[0])): + lo,hi=q(item['log_lower']),q(item['log_upper']) + val=q(item['exp_'+side]); cnt=best['bit']['child_multiplicities'][t] + emit(f'def {typ}_{t} : ℚ := {val}') + proof(f'{typ}_interval_{t}',f'(0 : ℚ) ≤ {saving}*{lo} ∧ {saving}*{lo} ≤ {saving}*{hi} ∧ {saving}*{hi} < 1','a') + expr=f'expUpper ({saving}*{hi}) ≤ {typ}_{t}' if side=='upper' else f'{typ}_{t} ≤ taylor8 ({saving}*{lo})' + proof(f'{typ}_taylor_{t}',expr,'expUpper, taylor8, a, '+f'{typ}_{t}') + moment.append(f'(({t}*{cnt} : ℚ)/(575*130417912))*{typ}_{t}') + recomputed.append(f'(({t}*(count {t} : ℚ))/(m*width))*{typ}_{t}') + emit(f'def {typ}Moment : ℚ :=\n '+ ' +\n '.join(moment)) + emit(f'def {typ}FromCounts : ℚ :=\n '+ ' +\n '.join(recomputed)) + proof(typ+'_profile_link',f'{typ}FromCounts = {typ}Moment',typ+'FromCounts, '+typ+'Moment, m, width, n, roles23, roles25, Nat.choose, '+', '.join(f'count_{t}' for t in terms)) + comparison=f'{typ}Moment < 1' if typ=='accepted' else f'1 < {typ}Moment' + proof(typ+'_moment', f'{comparison} ∧ {typ}Moment = {q(best[typ+"_moment"][side])}',typ+'Moment, '+', '.join(f'{typ}_{t}' for t in terms)) + claim=f'{typ}FromCounts < 1' if typ=='accepted' else f'1 < {typ}FromCounts' + emit(f'theorem {typ}_paid_moment : {claim} := by\n rw [{typ}_profile_link]\n exact {typ}_moment.1\n') +emit('end KappaCheck.AlignedFrameComposition') +theorems = [line.split()[1] for line in '\n'.join(out).splitlines() if line.startswith('theorem ')] +for name in theorems: + emit(f'#print axioms KappaCheck.AlignedFrameComposition.{name}') +(HERE/'AlignedFrameComposition.lean').write_text('\n'.join(out)+'\n') +print(json.dumps({'lines':len(('\n'.join(out)).splitlines()),'lean_sha256':sha256((HERE/'AlignedFrameComposition.lean').read_bytes()).hexdigest()})) diff --git a/research/aligned-composition/lean/independent-audit.json b/research/aligned-composition/lean/independent-audit.json new file mode 100644 index 0000000000..8cc7f302e6 --- /dev/null +++ b/research/aligned-composition/lean/independent-audit.json @@ -0,0 +1,21 @@ +{ + "Taylor_bounds": 54, + "Taylor_domains": 54, + "boundary": "No analytic log enclosure, real exponential remainder theorem, physical-profile derivation, or all-size multiplication theorem is formalized here. Exact arithmetic and source consistency only. No duplicate physical replay was run.", + "complete_positive_rank_counts": 27, + "frozen_selection_sha256": "43a762adf17b2338b2d7ec486fd6eb17d00d1d221e7f1e4041711cbce9964ea7", + "generator_sha256": "52435e20b06a65717910781101b372aaca7faf071b7bd8231d7ed1770b55b9aa", + "input_sha256": "c8c19d762d5f302a5b15a5103e88592b359e4c1f11add1776fd7c97725d8bdb9", + "moments": { + "accepted": "45921799999999999986718939153021994591711554531/45921800000000000000000000000000000000000000000", + "rejected": "32604478000000000005782543032459327907899102761243/32604478000000000000000000000000000000000000000000" + }, + "portable_regeneration": "PASS exact bytes from saved input in empty temporary directory", + "profile_linkage": "PASS actual Lean FromCounts sums use count t, m and width, with profile_link theorems", + "source_sha256": "282b1500f96c4ac8ac5dad5da844296ad41be109edcaca0310730304b50ca357", + "status": "PASS independent Lean supplement source and rational arithmetic audit; compilation is a 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b/research/aligned-composition/lean/receipts/compile/command.txt @@ -0,0 +1 @@ +/bin/sh -c export\ PATH=/home/cfky/research/integer-mult/src/lean-arithmetic-20261009/lean-4.21.0-linux_aarch64/bin:\$PATH\;\ /usr/bin/time\ -v\ lake\ env\ lean\ AlignedFrameComposition.lean diff --git a/research/aligned-composition/lean/receipts/compile/cwd.txt b/research/aligned-composition/lean/receipts/compile/cwd.txt new file mode 100644 index 0000000000..96c46af568 --- /dev/null +++ b/research/aligned-composition/lean/receipts/compile/cwd.txt @@ -0,0 +1 @@ +/home/cfky/research/integer-mult/src/lean-arithmetic-20261009/mathlib diff --git a/research/aligned-composition/lean/receipts/compile/exit-code b/research/aligned-composition/lean/receipts/compile/exit-code new file mode 100644 index 0000000000..573541ac97 --- /dev/null +++ b/research/aligned-composition/lean/receipts/compile/exit-code @@ -0,0 +1 @@ +0 diff --git a/research/aligned-composition/lean/receipts/compile/finished-at b/research/aligned-composition/lean/receipts/compile/finished-at new file mode 100644 index 0000000000..568b5f021e --- /dev/null +++ b/research/aligned-composition/lean/receipts/compile/finished-at @@ -0,0 +1 @@ +2026-10-08T21:16:02Z diff --git a/research/aligned-composition/lean/receipts/compile/output.log b/research/aligned-composition/lean/receipts/compile/output.log new file mode 100644 index 0000000000..96257ec618 --- /dev/null +++ b/research/aligned-composition/lean/receipts/compile/output.log @@ -0,0 +1,246 @@ +'KappaCheck.AlignedFrameComposition.network_counts' depends on axioms: [propext] +'KappaCheck.AlignedFrameComposition.rank_mass' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_1' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_2' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_3' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_4' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_5' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_6' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_7' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_8' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_9' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_10' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_11' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_12' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_13' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_14' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_15' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_16' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_17' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_18' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_19' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_20' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_21' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_22' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_23' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_25' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_481' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_525' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.count_529' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.complete_child_support' depends on axioms: [propext, Quot.sound] +'KappaCheck.AlignedFrameComposition.strict_child_contraction' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_a_positive' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_a_below_b' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_b_below_one_over32' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_beta_positive' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_beta_below_one' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_phase_leaf_above_bit' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_q_positive' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_q_below_internal' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_q_below_leaf' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_c_positive' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_c_below_one' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_q_below_reservations' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_lambda_above_tau' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_lambda_above_sigma' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_lambda_above_internal' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_lambda_prime_above_lambda' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_compact_leaf' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_compact_reservations' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_lambda_prime_below_one' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_epsilon_positive' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_epsilon_below_one' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_guard_width' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_K_geometry' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_K_dominates_log' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_record_suffix' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_phase_local' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_phase_boundary' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_gamma_sublinear' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_cell_above_band' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_prime_interval_packing' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_alpha_positive' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_alpha_below_one' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_alpha_below_one_fourth' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_delta_positive' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_delta_below_one_eighth' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_short_record_fallback' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_small_field_exposure' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_artificial_boundary' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_literal_scalar_guard' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_row_product_gap' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_g1_above_kappa' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_g2_above_kappa' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_g3_above_kappa' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_g4_above_kappa' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_g5_above_kappa' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_g6_above_kappa' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.slack_g7_above_kappa' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.margins_strict' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.balanced_identities' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.controlling_margin' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.gain_over_original' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.finite_bridge' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_1' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_1' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_2' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_2' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_3' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_3' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_4' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_4' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_5' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_5' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_6' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_6' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_7' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_7' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_8' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_8' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_9' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_9' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_10' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_10' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_11' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_11' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_12' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_12' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_13' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_13' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_14' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_14' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_15' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_15' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_16' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_16' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_17' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_17' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_18' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_18' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_19' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_19' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_20' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_20' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_21' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_21' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_22' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_22' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_23' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_23' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_25' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_25' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_481' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_481' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_525' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_525' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_interval_529' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_taylor_529' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_profile_link' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_moment' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.accepted_paid_moment' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_1' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_1' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_2' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_2' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_3' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_3' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_4' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_4' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_5' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_5' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_6' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_6' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_7' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_7' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_8' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_8' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_9' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_9' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_10' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_10' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_11' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_11' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_12' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_12' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_13' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_13' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_14' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_14' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_15' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_15' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_16' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_16' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_17' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_17' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_18' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_18' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_19' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_19' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_20' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_20' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_21' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_21' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_22' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_22' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_23' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_23' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_25' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_25' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_481' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_481' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_525' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_525' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_interval_529' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_taylor_529' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_profile_link' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_moment' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.AlignedFrameComposition.rejected_paid_moment' depends on axioms: [propext, Classical.choice, Quot.sound] + Command being timed: "lake env lean AlignedFrameComposition.lean" + User time (seconds): 86.36 + System time (seconds): 4.12 + Percent of CPU this job got: 484% + Elapsed (wall clock) time (h:mm:ss or m:ss): 0:18.69 + Average shared text size (kbytes): 0 + Average unshared data size (kbytes): 0 + Average stack size (kbytes): 0 + Average total size (kbytes): 0 + Maximum resident set size (kbytes): 1754196 + Average resident set size (kbytes): 0 + Major (requiring I/O) page faults: 0 + Minor (reclaiming a frame) page faults: 129151 + Voluntary context switches: 148375 + Involuntary context switches: 5479 + Swaps: 0 + File system inputs: 0 + File system outputs: 48 + Socket messages sent: 0 + Socket messages received: 0 + Signals delivered: 0 + Page size (bytes): 4096 + Exit status: 0 diff --git a/research/aligned-composition/lean/receipts/compile/started-at b/research/aligned-composition/lean/receipts/compile/started-at new file mode 100644 index 0000000000..f34c247440 --- /dev/null +++ b/research/aligned-composition/lean/receipts/compile/started-at @@ -0,0 +1 @@ +2026-10-08T21:15:43Z diff --git a/research/aligned-composition/lean/verification.json b/research/aligned-composition/lean/verification.json new file mode 100644 index 0000000000..a7226652ad --- /dev/null +++ b/research/aligned-composition/lean/verification.json @@ -0,0 +1,11 @@ +{ + "status": "PASS", + "lean": "4.21.0", + "mathlib_commit": "308445d7985027f538e281e18df29ca16ede2ba3", + "source_sha256": "282b1500f96c4ac8ac5dad5da844296ad41be109edcaca0310730304b50ca357", + "theorems": 197, + "command": "lake env lean AlignedFrameComposition.lean", + "exit_code": 0, + "kappa": "52789616935221/1000000000000000000", + "scope": "Rational arithmetic; physical arrays, real log/exp enclosure validity and all-size transfer remain external" +} diff --git a/research/aligned-composition/parameters.json b/research/aligned-composition/parameters.json new file mode 100644 index 0000000000..7b0063509e --- /dev/null +++ b/research/aligned-composition/parameters.json @@ -0,0 +1,11 @@ +{ + "W": 130417912, + "bit_saving": "10558480765231/200000000000000000", + "grid_denominator": 1000000000000000000, + "kappa": "52789616935221/1000000000000000000", + "roles": { + "23": 26387, + "25": 34772 + }, + "total_rank": 74988452500 +} diff --git a/research/aligned-composition/parent-result-23.json b/research/aligned-composition/parent-result-23.json new file mode 100644 index 0000000000..37b2728c8e --- /dev/null +++ b/research/aligned-composition/parent-result-23.json @@ -0,0 +1,51 @@ +{ + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 26387, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 110374, + "0": 399074, + "2": 63844, + "3": 7841, + "4": 18211, + "5": 4727, + "6": 4396, + "7": 1046, + "8": 1183, + "9": 489, + 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b/research/aligned-composition/reported-comparisons.json new file mode 100644 index 0000000000..5a410b726e --- /dev/null +++ b/research/aligned-composition/reported-comparisons.json @@ -0,0 +1,18 @@ +{ + "comparisons": { + "36": { + "kappa": "384569/10000000000" + }, + "74": { + "author": "tomdif", + "commit": "428b5c167686b42a83f1abf7003c6d17aec561ea", + "kappa": "5278214423139/100000000000000000" + }, + "88": { + "author": "chafreaky", + "commit": "3ffd9b1dc7ef2978fa1831fe3850cd4f534aea70", + "kappa": "52514124198891/1000000000000000000" + } + }, + "scope": "Reported baselines accepted without foreign producer replay; pinned historical comparisons only" +} diff --git a/research/aligned-composition/scalar-23.json b/research/aligned-composition/scalar-23.json new file mode 100644 index 0000000000..dc90387bea --- /dev/null +++ b/research/aligned-composition/scalar-23.json @@ -0,0 +1,18 @@ +{ + "h": 23, + "inputs": 1771, + "partial_outputs": 5336, + "additions": 84930, + "roles": 90266, 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Supplied open-PR baseline numerical claims remain accepted working inputs. Inherited all-size residual compiler, tape, prime selection, recovery and analytic transfer hypotheses remain. No global optimum or practical running-time claim. 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"parent_word_sha256": "8609a3934aa687428d6575892ccefa6908b5dab3018b209455b4c96c0ddd392d", + "profiles_sha256": "a0e3e711e0c1a6fad082554799f9799f5499f1775a0c0cbb49f1ec61ff5a15d8", + "word_sha256": "e3de786d598e37003e8fd587efc114d0cbd3dbe94ed6dd971bbbc464c0e99c9d" + } +} diff --git a/research/balanced-split/PROOF.md b/research/balanced-split/PROOF.md new file mode 100644 index 0000000000..c34f8542cc --- /dev/null +++ b/research/balanced-split/PROOF.md @@ -0,0 +1,251 @@ +# Finite certificate and inherited scope + +## 1. Exact change and provenance + +This construction preserves PR71's anchored `[1,1,2]` split recursion, +PR65 region schedules, PR67 profile-cost reclamation and PR68 pending live +controls with next-use scoring. It composes three finite choices: PR69's +balanced coarse parenthesization, future-compatible unit completion, and a +bounded adaptation of PR70 carry exchanges. The contributor originals, +licenses and notices are retained in hash-checked archives. The published +PR71 source, words and complete arithmetic certificate are preserved at +`1bef94fd40a746452548c84a4a8f8834670a3113` for the full-profile comparison. +The new namespace is `balanced-split`. Two portable engines differ from the +independently audited discovery engines only in the repository-relative ROOT +constant; their relocation patches and SHA256s are recorded. + +The h23 coarse cell uses columns when `i+j1. The exponential tail bound is `(v^9/9!)/(1-v/10)` for upper argument v<1. An independent atanh log expansion at base 3/2 with 60 terms and a degree-12 exponential bound confirms both signs. Complete pinned PR84 and reported PR74 child lists separately have lower moment greater than one at s. These are complete-profile historical comparisons; the foreign PR74 claim is an accepted working input, not an independent audit of its entire construction. + +The reconstructed bridge has bit wire bits 27, row coefficient 843, row degree 2000, gap `2000-(51/25)*843=7007/25`, and suffix slope 8000. Tests reject stale values. The complex saving stays 717/10^7 and the backoff stays 10^-12. All 47 strict assembly constraints and seven margins hold for κ=52514124198891/1000000000000000000. The next 10^-18 κ point violates a controlling strict margin; coarser-grid reassembly and original-prefix/old-guard/old-exposure negative controls also execute. Eventual arithmetic cutoffs are recomputed by the unchanged inherited routine. + +## 7. Provenance and proof boundary + +This proves the stated finite scalar, arbitrary-dirty physical, actual-frame/profile, complete-child and exact-inequality claims. The ordered affine residual compiler, all-size construction and recursion, finite scalar alphabet/overhead, routing, prime selection, exact recovery, fixed-tape simulation and analytic transfer remain inherited assumptions. Arithmetic cutoffs cover the recorded inequalities and do not establish every operational threshold. Existing Lean packages remain inherited checks, not a formalization of the complete multiplication theorem. + +The portable engine and node helper are byte-identical to the independently audited 90-pin final R10 discovery runtime. Relative to the archived R5 engine, the only AST changes are the coordinate-aware oracle writer and the audited three-donor helper/call. The graph provider preserves the frozen split/coarse construction and passes the selected order explicitly. The complete 590-file PR84 construction archive preserves all original source/finite inputs and construction certificates. Original PR74/78/82 contributor inputs and all older archives remain immutable. The local source closure binds selected configurations, wrappers, engine, tests, proof, physical words, transition profiles and additive integration files. Derived arithmetic and validation receipts are excluded to avoid circular pins. + +Source credits: @eumemic [#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57) and [#69](https://github.com/CrocSwap/integer-mult-bounds/pull/69), reversible compilation and balanced coarse sums; @rohangar1 [#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59), split recursion; @ikeboy [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62), interval strips and core-aware assembly; @DominikScholz [#63](https://github.com/CrocSwap/integer-mult-bounds/pull/63) and [#68](https://github.com/CrocSwap/integer-mult-bounds/pull/68), ranked composition and pending live controls; @rohanarun [#65](https://github.com/CrocSwap/integer-mult-bounds/pull/65), [#67](https://github.com/CrocSwap/integer-mult-bounds/pull/67) [#78](https://github.com/CrocSwap/integer-mult-bounds/pull/78) and [#82](https://github.com/CrocSwap/integer-mult-bounds/pull/82), exact refined assembly, profile-cost reclamation, coordinate-flag search and coordinate-aware pricing; @alejandrozu [#70](https://github.com/CrocSwap/integer-mult-bounds/pull/70), carry exchanges; Thomas DiFiore (@tomdif) [#74](https://github.com/CrocSwap/integer-mult-bounds/pull/74), original rank-first node order and exact coordinate relabeling; @chafreaky [#60](https://github.com/CrocSwap/integer-mult-bounds/pull/60), [#71](https://github.com/CrocSwap/integer-mult-bounds/pull/71), [#79](https://github.com/CrocSwap/integer-mult-bounds/pull/79) [#84](https://github.com/CrocSwap/integer-mult-bounds/pull/84) and this composition, rank-preserving tie orders, three-donor cycles, ranked reclamation, anchored splits, future completion, integer scoring, exact indexes, two-cycles, output routing, search and certification. + +Chafik Boukhalfa prepared this package with OpenAI Codex assistance. Original contributor, OpenAI/manuscript, Apache-2.0, and AI-assistance notices remain attached. In particular Avi Eisenberg's Claude assistance and the original contributors' OpenAI disclosures are retained verbatim in the archives. PR78 inspires the coordinate search; its published selected permutations are not claimed as the selected permutations here. diff --git a/research/final-frame/README.md b/research/final-frame/README.md new file mode 100644 index 0000000000..b0d77bdd00 --- /dev/null +++ b/research/final-frame/README.md @@ -0,0 +1,31 @@ +# Final frame composition + +The frozen finite conditional witness has **κ = 52514124198891/1000000000000000000 = 5.2514124198891e-5**, with bit saving **52516882077117/1000000000000000000**. It is **0.4645669003% above the pinned PR84 construction** `88ca39571907343a49e97f328971ec7bcd26fbfd`. This is a historical pinned comparison, not a claim about the current global frontier. Complete PR84 and reported PR74 paid child profiles are strictly excluded at the accepted bit saving. + +| Quantity | This witness | +|---|---:| +| h23 / h25 auxiliary roles | 26,581 / 35,133 | +| Physical width W | 131,503,443 | +| Total recursive rank | 75,612,632,825 | +| Rank deficit | 1,846,900 | +| Largest child / parent dimension | 529 / 575 | +| Bit wire bits / row coefficient | 27 / 843 | + +Both axes use anchored point order, balanced half-plane coarse sums, exact retired/pending indexes, future-compatible unit completion, pending next-use prices and up to three single/two-cycle passes. The h23 split vector is `[4,4,4]`, with descending cover/core rank ties, baseline output order, identity oracle pricing and no three-cycles. The h25 split vector is `[4,4,1]`, with PR74 node order, late output order, coordinate-aware oracle pricing and up to three three-cycle passes (two accepted). Explicit coordinate maps are in the certified configs; they come from our bounded R6 search. + +```sh +make final-frame-verify +make verify +``` + +The focused gate regenerates original and relabeled words byte-for-byte, reconstructs dense scalar supports, replays every ordinary and arbitrary-dirty basis column in both orientations, and computes fresh literal frame/CRT profiles. Every copied center, endpoint, data-growth block, cleanup and complex cost remains charged. Exact assembly checks two independent rational moment enclosures, neighboring 10^-18 grid rejection, all 47 inequalities and seven margins. Actual-source audits cover both indexes, completion, single/two/three-cycle exchanges and coordinate-aware oracle serialization. Mutation controls reject invalid words, sources, configurations and bridge fields. + +The selected words, paid profiles and source are immutable. The 51,525-pair discovery portfolio has two equivalent best pairs, differing only in an inactive h23 three-cycle setting; the freeze selects zero passes. That finite portfolio result is not a global optimality theorem. Discovery paths are retained only as provenance; executable verification uses repository-relative inputs. + +The [proof](PROOF.md) separates general compatibility arguments from finite evidence. Ordered residual compilation, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery, fixed-tape simulation and analytic transfer remain inherited assumptions. Arithmetic cutoffs are not full operational thresholds. No measured practical speedup or complete formal multiplication theorem is asserted. + +The complete PR84 construction and original contributor archives are preserved byte-for-byte. `reported-comparisons.json` records external reported values and pinned heads without replaying foreign producers. The actual coordinate-aware pricing source is PR82. + +Source credits: @eumemic [#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57) and [#69](https://github.com/CrocSwap/integer-mult-bounds/pull/69), reversible compilation and balanced coarse sums; @rohangar1 [#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59), split recursion; @ikeboy [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62), interval strips and core-aware assembly; @DominikScholz [#63](https://github.com/CrocSwap/integer-mult-bounds/pull/63) and [#68](https://github.com/CrocSwap/integer-mult-bounds/pull/68), ranked composition and pending live controls; @rohanarun [#65](https://github.com/CrocSwap/integer-mult-bounds/pull/65), [#67](https://github.com/CrocSwap/integer-mult-bounds/pull/67) [#78](https://github.com/CrocSwap/integer-mult-bounds/pull/78) and [#82](https://github.com/CrocSwap/integer-mult-bounds/pull/82), exact refined assembly, profile-cost reclamation, coordinate-flag search and coordinate-aware pricing; @alejandrozu [#70](https://github.com/CrocSwap/integer-mult-bounds/pull/70), carry exchanges; Thomas DiFiore (@tomdif) [#74](https://github.com/CrocSwap/integer-mult-bounds/pull/74), original rank-first node order and exact coordinate relabeling; @chafreaky [#60](https://github.com/CrocSwap/integer-mult-bounds/pull/60), [#71](https://github.com/CrocSwap/integer-mult-bounds/pull/71), [#79](https://github.com/CrocSwap/integer-mult-bounds/pull/79) [#84](https://github.com/CrocSwap/integer-mult-bounds/pull/84) and this composition, rank-preserving tie orders, three-donor cycles, ranked reclamation, anchored splits, future completion, integer scoring, exact indexes, two-cycles, output routing, search and certification. + +Chafik Boukhalfa prepared this package with OpenAI Codex assistance. Original contributor, OpenAI/manuscript, Apache-2.0, and AI-assistance notices remain attached. In particular Avi Eisenberg's Claude assistance and the original contributors' OpenAI disclosures are retained verbatim in the archives. 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If the envelopes differ, cover-size minus core-size strictly increases. Consequently any ordering whose first key is that rank is topological between different frames; retaining original node order inside each frame preserves the remaining dependencies. Both actual keys preserve every scalar edge, envelope, source prefix, output and provenance record.", + "Node renumbering happens before compiler build and carrier eligibility are reconstructed. Each generate call creates a fresh compiler module; order mode is passed explicitly, and price coordinate map and three-cycle pass count are assigned on that module before compilation. Thus workers or successive cases cannot inherit those settings implicitly.", + "The new coordinate writer changes only serialized oracle core/cover masks, leaving block indices, ranks, all in-memory graph frames, scalar signals and candidate eligibility untouched. Identity pricing is byte-identical to the previous writer. Bijective coordinate maps preserve frame inclusion and dimension, and the oracle queries address the same permuted frames later used by physical relabeling.", + "Oracle answers enter only fixed integer carry prices and legal retired-slot candidate comparison. Each emitted candidate still satisfies the unchanged frame containment, temporal edge, linear-independence, unique-future-use and literal clearing checks. Pricing quality is not a correctness assumption; actual final word profiles must still be regenerated after selection.", + "Three-donor source is byte-identical to the independently audited helper and parent integration. After any order/pricing choice, its proof applies to the newly constructed eligible edges with arbitrary fixed integer prices. All three affected bases, use ownership and global cardinality are preserved by each strictly improving atomic cycle.", + "The exact pinned batch covers two order modes times two pricing settings times zero/three cycle passes per axis, with the default combination supplied as the exact parent canary. The wrapper adds only those settings, explicit order dispatch, dense verification and receipt fields to the previously audited R7 construction." + ], + "scope": "General composition/source guards only. No final selected physical-word or arithmetic clearance, no numerical frontier/global-optimality claim, and no foreign PR82 producer replay. Final selected literal physical operations, fresh profiles and complete exact assembly remain separate gates. 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6, + 5, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 22, + 21, + 23, + 24, + 0 + ], + "groups": "441", + "h": 25, + "node_order": "pr74", + "oracle_coordinate_pricing": true, + "output_mode": "route-late", + "profile_sha256": "1ca57426564eb285f0d092dac5433531505f08f53ea169c3f12df9a2d47e1659", + "rank_mass": 878925, + "raw_word_sha256": "81accb74c4697f5fb7569636023cd212b6995de44fe2ba862f89b80316cb3756", + "roles": 35133, + "three_cycle_passes": 3 + } + ], + "bit_saving": "52516882077117/1000000000000000000", + "equivalent_selected_profiles": 2, + "gain_over_PR84": "242835107491/1000000000000000000", + "kappa": "52514124198891/1000000000000000000", + "paid_complete_portfolio_pairs": 51525, + "portfolio_sha256": "f6ea5d218deb38dd4cb9188df65728d8cb0d5d6468c3f5a4232250872510f2d0", + "prior_PR84_clearance_sha256": "f15ca34fd8c211f11bc7d9226f1a65de29d18644f0a400f8ba4a65c46810566c", + "rank_mass": 75612632825, + "receipts_and_audit_sources_sha256": { + "composition-final-independent/arithmetic-receipt.json": "d94e8b6c51888696ac1d9757597ad6fb1497c0da16e5283d0f31ab3429cdc6d0", + "composition-final-independent/arithmetic_audit.py": "c6eab642803842d187a3c030fcbe347ee6599968504086c8742a2f329f04f255", + "composition-final-independent/final_clearance.py": "3bf62a86aaf3bceb9a3934451d5ff0aa8b1cd0d8172e2b1ed7dc43a17d4cca57", + "composition-final-independent/h23/physical-receipt.json": "aad7c6364719e908bada0b5b8d27c6b219ce2474ff80a7a5e0d0e7ab31613f22", + "composition-final-independent/h23/physical.py": "dfd0f0ca1fa4d1e116a8950263108f89377ee475fbbf3384143db08c982167ec", + "composition-final-independent/h25/physical-h25-receipt.json": "045921a6a08bde497f75e2a923e6b29d71f595f92dabb8efe30f54c865148231", + "composition-final-independent/h25/physical.py": "8f64060a968f20b356a18b78f421c90a15349d17bf8fe5910bf5e3ccb8b493d3", + "composition-final-independent/profile-receipt.json": "47d78d40aa64a8ca1da24c263a7a2369344d5ab376cb836a70b916865edadee3", + "composition-final-independent/profile_audit.py": "ed3379db42404d01bad165125670808afb5507a694973a0c0a750e11d92a3cfc", + "final-combination-independent/source-receipt.json": "086532c924990407cf730dc5b2ea8f65e94539587eea52d1026644096ed62168", + "final-combination-independent/source_audit.py": "ca872197b0810676f7dbfd41fcb3c161e0e239713bc92832c71ddfdec0a4aa62", + "three-cycle-independent/audit.py": "d197de05259ff039aa4886ac1c21d0ee6eb09281a028a132487f52beb039b2bf", + "three-cycle-independent/receipt.json": "2e026e98822c714daa247c5b2b5f9d5f1e1b43ea9a70c1ead42f7b0b75667f2b" + }, + "relative_gain_over_PR84": "242835107491/52271289091400", + "row_coefficient": 843, + "scope": "Independent proof and verification of the frozen new finite composition, ordering and pricing transformations, legal atomic three-donor exchanges, literal physical operations in both orientations on every ordinary/dirty basis input, fresh exact actual CRT profiles, complete paid arithmetic, exact analytic interface and all 51525 complete paid portfolio comparisons. Supplied open-PR baseline numerical claims remain accepted working inputs. Inherited all-size residual compiler, tape, prime selection, recovery and analytic transfer hypotheses remain. No global optimum or practical running-time claim. PR84 freeze is unchanged; this is a separate stronger result.", + "selected_exact_constraints": 47, + "selected_files_sha256": { + "spark-results/spark/final-composition-r10/results/23-444-envelope-half-baseline-cover-minus-core-minus-pricing0-cycles0/compiler-result.json": "7943956321b71ff22ef2beabd13370f66e38c447d6b374ee8dda050dff78f9fc", + "spark-results/spark/final-composition-r10/results/23-444-envelope-half-baseline-cover-minus-core-minus-pricing0-cycles0/exact-result.json": "b0a56281ebb137be54acb5e86debf05f7b28bd2a2ee753eed82c33fc727a08ac", + "spark-results/spark/final-composition-r10/results/23-444-envelope-half-baseline-cover-minus-core-minus-pricing0-cycles0/oracle-input.bin": "7817a61c9a43b96a18005ad3844531d980471743a1f1aad84dffed2cfa301315", + "spark-results/spark/final-composition-r10/results/23-444-envelope-half-baseline-cover-minus-core-minus-pricing0-cycles0/profiles.json": "45708723716dded9bb2688fc9e576de4550b31ff4762a41d533c486374ac8664", + 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"selected_strict_margins": 7, + "selection_sha256": "c05715807ad48d2c292f6e3431c338c39d4e7ae80b9758a8c3f8ace520178e23", + "source_manifest_sha256": "45c1f1e6da14472859d89b3247ad6591a596f0729eff369e21c7581d3794859e", + "source_pins": 90, + "status": "PASS final frozen R10 composition cleared for portable packaging", + "strictly_excluded_other_complete_profiles": 51523, + "verified_utc": "2026-10-08T21:00:47.956803+00:00", + "wire_bits": 27 +} diff --git a/research/final-frame/word-bindings.json b/research/final-frame/word-bindings.json new file mode 100644 index 0000000000..27df9e8540 --- /dev/null +++ b/research/final-frame/word-bindings.json @@ -0,0 +1,12 @@ +{ + "23": { + "parent_word_sha256": "a6702539987f29202e6aef9559eef854df59313195423cc62f69f32173fc7541", + "profiles_sha256": "45708723716dded9bb2688fc9e576de4550b31ff4762a41d533c486374ac8664", + "word_sha256": "3b6aac37d3e39d60381fa05250a4c0a88ed665cc2dccca7242e8c1ad5f9b3a66" + }, + "25": { + "parent_word_sha256": "cf2783c6566ff3ff7537cc30b89a37485bc6b76e932cbbd89fcf847d67cb6996", + "profiles_sha256": "1ca57426564eb285f0d092dac5433531505f08f53ea169c3f12df9a2d47e1659", + "word_sha256": "81accb74c4697f5fb7569636023cd212b6995de44fe2ba862f89b80316cb3756" + } +} diff --git a/research/indexed-cycle/PROOF.md b/research/indexed-cycle/PROOF.md new file mode 100644 index 0000000000..61621dd74e --- /dev/null +++ b/research/indexed-cycle/PROOF.md @@ -0,0 +1,63 @@ +# Finite indexed-cycle certificate and inherited scope + +## 1. Frozen construction and general weighted recursion + +At level d, start with the inherited ordered groups of size one or two. The chosen vector requests first/middle pair splits: h23 `[4,1,1]`, h25 `[1,4,1]`, where 1 requests the first group and 4 requests first then middle. Requested indices are deduplicated, valid, and must contain two points. Before admitting the kth split require `number_of_groups + admitted_splits + 1 < number_of_points`. Apply admitted splits in decreasing index order so earlier indices keep their meaning. Each split replaces one pair by its two ordered singletons; the point partition and ordering are unchanged. + +The admission guard proves that the final number of groups is strictly less than the number of points, even for multiple requested splits and overlapping first/middle indices. Splits are disabled for n≤3; n=3 has two coarse groups and n≤2 uses the direct base case. Thus every recursive call strictly contracts, for every input size allowed by the grouping interface. + +Coarse vertex weights contain the original vertex weights in that group and its internal edges. Each coarse edge contains exactly the Cartesian-product edges between its two groups. These sets partition the original weighted total. Recursive total and single/pair exclusions therefore have the required support by induction on size. Row and column coarse parenthesizations partition the same Cartesian product into disjoint sets, so changing between them preserves every identity. The half-plane rule uses fixed indices only. The generic singleton/pair assembly and interval-strip identities are inherited; tests independently check weighted exclusions at each recursive call. + +At common coordinate c, choose the smallest intact fixed global pair disjoint from c and move it to the front of the inherited alternating order, preserving all other relative positions. This is a permutation of precisely the other coordinates and preserves scalar exclusions. Dense graph verification checks the full triple-input map and all disjoint additions in both selected dimensions. + +## 2. PR74 node order, synthesis, and completion + +Group active computed nodes by exact `(core,cover)` frame and sort groups by `(rank,-core,cover,min_node)`, where rank is cover size minus core size. Keep input IDs fixed and retain original node order inside each group. Remap every dependency, active ID, output ID and provenance entry, and clear support caches. This is a bijective graph renaming; the preserved within-frame order and rank order retain scalar dependencies. The graph verifier recomputes the dense supports, and the compiler recomputes fixed linear signals before accepting the natural region order `(rank,min_node)`. Candidate carriers target strictly later regions with containing frames. No PR65 schedule wrapper is applied. + +The output rows and selected carriers form an independent prefix. Scan every standard input unit vector in future-use priority order and retain it only if independent. Every rejected unit is already in the current span and remains there; after the scan every standard unit is in the span. The final rows therefore form a full basis and keep the chosen prefix. Gaussian elimination and its reversed literal XOR synthesis implement an invertible transformation on arbitrary inputs and dirty roles. Future-use priority depends only on fixed graph incidence, symbolic signal supports and indices. It never examines runtime input data. + +Retired roles are reclaimed only by a valid literal clearing expression in an eligible signal span. Pending live controls have current frame F and assigned future frame G. They may clear a retired role in frame E only when F⊆E⊆G. A control's value does not change; its literal frame raise is charged, and the future inclusion remains valid. Candidate comparison makes no physical mutation until a chosen expression is emitted. Exact integer profile scores only order legal candidates; they do not certify the final recurrence. + +## 3. Exact retired and pending indexes + +For frames `(core,cover)`, containment F⊆E means `core(E)⊆core(F)` and `cover(F)⊆cover(E)`. The retired index intersects active-role core bitmaps for each coordinate in core(E), and removes roles whose cover includes any coordinate outside cover(E). This selects exactly the eligible roles. Rank bitmaps partition that set; descending rank and ascending set-bit order exactly reproduce the original `(-rank,slot)` enumeration. + +The pending index first enforces F⊆E using the same lower-frame index. It then removes target cores containing coordinates outside core(E) and intersects target-cover bitmaps for coordinates in cover(E). The result is precisely F⊆E⊆G. Each insertion receives a serial; removal deletes it; frame moves keep it. Sorting eligible roles by serial reproduces pending dictionary insertion order, including removal/reinsertion of reused slots. + +Insertion, reclamation and incoming-use removal update both representations. Every frame raise updates a retired role's old/new rank/frame index, or a pending control's lower frame without changing serial order. Retired and pending lifecycles remain disjoint. Actual-source exhaustive and randomized audits compare ordered queries with the direct predicates and exercise actual frame-raise functions, not copies of those functions. These indexes preserve compiler semantics; no measured speedup is claimed. + +## 4. Carry exchanges, two-cycles, and output routing + +Candidate edges remain subject to inherited temporal/frame eligibility. A single exchange removes the selected owner of an occupied future use, or drops a carrier from the receiving region for an unoccupied future use. The full output/carrier basis of the receiving region is checked after the removal. A distinct donor region only loses a row, preserving independence. Thus cardinality, linear independence and unique future-use ownership remain valid. Each accepted exchange decreases a fixed integer score; at most three deterministic passes execute. + +A two-cycle swaps carriers between distinct regions and distinct already-owned future uses. For new edge e and its complementary edge other, `carry_can(e,z)` checks the receiving region after removing z and `carry_can(other,f)` checks the other region after removing f. Because the regions differ, these tests describe exactly the final two bases. Remove both old edges before inserting either new edge; the two freed future uses are distinct, so unique ownership and global cardinality are preserved. Both regions lose and gain one carrier. The `(region,use)` lookup is checked for uniqueness. Accept only a strictly positive decrease of the sum of the two fixed integer scores; execute at most three passes. The source audit instruments every accepted exchange in 1,204 cases, including adverse linear dependence, equal-price, missing-complement and duplicate-key cases. This is a bounded legal heuristic, not an optimality proof. + +For h25, outgoing non-carrier uses are visited by descending fixed future-region deadline, with original use ID as tie-breaker. Terminal uses keep the explicit terminal deadline. This permutes a fixed list of uses; each is still assigned exactly once to a physical role. It may affect later reclamation choices, but changes no scalar target or candidate legality. h23 retains baseline output order. Both final physical words are independently regenerated and checked, including every charged allocation, XOR, raise and copy. + +## 5. Coordinate bijection and physical evidence + +For a permutation π of h coordinates, map every triple input to its sorted π-image, every frame's core/cover bitmask by π, each source's triple index, scatter input row, output common coordinate and output triple. Physical role IDs, operation order, operation frame IDs and transition event IDs are unchanged. Coordinate permutation is a bijection on triples, preserves set inclusion, and conjugates the scalar linear map. The scatter mapping changes only designated data-bank target rows and leaves auxiliary control rows fixed. Therefore arbitrary-dirty reversibility and the scalar target identities transport to the new word. + +The fixed I+J geometry is preserved by coordinate permutations, but the ordered fixed-coordinate child profile need not be invariant. Consequently profiles are freshly computed from the relabeled word's actual transitions; parent profiles are not reused. Full-basis replay checks both orientations on every ordinary and dirty column. The transition checker reconstructs every raise from literal XORs, splits side growth into paid singletons and requires exact equality with the event list. The original bounded-minor/CRT profiler verifies sufficient modulus product and agreement. Missing XORs, frames, centers, transitions, aliased terminals and understated width fail adverse tests. + +## 6. Complete recursive multiset and exact inequalities + +Let a=23, b=25, m=575, and N=binom(23,3)binom(25,3)=4,073,300. With R23=26,834 and R25=35,348, + + W = 2N + (N/binom(23,3))R23 + (N/binom(25,3))R25 = 132,466,108. + +Include all 18N rank-one data children and 2N at each data rank 21,17,481; N endpoint-copy singletons; every axis profile block replicated N/binom(h,3) times; (N/binom(h,3))Rh exterior children at each rank h and m−2h; and 2N growth children at each rank 1 and h−2. Each axis has rank sum hRh+h(h−1). Thus total rank is 76,166,165,200, deficit from mW is 1,846,900, and every child lies between 1 and 5291. The exponential tail bound is `(v^9/9!)/(1-v/10)` for upper argument v<1. An independent atanh log expansion at base 3/2 with 60 terms and a degree-12 exponential bound confirms both signs. Complete pinned PR79 and reported PR74 child lists separately have lower moment greater than one at s. These are complete-profile historical comparisons; the foreign PR74 claim is an accepted working input, not an independent audit of its entire construction. + +The reconstructed bridge has bit wire bits 27, row coefficient 843, row degree 2000, gap `2000-(51/25)*843=7007/25`, and suffix slope 8000. Tests reject stale values. The complex saving stays 717/10^7 and the backoff stays 10^-12. All 47 strict assembly constraints and seven margins hold for κ=261356445457/5000000000000000. The next 10^-18 κ point violates a controlling strict margin; coarser-grid reassembly and original-prefix/old-guard/old-exposure negative controls also execute. Eventual arithmetic cutoffs are recomputed by the unchanged inherited routine. + +## 7. Provenance and proof boundary + +This proves the stated finite scalar, arbitrary-dirty physical, actual-frame/profile, complete-child and exact-inequality claims. The ordered affine residual compiler, all-size construction and recursion, finite scalar alphabet/overhead, routing, prime selection, exact recovery, fixed-tape simulation and analytic transfer remain inherited assumptions. Arithmetic cutoffs cover the recorded inequalities and do not establish every operational threshold. Existing Lean packages remain inherited checks, not a formalization of the complete multiplication theorem. + +The engine is byte-identical to the preserved R5 compiler; the graph wrapper implements its selected split/coarse branch; PR74 order/relabel functions are byte-identical extracts. PR79's complete published construction archive and PR74/78 original input archives are immutable. The full source closure binds the selected configs, wrapper, engine, tests, proof, words, transition profiles and integration files. Derived arithmetic and validation receipts are excluded to avoid circular pins. + +Source credits: @eumemic [#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57) and [#69](https://github.com/CrocSwap/integer-mult-bounds/pull/69), reversible compilation and balanced coarse sums; @rohangar1 [#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59), split recursion; @ikeboy [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62), interval strips and core-aware assembly; @DominikScholz [#63](https://github.com/CrocSwap/integer-mult-bounds/pull/63) and [#68](https://github.com/CrocSwap/integer-mult-bounds/pull/68), ranked composition and pending live controls; @rohanarun [#65](https://github.com/CrocSwap/integer-mult-bounds/pull/65), [#67](https://github.com/CrocSwap/integer-mult-bounds/pull/67) and [#78](https://github.com/CrocSwap/integer-mult-bounds/pull/78), exact refined assembly, profile-cost reclamation and coordinate-flag search; @alejandrozu [#70](https://github.com/CrocSwap/integer-mult-bounds/pull/70), carry exchanges; Thomas DiFiore (@tomdif) [#74](https://github.com/CrocSwap/integer-mult-bounds/pull/74), exact node order, coordinate relabeling and the selected h25 permutation; @chafreaky [#60](https://github.com/CrocSwap/integer-mult-bounds/pull/60), [#71](https://github.com/CrocSwap/integer-mult-bounds/pull/71), [#79](https://github.com/CrocSwap/integer-mult-bounds/pull/79) and this composition, ranked reclamation, anchored splits, future completion, integer scoring, exact indexes, two-cycles, output routing, search and certification. + +Chafik Boukhalfa prepared this package with OpenAI Codex assistance. Original contributor, OpenAI/manuscript, Apache-2.0, and AI-assistance notices remain attached. In particular Avi Eisenberg's Claude assistance and the original contributors' OpenAI disclosures are retained verbatim in the archives. PR78 inspires the coordinate search; its published selected permutations are not claimed as the selected permutations here. diff --git a/research/indexed-cycle/README.md b/research/indexed-cycle/README.md new file mode 100644 index 0000000000..c6c59c54b6 --- /dev/null +++ b/research/indexed-cycle/README.md @@ -0,0 +1,32 @@ +# Indexed two-cycles with balanced multi-splits and coordinate flags + +The frozen finite conditional witness has **κ = 261356445457/5000000000000000 = 5.22712890914e-5**, with bit saving **408390793141/7812500000000000**. This is about **0.8494742%** above the reported PR74 value at `3f78d8967c009153f2df5c6a6577b6ab1d37e2ca`, observed 2026-10-08. This is a historical pinned comparison, not a claim about the current community frontier. The complete pinned PR74 and PR79 recursive profiles are strictly excluded at the new accepted bit saving. + +| Quantity | This witness | +|---|---:| +| h23 auxiliary roles | 26,834 | +| h25 auxiliary roles | 35,348 | +| Physical width W | 132,466,108 | +| Total recursive rank | 76,166,165,200 | +| Rank deficit | 1,846,900 | +| Largest child / parent dimension | 529 / 575 | +| Bit wire bits / row coefficient | 27 / 843 | + +Additional reported comparisons observed on 2026-10-08: PR81 at `acae4964aef41c69f3c57e72a45e76afc4d4934d` reports κ=5.1915547765237e-5; PR82 at `3410b940aa26e5876202152dfa7c4f66451ee22c` reports κ=5.203279888519e-5. This frozen witness is about 0.4583459% above the reported PR82 value. These are metadata comparisons only; their foreign producers were not replayed. Exact rational ratios and authors are recorded in `reported-comparisons.json`. + +Both axes use balanced coarse columns when `i+j1 for b in blocks) ++ slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();pending={};stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): +@@ -149,7 +151,8 @@ + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 +- return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) ++ endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 ++ return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} +@@ -161,6 +164,9 @@ + old,e=bb[p];row^=old;expr^=e + return expr + for s in anchors:ins(s) ++ for s,target in pending.items(): ++ if contains(blocks[frames[s]]['frame'],blocks[g]['frame']) and contains(blocks[g]['frame'],blocks[target]['frame']): ++ ins(s);stats['live_anchor_candidates']+=1 + best=None + # Inspect every eligible dependent candidate across all retired ranks. + # Rank the actual fixed-basis growth/cleanup profiles by an integer entropy score. +@@ -176,7 +182,9 @@ + if best is None or key 1 and kappa > previous_kappa + prior74 = json.loads((ROOT/'references/frame-compiler/pr74-aligned/research/aligned-exchange-frames/certificate.json').read_text()) + rows74 = {int(t):n for t,n in prior74['child_multiplicities'].items()} + prior74_lower = refine.exact_moment(575, prior74['W'], rows74, bit_saving)['lower'] + reported74 = Q('5278214423139/100000000000000000') + assert prior74_lower > 1 and kappa > reported74 + bridge = finite_bridge(p['W']) + validate_bridge(bridge, p['W']) + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/aligned-composition/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr88_commit='3ffd9b1dc7ef2978fa1831fe3850cd4f534aea70', + pr74_commit='428b5c167686b42a83f1abf7003c6d17aec561ea', reported_pr74_kappa=reported74, + ratio_reported_pr74=kappa/reported74, pr74_complete_profile_exclusion_lower=prior74_lower, + pr88_kappa=previous_kappa, ratio_pr88=kappa/previous_kappa, + absolute_gain_pr88=kappa-previous_kappa, + pr88_complete_profile_exclusion_lower=prior71_lower, + full_pr88_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected aligned-composition partition and point permutation, rank-preserving selected node order, natural execution, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring, PR69 balanced coarse sums, future unit completion and bounded PR70-derived single exchanges, two-cycles and selected three-donor cycles, PR82 coordinate-aware heuristic pricing, exact frame indices, late-output routing and PR74/78-inspired coordinate relabeling; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'aligned-composition-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/scripts/experiments/aligned_composition_engine.py b/scripts/experiments/aligned_composition_engine.py new file mode 100644 index 0000000000..5c82d20ab0 --- /dev/null +++ b/scripts/experiments/aligned_composition_engine.py @@ -0,0 +1,462 @@ +# Coordinate-conjugated oracle pricing adapted from Rohan Arun PR82, with OpenAI Codex assistance. +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<0 and carry_can(x,f) and carry_can(other,y): + options.append((-gain,z,x,y,other)) + if not options:continue + _,z,x,y,other=min(options) + old=(f,z,y);new=(e,x,other) + assert len(set(old))==len(set(new))==3 and not set(old)&set(new) + assert {edges[t][1] for t in old}=={edges[t][1] for t in new} + assert len({edges[t][0] for t in old})==len({edges[t][0] for t in new})==3 + for t in old: + tg,tu,ti=edges[t];chosen.remove(t);blocks[tg]['selected'].remove(t);del right[tu] + for t in new: + tg,tu,ti=edges[t];assert tu not in right;chosen.add(t);blocks[tg]['selected'].add(t);right[tu]=t + changes+=1 + return changes + + +def compile_(h,matching=True,reclaim=False,dirty=True): + t0=time.time();c,blocks,uses,value_uses,owner,signal,order,contains=build(h);v=len(c.inputs);position={g:i for i,g in enumerate(order)} + print('built',h,len(blocks),'regions',flush=True,file=sys.stderr) + mode=globals().get('OUTPUT_MODE','baseline') + edges,chosen,right,stats=match(blocks,uses,matching) + print('matched',len(chosen),'seconds',time.time()-t0,flush=True,file=sys.stderr) + slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();retired_index=RetiredIndex(h);pending={};pending_index=PendingIndex(h);stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + oracle_map=globals().get('ORACLE_COORDINATES',list(range(h))) + assert sorted(oracle_map)==list(range(h)), 'Invalid oracle coordinate permutation' + for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + for phase in range(globals().get('THREE_CYCLE_PASSES',0)): + changes=improve_three_cycles(blocks,edges,chosen,right,prices,priority,carry_can) + stats['carry_three_cycles']+=changes + print('carry three-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + first,mid,last = 0,(len(groups)-1)//2,len(groups)-1 + requested = (list(range(min(int(choice[5:]),len(groups)))) if isinstance(choice,str) and choice.startswith('first') and choice[5:].isdigit() else {1:[first],2:[mid],3:[last],4:[first,mid],5:[first,last],6:[mid,last],7:[first,mid,last],8:[first,first+1],9:[last-1,last]}[choice]) + chosen=[] + for k in requested: + if k not in chosen and 0<=k>common&1 and not(mask&forbidden)) + assert support[x]==expected + return {'status':'PASS all global supports, exact envelopes, disjoint additions and target outputs','nodes':len(c.active),'outputs':len(c.outputs),'sha256':digest.hexdigest()} + +# Coordinate action preserves the literal physical word under a global input relabel. +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word diff --git a/scripts/experiments/audit_aligned_composition_completion.py b/scripts/experiments/audit_aligned_composition_completion.py new file mode 100644 index 0000000000..6a49cb4eed --- /dev/null +++ b/scripts/experiments/audit_aligned_composition_completion.py @@ -0,0 +1,53 @@ +"""Focused actual-source audit. Chafik Boukhalfa with OpenAI Codex assistance; Apache-2.0.""" +from pathlib import Path +from hashlib import sha256 +from datetime import datetime,timezone +from random import Random +from collections import Counter +from copy import deepcopy +import ast,gzip,json,io,types,sys +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1] +SOURCE=HERE/'aligned_composition_engine.py';NEW=SOURCE +source=SOURCE.read_text();tree=ast.parse(source) +def check(ok,why): + if not ok:raise ValueError(why) +s=source +tree=ast.parse(s) +helpers=[n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name in ('basis','independent')] +namespace={};exec(compile(ast.Module(body=helpers,type_ignores=[]),str(SOURCE),'exec'),namespace) +basis=namespace['basis'];independent=namespace['independent'] +future=next(n for n in ast.walk(tree) if isinstance(n,ast.FunctionDef) and n.name=='future_priority') +contains=lambda a,b:not(b[0]&~a[0]) and not(a[1]&~b[1]) +# Actual-use fixtures distinguish future compatible uses from backward or nonnested uses. +ns=dict(position={0:0,1:1,2:2,3:3},step=1,b={'frame':(1,3),'inputs':[10,11,12,13]},blocks=[{'frame':(1,3)},{'frame':(1,3)},{'frame':(1,7)},{'frame':(1,5)}],uses=[(10,2,None),(10,2,('terminal',)),(11,2,None),(11,0,None),(12,3,None),(13,3,None)],value_uses={10:[0,1],11:[2,3],12:[4],13:[5]},contains=contains,slots=[7,1,3,3],ins=[0,1,2,3]) +exec(compile(ast.Module(body=[future],type_ignores=[]),str(SOURCE),'exec'),ns) +check([ns['future_priority'](i) for i in range(4)]==[(-2,3,0),(-1,1,1),(0,2,2),(0,2,3)],'Priority does not use compatible actual future uses, symbolic support, index') +check(sorted(range(4),key=ns['future_priority'])==[0,1,2,3],'Priority is not deterministic') +# General span argument is below; these adversarial numerical fixtures check the actual helpers and literal synthesis. +rng=Random(20261008);cases=0;operations=0 +for n in range(1,10): + for trial in range(250): + rows=[] + for _ in range(rng.randrange(n+1)*3): + candidate=rng.randrange(1,1<>i&1) + if j!=i: + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];ops.append((a,z)) + for j in range(n): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];ops.append((j,i)) + check(rr==[1<0 and current==previous-gain,'Fixed integer price does not strictly improve') + previous=current;observed.append([e,other,f,z]) + invariant() + env=dict(blocks=blocks,edges=edges,chosen=chosen,right=right,prices=prices,priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])),basis=basis,independent=independent,stats=Counter(),sys=types.SimpleNamespace(stderr=io.StringIO()),audit_cycle=audit_cycle) + exec(code,env);invariant();check(env['stats']['carry_two_cycles']==len(observed),'Cycle count differs') + if expected is not None:check(len(observed)==expected,'Targeted cycle outcome differs') + cycles+=len(observed);cases+=1 + return observed + +# Each group is full (one outbasis row + one carrier). Neither cross-group +# single addition is independent, but simultaneous replacement is legal. +blocks=[{'outbasis':[3]},{'outbasis':[3]}] +edges=[(1,0,0),(0,1,0),(0,0,1),(1,1,1)] +run(blocks,edges,{0,1},[10,10,9,9],1) +run(blocks,edges,{0,1},[10,10,10,10],0) +# With the receiving group's unit vector already in its output span, reject. +run([{'outbasis':[2]},{'outbasis':[3]}],edges,{0,1},[10,10,9,9],0) +# Missing the complementary future-use edge also rejects. +run(blocks,edges[:3],{0,1},[10,10,9],0) +# Duplicate group/use lookup keys are explicitly rejected before iteration. +try:run(blocks,edges+[(0,0,0)],{0,1},[10,10,9,9,1]) +except AssertionError:duplicate_rejected=True +else:raise ValueError('Ambiguous group/use candidate key accepted') +rng=Random(231025) +for trial in range(1200): + ng=rng.randrange(2,6);nuses=rng.randrange(2,14);blocks=[];edges=[] + for g in range(ng): + width=rng.randrange(2,6);rows=[] + for _ in range(rng.randrange(width)*2): + v=rng.randrange(1,1<150 or choice<.34): + s=rng.choice(list(records));f,g=records.pop(s);idx.remove(s,f,g) + elif records and choice<.66: + s=rng.choice(list(records));f,g=records[s];new=between(f,g);check(contains(f,new) and contains(new,g),'Invalid random promotion') + before_order=dict(idx.order);idx.move(s,f,new);records[s]=(new,g);check(idx.order==before_order,'Frame move changes insertion order') + else: + s=rng.randrange(1200) + if s in records:continue + f=envelope();g=extend(f);idx.insert(s,f,g);records[s]=(f,g) + mutations+=1 + if iteration%4==0: + for target in (envelope(),(1,mask)): + check(idx.eligible(target)==query(records,target),'Random ordered pending query differs');queries+=1 + if iteration%100==0: + check(idx.lower.all==sum(1<>k&1),'Target core bitmap stale') + check(idx.cover[k]==sum(1<>k&1),'Target cover bitmap stale') +idx=Pending(4);idx.insert(1,(1,3),(1,5)) +check(idx.lower.eligible_mask((1,7))==2 and idx.eligible((1,7))==[],'Fixture does not reject missing future containment') +# Audit the actual integrated raise_ function on passive live controls. +compile_node=next(n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name=='compile_');raise_node=next(n for n in compile_node.body if isinstance(n,ast.FunctionDef) and n.name=='raise_') +blocks=[dict(frame=(3,3),rank=1),dict(frame=(1,7),rank=2),dict(frame=(1,15),rank=3)] +idx=Pending(4);idx.insert(0,blocks[0]['frame'],blocks[2]['frame']);idx.insert(1,blocks[0]['frame'],blocks[2]['frame']) +env=dict(frames=[0,0],blocks=blocks,contains=contains,retired=set(),retired_index=Retired(4),pending={0:2,1:2},pending_index=idx,hist=Counter(),events=[]) +exec(compile(ast.Module(body=[raise_node],type_ignores=[]),str(NEW),'exec'),env);env['raise_'](0,1) +check(idx.eligible(blocks[0]['frame'])==[1] and idx.eligible(blocks[1]['frame'])==[0,1],'Actual raise changes pending selection incorrectly') +check(idx.order=={0:0,1:1},'Actual raise changes pending order') +receipt=dict(status='PASS actual ordered two-envelope pending index and frame lifecycle',source_sha256=sha256(SOURCE.read_bytes()).hexdigest(),mutations=mutations,ordered_queries=queries,actual_raise_fixture=True,future_containment_negative_fixture=True) +(ROOT/'certificates/aligned-composition-pending-index-validation.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt)) diff --git a/scripts/experiments/audit_aligned_composition_pricing.py b/scripts/experiments/audit_aligned_composition_pricing.py new file mode 100644 index 0000000000..828b9e90bf --- /dev/null +++ b/scripts/experiments/audit_aligned_composition_pricing.py @@ -0,0 +1,43 @@ +"""Audit the actual coordinate-pricing writer and whole-engine delta. Apache-2.0.""" +from pathlib import Path +from hashlib import sha256 +from copy import deepcopy +from itertools import combinations +from random import Random +import ast,io,json,struct,sys +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +ROOT=Path(__file__).resolve().parents[2] +def check(ok,why): + if not ok:raise ValueError(why) +# At source level, restore only the oracle writer and remove the audited helper/call. +engine=ast.parse((ROOT/'scripts/experiments/aligned_composition_engine.py').read_text());base=ast.parse((ROOT/'references/frame-compiler/indexed-r5/scripts/experiments/compiler.py').read_text());new_compile=next(n for n in engine.body if isinstance(n,ast.FunctionDef) and n.name=='compile_');base_compile=next(n for n in base.body if isinstance(n,ast.FunctionDef) and n.name=='compile_') +writer=next(n for n in new_compile.body if isinstance(n,ast.With) and 'oracle_input.open' in ast.unparse(n.items[0].context_expr));base_writer=next(n for n in base_compile.body if isinstance(n,ast.With) and 'oracle_input.open' in ast.unparse(n.items[0].context_expr)) +trim=deepcopy(engine);trim.body=[n for n in trim.body if not(isinstance(n,ast.FunctionDef) and n.name=='improve_three_cycles')];fn=next(n for n in trim.body if isinstance(n,ast.FunctionDef) and n.name=='compile_');fn.body=[deepcopy(base_writer) if isinstance(n,ast.With) and 'oracle_input.open' in ast.unparse(n.items[0].context_expr) else n for n in fn.body];fn.body=[n for n in fn.body if not(isinstance(n,ast.For) and 'THREE_CYCLE_PASSES' in ast.unparse(n.iter))];check(ast.dump(trim,include_attributes=False)==ast.dump(base,include_attributes=False),'Whole engine changes exceed pricing writer plus cleared three-cycle helper/call') +# Exercise the ACTUAL binary oracle writer in memory. The block objects must stay +# untouched; only serialized core/cover masks are conjugated, while IDs/ranks stay. +class Capture: + def __init__(self):self.stream=None;self.bytes=None + def open(self,mode):check(mode=='wb','Unexpected oracle file mode');self.stream=io.BytesIO();return self + def __enter__(self):return self.stream + def __exit__(self,*args):self.bytes=self.stream.getvalue();return False +writer_code=compile(ast.Module(body=[deepcopy(writer)],type_ignores=[]),'actual_coordinate_oracle_writer','exec');base_code=compile(ast.Module(body=[deepcopy(base_writer)],type_ignores=[]),'original_oracle_writer','exec') +rng=Random(202610092046);writer_cases=0 +for h in (3,5,23,25): + for trial in range(100): + blocks=[] + for _ in range(rng.randrange(1,30)): + cover=rng.randrange(1,1<150 or rng.random()<0.48): + s=rng.choice(list(records));f,r=records.pop(s);idx.remove(s,f,r) + else: + s=rng.randrange(1200) + if s in records:continue + f=frame();r=rng.randrange(h+1);idx.insert(s,f,r);records[s]=(f,r) + mutations+=1 + if iteration%4==0: + for target in (frame(),(1,full)): + check(list(idx.eligible(target))==order(records,target),'Random exact frame/order query differs');queries+=1 + if iteration%100==0: + check(idx.all==sum(1<>k&1),'Core bitmap stale') + check(idx.cover[k]==sum(1<>k&1),'Cover bitmap stale') +# The actual integrated raise function keeps already-retired controls indexed at their new frame. +compile_node=next(n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name=='compile_') +raise_node=next(n for n in compile_node.body if isinstance(n,ast.FunctionDef) and n.name=='raise_') +blocks=[dict(frame=(3,3),rank=1),dict(frame=(1,7),rank=2),dict(frame=(1,15),rank=3)] +idx=Index(4);idx.insert(0,blocks[0]['frame'],1) +env=dict(frames=[0,0],blocks=blocks,contains=contains,retired={0},retired_index=idx,pending={},pending_index=space['PendingIndex'](4),hist=Counter(),events=[]) +exec(compile(ast.Module(body=[raise_node],type_ignores=[]),str(NEW),'exec'),env) +env['raise_'](0,1) +check(list(idx.eligible(blocks[0]['frame']))==[] and list(idx.eligible(blocks[1]['frame']))==[0],'Actual retired control frame promotion not reflected') +env['raise_'](1,1) +check(idx.all==1 and env['frames']==[1,1],'Nonretired raise inserted an indexed role') +env['raise_'](0,2);idx.remove(0,blocks[2]['frame'],3) +check(idx.all==0 and not any(idx.ranks) and not any(idx.core) and not any(idx.cover),'Actual promoted role removal leaves stale bits') +receipt=dict(status='PASS actual ordered retired index and frame lifecycle',source_sha256=sha256(SOURCE.read_bytes()).hexdigest(),mutations=mutations,ordered_queries=queries,actual_raise_fixture=True) +(ROOT/'certificates/aligned-composition-retired-index-validation.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt)) diff --git a/scripts/experiments/audit_aligned_composition_three_cycles.py b/scripts/experiments/audit_aligned_composition_three_cycles.py new file mode 100644 index 0000000000..4b884bc664 --- /dev/null +++ b/scripts/experiments/audit_aligned_composition_three_cycles.py @@ -0,0 +1,54 @@ +"""Actual-source exchange tests: cardinality, matroid feasibility, integer descent.""" +import ast,copy,random,json +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2] +source=ast.parse((ROOT/'scripts/experiments/aligned_composition_engine.py').read_text());fn=next(n for n in source.body if isinstance(n,ast.FunctionDef) and n.name=='improve_three_cycles');ns={};exec(compile(ast.Module(body=[fn],type_ignores=[]),'actual-source-three-cycle','exec'),ns);improve=ns[fn.name] +def rank(rows): + pivots={} + for row in rows: + while row: + bit=row.bit_length()-1 + if bit not in pivots:pivots[bit]=row;break + row^=pivots[bit] + return len(pivots) +def exercise(blocks,edges,chosen,prices,passes=3): + chosen=set(chosen);blocks=copy.deepcopy(blocks);right={edges[e][1]:e for e in chosen};assert len(right)==len(chosen) + count=len(chosen);initial=sum(prices[e] for e in chosen);priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e]));changes=0 + def can(e,drop): + g,u,i=edges[e];rows=blocks[g]['outbasis']+[1<=3 or result[0]==0 +assert accepted>0 +print(json.dumps({'status':'PASS','actual_source':str(ROOT/'scripts/experiments/aligned_composition_engine.py'),'fixtures':1604,'accepted_three_cycles':accepted,'checks':['strict-cycle-only fixture','equal and worsening cost rejected','dependent replacement rejected','cardinality','one use per choice','local vector independence','exact integer descent','determinism','distinct block requirement']})) diff --git a/scripts/experiments/audit_balanced_split_completion.py b/scripts/experiments/audit_balanced_split_completion.py new file mode 100644 index 0000000000..93a4875262 --- /dev/null +++ b/scripts/experiments/audit_balanced_split_completion.py @@ -0,0 +1,59 @@ +"""Focused strategy audit by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0.""" +from pathlib import Path +from hashlib import sha256 +from datetime import datetime,timezone +from random import Random +import ast,json +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1] +import sys +if sys.flags.optimize: raise ValueError('Assertions must remain enabled') +SOURCE=HERE/'balanced_split_engine.py';OLD=HERE/'split_pair_engine.py' +def check(ok,why): + if not ok:raise ValueError(why) +s=SOURCE.read_text();old=OLD.read_text() +changed_start='t0=time.time();c,blocks,uses,value_uses,owner,signal,order,contains=build(h);v=len(c.inputs);position={g:i for i,g in enumerate(order)}' +old_start=changed_start.split(';position=')[0] +completion=''' def future_priority(i): + compatible=sum(position[uses[u][1]]>step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority):''' +check(s.count(completion)==1 and s.count(changed_start)==1,'Changed source not uniquely recognized') +check(s.replace(changed_start,old_start).replace(completion,' for i in range(len(ins)):')==old,'Compiler changed beyond the claimed unit-completion priority') +tree=ast.parse(s) +helpers=[n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name in ('basis','independent')] +namespace={};exec(compile(ast.Module(body=helpers,type_ignores=[]),str(SOURCE),'exec'),namespace) +basis=namespace['basis'];independent=namespace['independent'] +future=next(n for n in ast.walk(tree) if isinstance(n,ast.FunctionDef) and n.name=='future_priority') +contains=lambda a,b:not(b[0]&~a[0]) and not(a[1]&~b[1]) +# Actual-use fixtures distinguish future compatible uses from backward or nonnested uses. +ns=dict(position={0:0,1:1,2:2,3:3},step=1,b={'frame':(1,3),'inputs':[10,11,12,13]},blocks=[{'frame':(1,3)},{'frame':(1,3)},{'frame':(1,7)},{'frame':(1,5)}],uses=[(10,2,None),(10,2,('terminal',)),(11,2,None),(11,0,None),(12,3,None),(13,3,None)],value_uses={10:[0,1],11:[2,3],12:[4],13:[5]},contains=contains,slots=[7,1,3,3],ins=[0,1,2,3]) +exec(compile(ast.Module(body=[future],type_ignores=[]),str(SOURCE),'exec'),ns) +check([ns['future_priority'](i) for i in range(4)]==[(-2,3,0),(-1,1,1),(0,2,2),(0,2,3)],'Priority does not use compatible actual future uses, symbolic support, index') +check(sorted(range(4),key=ns['future_priority'])==[0,1,2,3],'Priority is not deterministic') +# General span argument is below; these adversarial numerical fixtures check the actual helpers and literal synthesis. +rng=Random(20261008);cases=0;operations=0 +for n in range(1,10): + for trial in range(250): + rows=[] + for _ in range(rng.randrange(n+1)*3): + candidate=rng.randrange(1,1<>i&1) + if j!=i: + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];ops.append((a,z)) + for j in range(n): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];ops.append((j,i)) + check(rr==[1<>i&1) + if j!=i: + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];ops.append((a,z)) + for j in range(n): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];ops.append((j,i)) + check(rr==[1<0 and current==previous-gain,'Fixed integer price does not strictly improve') + previous=current;observed.append([e,other,f,z]) + invariant() + env=dict(blocks=blocks,edges=edges,chosen=chosen,right=right,prices=prices,priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])),basis=basis,independent=independent,stats=Counter(),sys=types.SimpleNamespace(stderr=io.StringIO()),audit_cycle=audit_cycle) + exec(code,env);invariant();check(env['stats']['carry_two_cycles']==len(observed),'Cycle count differs') + if expected is not None:check(len(observed)==expected,'Targeted cycle outcome differs') + cycles+=len(observed);cases+=1 + return observed + +# Each group is full (one outbasis row + one carrier). Neither cross-group +# single addition is independent, but simultaneous replacement is legal. +blocks=[{'outbasis':[3]},{'outbasis':[3]}] +edges=[(1,0,0),(0,1,0),(0,0,1),(1,1,1)] +run(blocks,edges,{0,1},[10,10,9,9],1) +run(blocks,edges,{0,1},[10,10,10,10],0) +# With the receiving group's unit vector already in its output span, reject. +run([{'outbasis':[2]},{'outbasis':[3]}],edges,{0,1},[10,10,9,9],0) +# Missing the complementary future-use edge also rejects. +run(blocks,edges[:3],{0,1},[10,10,9],0) +# Duplicate group/use lookup keys are explicitly rejected before iteration. +try:run(blocks,edges+[(0,0,0)],{0,1},[10,10,9,9,1]) +except AssertionError:duplicate_rejected=True +else:raise ValueError('Ambiguous group/use candidate key accepted') +rng=Random(231025) +for trial in range(1200): + ng=rng.randrange(2,6);nuses=rng.randrange(2,14);blocks=[];edges=[] + for g in range(ng): + width=rng.randrange(2,6);rows=[] + for _ in range(rng.randrange(width)*2): + v=rng.randrange(1,1<150 or choice<.34): + s=rng.choice(list(records));f,g=records.pop(s);idx.remove(s,f,g) + elif records and choice<.66: + s=rng.choice(list(records));f,g=records[s];new=between(f,g);check(contains(f,new) and contains(new,g),'Invalid random promotion') + before_order=dict(idx.order);idx.move(s,f,new);records[s]=(new,g);check(idx.order==before_order,'Frame move changes insertion order') + else: + s=rng.randrange(1200) + if s in records:continue + f=envelope();g=extend(f);idx.insert(s,f,g);records[s]=(f,g) + mutations+=1 + if iteration%4==0: + for target in (envelope(),(1,mask)): + check(idx.eligible(target)==query(records,target),'Random ordered pending query differs');queries+=1 + if iteration%100==0: + check(idx.lower.all==sum(1<>k&1),'Target core bitmap stale') + check(idx.cover[k]==sum(1<>k&1),'Target cover bitmap stale') +idx=Pending(4);idx.insert(1,(1,3),(1,5)) +check(idx.lower.eligible_mask((1,7))==2 and idx.eligible((1,7))==[],'Fixture does not reject missing future containment') +# Audit the actual integrated raise_ function on passive live controls. +compile_node=next(n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name=='compile_');raise_node=next(n for n in compile_node.body if isinstance(n,ast.FunctionDef) and n.name=='raise_') +blocks=[dict(frame=(3,3),rank=1),dict(frame=(1,7),rank=2),dict(frame=(1,15),rank=3)] +idx=Pending(4);idx.insert(0,blocks[0]['frame'],blocks[2]['frame']);idx.insert(1,blocks[0]['frame'],blocks[2]['frame']) +env=dict(frames=[0,0],blocks=blocks,contains=contains,retired=set(),retired_index=Retired(4),pending={0:2,1:2},pending_index=idx,hist=Counter(),events=[]) +exec(compile(ast.Module(body=[raise_node],type_ignores=[]),str(NEW),'exec'),env);env['raise_'](0,1) +check(idx.eligible(blocks[0]['frame'])==[1] and idx.eligible(blocks[1]['frame'])==[0,1],'Actual raise changes pending selection incorrectly') +check(idx.order=={0:0,1:1},'Actual raise changes pending order') +receipt=dict(status='PASS actual ordered two-envelope pending index and frame lifecycle',source_sha256=sha256(SOURCE.read_bytes()).hexdigest(),mutations=mutations,ordered_queries=queries,actual_raise_fixture=True,future_containment_negative_fixture=True) +(ROOT/'certificates/final-frame-pending-index-validation.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt)) diff --git a/scripts/experiments/audit_final_frame_pricing.py b/scripts/experiments/audit_final_frame_pricing.py new file mode 100644 index 0000000000..13f3b1abea --- /dev/null +++ b/scripts/experiments/audit_final_frame_pricing.py @@ -0,0 +1,43 @@ +"""Audit the actual coordinate-pricing writer and whole-engine delta. Apache-2.0.""" +from pathlib import Path +from hashlib import sha256 +from copy import deepcopy +from itertools import combinations +from random import Random +import ast,io,json,struct,sys +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +ROOT=Path(__file__).resolve().parents[2] +def check(ok,why): + if not ok:raise ValueError(why) +# At source level, restore only the oracle writer and remove the audited helper/call. +engine=ast.parse((ROOT/'scripts/experiments/final_frame_engine.py').read_text());base=ast.parse((ROOT/'references/frame-compiler/indexed-r5/scripts/experiments/compiler.py').read_text());new_compile=next(n for n in engine.body if isinstance(n,ast.FunctionDef) and n.name=='compile_');base_compile=next(n for n in base.body if isinstance(n,ast.FunctionDef) and n.name=='compile_') +writer=next(n for n in new_compile.body if isinstance(n,ast.With) and 'oracle_input.open' in ast.unparse(n.items[0].context_expr));base_writer=next(n for n in base_compile.body if isinstance(n,ast.With) and 'oracle_input.open' in ast.unparse(n.items[0].context_expr)) +trim=deepcopy(engine);trim.body=[n for n in trim.body if not(isinstance(n,ast.FunctionDef) and n.name=='improve_three_cycles')];fn=next(n for n in trim.body if isinstance(n,ast.FunctionDef) and n.name=='compile_');fn.body=[deepcopy(base_writer) if isinstance(n,ast.With) and 'oracle_input.open' in ast.unparse(n.items[0].context_expr) else n for n in fn.body];fn.body=[n for n in fn.body if not(isinstance(n,ast.For) and 'THREE_CYCLE_PASSES' in ast.unparse(n.iter))];check(ast.dump(trim,include_attributes=False)==ast.dump(base,include_attributes=False),'Whole engine changes exceed pricing writer plus cleared three-cycle helper/call') +# Exercise the ACTUAL binary oracle writer in memory. The block objects must stay +# untouched; only serialized core/cover masks are conjugated, while IDs/ranks stay. +class Capture: + def __init__(self):self.stream=None;self.bytes=None + def open(self,mode):check(mode=='wb','Unexpected oracle file mode');self.stream=io.BytesIO();return self + def __enter__(self):return self.stream + def __exit__(self,*args):self.bytes=self.stream.getvalue();return False +writer_code=compile(ast.Module(body=[deepcopy(writer)],type_ignores=[]),'actual_coordinate_oracle_writer','exec');base_code=compile(ast.Module(body=[deepcopy(base_writer)],type_ignores=[]),'original_oracle_writer','exec') +rng=Random(202610092046);writer_cases=0 +for h in (3,5,23,25): + for trial in range(100): + blocks=[] + for _ in range(rng.randrange(1,30)): + cover=rng.randrange(1,1<150 or rng.random()<0.48): + s=rng.choice(list(records));f,r=records.pop(s);idx.remove(s,f,r) + else: + s=rng.randrange(1200) + if s in records:continue + f=frame();r=rng.randrange(h+1);idx.insert(s,f,r);records[s]=(f,r) + mutations+=1 + if iteration%4==0: + for target in (frame(),(1,full)): + check(list(idx.eligible(target))==order(records,target),'Random exact frame/order query differs');queries+=1 + if iteration%100==0: + check(idx.all==sum(1<>k&1),'Core bitmap stale') + check(idx.cover[k]==sum(1<>k&1),'Cover bitmap stale') +# The actual integrated raise function keeps already-retired controls indexed at their new frame. +compile_node=next(n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name=='compile_') +raise_node=next(n for n in compile_node.body if isinstance(n,ast.FunctionDef) and n.name=='raise_') +blocks=[dict(frame=(3,3),rank=1),dict(frame=(1,7),rank=2),dict(frame=(1,15),rank=3)] +idx=Index(4);idx.insert(0,blocks[0]['frame'],1) +env=dict(frames=[0,0],blocks=blocks,contains=contains,retired={0},retired_index=idx,pending={},pending_index=space['PendingIndex'](4),hist=Counter(),events=[]) +exec(compile(ast.Module(body=[raise_node],type_ignores=[]),str(NEW),'exec'),env) +env['raise_'](0,1) +check(list(idx.eligible(blocks[0]['frame']))==[] and list(idx.eligible(blocks[1]['frame']))==[0],'Actual retired control frame promotion not reflected') +env['raise_'](1,1) +check(idx.all==1 and env['frames']==[1,1],'Nonretired raise inserted an indexed role') +env['raise_'](0,2);idx.remove(0,blocks[2]['frame'],3) +check(idx.all==0 and not any(idx.ranks) and not any(idx.core) and not any(idx.cover),'Actual promoted role removal leaves stale bits') +receipt=dict(status='PASS actual ordered retired index and frame lifecycle',source_sha256=sha256(SOURCE.read_bytes()).hexdigest(),mutations=mutations,ordered_queries=queries,actual_raise_fixture=True) +(ROOT/'certificates/final-frame-retired-index-validation.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt)) diff --git a/scripts/experiments/audit_final_frame_three_cycles.py b/scripts/experiments/audit_final_frame_three_cycles.py new file mode 100644 index 0000000000..f16e5e8555 --- /dev/null +++ b/scripts/experiments/audit_final_frame_three_cycles.py @@ -0,0 +1,54 @@ +"""Actual-source exchange tests: cardinality, matroid feasibility, integer descent.""" +import ast,copy,random,json +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2] +source=ast.parse((ROOT/'scripts/experiments/final_frame_engine.py').read_text());fn=next(n for n in source.body if isinstance(n,ast.FunctionDef) and n.name=='improve_three_cycles');ns={};exec(compile(ast.Module(body=[fn],type_ignores=[]),'actual-source-three-cycle','exec'),ns);improve=ns[fn.name] +def rank(rows): + pivots={} + for row in rows: + while row: + bit=row.bit_length()-1 + if bit not in pivots:pivots[bit]=row;break + row^=pivots[bit] + return len(pivots) +def exercise(blocks,edges,chosen,prices,passes=3): + chosen=set(chosen);blocks=copy.deepcopy(blocks);right={edges[e][1]:e for e in chosen};assert len(right)==len(chosen) + count=len(chosen);initial=sum(prices[e] for e in chosen);priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e]));changes=0 + def can(e,drop): + g,u,i=edges[e];rows=blocks[g]['outbasis']+[1<=3 or result[0]==0 +assert accepted>0 +print(json.dumps({'status':'PASS','actual_source':str(ROOT/'scripts/experiments/final_frame_engine.py'),'fixtures':1604,'accepted_three_cycles':accepted,'checks':['strict-cycle-only fixture','equal and worsening cost rejected','dependent replacement rejected','cardinality','one use per choice','local vector independence','exact integer descent','determinism','distinct block requirement']})) diff --git a/scripts/experiments/audit_indexed_cycle_completion.py b/scripts/experiments/audit_indexed_cycle_completion.py new file mode 100644 index 0000000000..ce42fce3b6 --- /dev/null +++ b/scripts/experiments/audit_indexed_cycle_completion.py @@ -0,0 +1,53 @@ +"""Focused actual-source audit. Chafik Boukhalfa with OpenAI Codex assistance; Apache-2.0.""" +from pathlib import Path +from hashlib import sha256 +from datetime import datetime,timezone +from random import Random +from collections import Counter +from copy import deepcopy +import ast,gzip,json,io,types,sys +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1] +SOURCE=HERE/'indexed_cycle_engine.py';NEW=SOURCE +source=SOURCE.read_text();tree=ast.parse(source) +def check(ok,why): + if not ok:raise ValueError(why) +s=source +tree=ast.parse(s) +helpers=[n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name in ('basis','independent')] +namespace={};exec(compile(ast.Module(body=helpers,type_ignores=[]),str(SOURCE),'exec'),namespace) +basis=namespace['basis'];independent=namespace['independent'] +future=next(n for n in ast.walk(tree) if isinstance(n,ast.FunctionDef) and n.name=='future_priority') +contains=lambda a,b:not(b[0]&~a[0]) and not(a[1]&~b[1]) +# Actual-use fixtures distinguish future compatible uses from backward or nonnested uses. +ns=dict(position={0:0,1:1,2:2,3:3},step=1,b={'frame':(1,3),'inputs':[10,11,12,13]},blocks=[{'frame':(1,3)},{'frame':(1,3)},{'frame':(1,7)},{'frame':(1,5)}],uses=[(10,2,None),(10,2,('terminal',)),(11,2,None),(11,0,None),(12,3,None),(13,3,None)],value_uses={10:[0,1],11:[2,3],12:[4],13:[5]},contains=contains,slots=[7,1,3,3],ins=[0,1,2,3]) +exec(compile(ast.Module(body=[future],type_ignores=[]),str(SOURCE),'exec'),ns) +check([ns['future_priority'](i) for i in range(4)]==[(-2,3,0),(-1,1,1),(0,2,2),(0,2,3)],'Priority does not use compatible actual future uses, symbolic support, index') +check(sorted(range(4),key=ns['future_priority'])==[0,1,2,3],'Priority is not deterministic') +# General span argument is below; these adversarial numerical fixtures check the actual helpers and literal synthesis. +rng=Random(20261008);cases=0;operations=0 +for n in range(1,10): + for trial in range(250): + rows=[] + for _ in range(rng.randrange(n+1)*3): + candidate=rng.randrange(1,1<>i&1) + if j!=i: + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];ops.append((a,z)) + for j in range(n): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];ops.append((j,i)) + check(rr==[1<0 and current==previous-gain,'Fixed integer price does not strictly improve') + previous=current;observed.append([e,other,f,z]) + invariant() + env=dict(blocks=blocks,edges=edges,chosen=chosen,right=right,prices=prices,priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])),basis=basis,independent=independent,stats=Counter(),sys=types.SimpleNamespace(stderr=io.StringIO()),audit_cycle=audit_cycle) + exec(code,env);invariant();check(env['stats']['carry_two_cycles']==len(observed),'Cycle count differs') + if expected is not None:check(len(observed)==expected,'Targeted cycle outcome differs') + cycles+=len(observed);cases+=1 + return observed + +# Each group is full (one outbasis row + one carrier). Neither cross-group +# single addition is independent, but simultaneous replacement is legal. +blocks=[{'outbasis':[3]},{'outbasis':[3]}] +edges=[(1,0,0),(0,1,0),(0,0,1),(1,1,1)] +run(blocks,edges,{0,1},[10,10,9,9],1) +run(blocks,edges,{0,1},[10,10,10,10],0) +# With the receiving group's unit vector already in its output span, reject. +run([{'outbasis':[2]},{'outbasis':[3]}],edges,{0,1},[10,10,9,9],0) +# Missing the complementary future-use edge also rejects. +run(blocks,edges[:3],{0,1},[10,10,9],0) +# Duplicate group/use lookup keys are explicitly rejected before iteration. +try:run(blocks,edges+[(0,0,0)],{0,1},[10,10,9,9,1]) +except AssertionError:duplicate_rejected=True +else:raise ValueError('Ambiguous group/use candidate key accepted') +rng=Random(231025) +for trial in range(1200): + ng=rng.randrange(2,6);nuses=rng.randrange(2,14);blocks=[];edges=[] + for g in range(ng): + width=rng.randrange(2,6);rows=[] + for _ in range(rng.randrange(width)*2): + v=rng.randrange(1,1<150 or choice<.34): + s=rng.choice(list(records));f,g=records.pop(s);idx.remove(s,f,g) + elif records and choice<.66: + s=rng.choice(list(records));f,g=records[s];new=between(f,g);check(contains(f,new) and contains(new,g),'Invalid random promotion') + before_order=dict(idx.order);idx.move(s,f,new);records[s]=(new,g);check(idx.order==before_order,'Frame move changes insertion order') + else: + s=rng.randrange(1200) + if s in records:continue + f=envelope();g=extend(f);idx.insert(s,f,g);records[s]=(f,g) + mutations+=1 + if iteration%4==0: + for target in (envelope(),(1,mask)): + check(idx.eligible(target)==query(records,target),'Random ordered pending query differs');queries+=1 + if iteration%100==0: + check(idx.lower.all==sum(1<>k&1),'Target core bitmap stale') + check(idx.cover[k]==sum(1<>k&1),'Target cover bitmap stale') +idx=Pending(4);idx.insert(1,(1,3),(1,5)) +check(idx.lower.eligible_mask((1,7))==2 and idx.eligible((1,7))==[],'Fixture does not reject missing future containment') +# Audit the actual integrated raise_ function on passive live controls. +compile_node=next(n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name=='compile_');raise_node=next(n for n in compile_node.body if isinstance(n,ast.FunctionDef) and n.name=='raise_') +blocks=[dict(frame=(3,3),rank=1),dict(frame=(1,7),rank=2),dict(frame=(1,15),rank=3)] +idx=Pending(4);idx.insert(0,blocks[0]['frame'],blocks[2]['frame']);idx.insert(1,blocks[0]['frame'],blocks[2]['frame']) +env=dict(frames=[0,0],blocks=blocks,contains=contains,retired=set(),retired_index=Retired(4),pending={0:2,1:2},pending_index=idx,hist=Counter(),events=[]) +exec(compile(ast.Module(body=[raise_node],type_ignores=[]),str(NEW),'exec'),env);env['raise_'](0,1) +check(idx.eligible(blocks[0]['frame'])==[1] and idx.eligible(blocks[1]['frame'])==[0,1],'Actual raise changes pending selection incorrectly') +check(idx.order=={0:0,1:1},'Actual raise changes pending order') +receipt=dict(status='PASS actual ordered two-envelope pending index and frame lifecycle',source_sha256=sha256(SOURCE.read_bytes()).hexdigest(),mutations=mutations,ordered_queries=queries,actual_raise_fixture=True,future_containment_negative_fixture=True) +(ROOT/'certificates/indexed-cycle-pending-index-validation.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt)) diff --git a/scripts/experiments/audit_indexed_cycle_retired.py b/scripts/experiments/audit_indexed_cycle_retired.py new file mode 100644 index 0000000000..10fc7fe4b2 --- /dev/null +++ b/scripts/experiments/audit_indexed_cycle_retired.py @@ -0,0 +1,67 @@ +"""Focused actual-source audit. Chafik Boukhalfa with OpenAI Codex assistance; Apache-2.0.""" +from pathlib import Path +from hashlib import sha256 +from datetime import datetime,timezone +from random import Random +from collections import Counter +from copy import deepcopy +import ast,gzip,json,io,types,sys +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1] +SOURCE=HERE/'indexed_cycle_engine.py';NEW=SOURCE +source=SOURCE.read_text();tree=ast.parse(source) +def check(ok,why): + if not ok:raise ValueError(why) +klass=next(n for n in tree.body if isinstance(n,ast.ClassDef) and n.name=='RetiredIndex') +space={};exec(compile(ast.Module(body=[n for n in tree.body if isinstance(n,ast.ClassDef)],type_ignores=[]),str(SOURCE),'exec'),space);Index=space['RetiredIndex'] +contains=lambda f,g:not(g[0]&~f[0]) and not(f[1]&~g[1]) +def valid_frames(h): + return [(c,d) for d in range(1,1<150 or rng.random()<0.48): + s=rng.choice(list(records));f,r=records.pop(s);idx.remove(s,f,r) + else: + s=rng.randrange(1200) + if s in records:continue + f=frame();r=rng.randrange(h+1);idx.insert(s,f,r);records[s]=(f,r) + mutations+=1 + if iteration%4==0: + for target in (frame(),(1,full)): + check(list(idx.eligible(target))==order(records,target),'Random exact frame/order query differs');queries+=1 + if iteration%100==0: + check(idx.all==sum(1<>k&1),'Core bitmap stale') + check(idx.cover[k]==sum(1<>k&1),'Cover bitmap stale') +# The actual integrated raise function keeps already-retired controls indexed at their new frame. +compile_node=next(n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name=='compile_') +raise_node=next(n for n in compile_node.body if isinstance(n,ast.FunctionDef) and n.name=='raise_') +blocks=[dict(frame=(3,3),rank=1),dict(frame=(1,7),rank=2),dict(frame=(1,15),rank=3)] +idx=Index(4);idx.insert(0,blocks[0]['frame'],1) +env=dict(frames=[0,0],blocks=blocks,contains=contains,retired={0},retired_index=idx,pending={},pending_index=space['PendingIndex'](4),hist=Counter(),events=[]) +exec(compile(ast.Module(body=[raise_node],type_ignores=[]),str(NEW),'exec'),env) +env['raise_'](0,1) +check(list(idx.eligible(blocks[0]['frame']))==[] and list(idx.eligible(blocks[1]['frame']))==[0],'Actual retired control frame promotion not reflected') +env['raise_'](1,1) +check(idx.all==1 and env['frames']==[1,1],'Nonretired raise inserted an indexed role') +env['raise_'](0,2);idx.remove(0,blocks[2]['frame'],3) +check(idx.all==0 and not any(idx.ranks) and not any(idx.core) and not any(idx.cover),'Actual promoted role removal leaves stale bits') +receipt=dict(status='PASS actual ordered retired index and frame lifecycle',source_sha256=sha256(SOURCE.read_bytes()).hexdigest(),mutations=mutations,ordered_queries=queries,actual_raise_fixture=True) +(ROOT/'certificates/indexed-cycle-retired-index-validation.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt)) diff --git a/scripts/experiments/balanced_split_compiler.py b/scripts/experiments/balanced_split_compiler.py new file mode 100644 index 0000000000..9e46dd08fd --- /dev/null +++ b/scripts/experiments/balanced_split_compiler.py @@ -0,0 +1,101 @@ +#!/usr/bin/env python3 +"""Compile aligned split frames with profile-cost pending live reclamation.""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode = True + +import argparse +import gzip +from hashlib import sha256 +import json +from pathlib import Path +import os +import shlex +import subprocess +import tempfile + +import balanced_split_engine +import balanced_split_exchange_engine +ENGINES = {23: balanced_split_engine, 25: balanced_split_exchange_engine} +import balanced_split_graph as producer + +ROOT = Path(__file__).resolve().parents[2] + + +def source_record(): + return dict(pr65=producer.checked_manifest(producer.BASELINE), + pr67=producer.checked_manifest(ROOT / 'references/frame-compiler/pr67'), + pr68=producer.checked_manifest(ROOT / 'references/frame-compiler/pr68'), + pr69=producer.checked_manifest(ROOT/'references/frame-compiler/pr69'), + pr70=producer.checked_manifest(ROOT/'references/frame-compiler/pr70'), + pr71=producer.checked_manifest(ROOT/'references/frame-compiler/pr71'), + inherited=producer.checked_manifest(ROOT / 'references/frame-compiler/pr48')) + + +def compile_axis(h): + config = producer.configuration(h) + compiler = ENGINES[h] + provenance = json.loads((ROOT/'research/balanced-split/engine-provenance.json').read_text()) + assert sha256(Path(compiler.__file__).read_bytes()).hexdigest() == provenance[str(h)]['portable_engine_sha256'], 'Selected engine changed' + previous_graph, previous_build = compiler.graph, compiler.build + absent = object() + runtime_names = ('oracles', 'ORACLE_EXE', 'ORACLE_INPUT', 'PENDING_COST') + previous_runtime = {name:getattr(compiler, name, absent) for name in runtime_names} + try: + compiler.graph = producer.graph + compiler.build = producer.ordered_build(previous_build, h) + compiler.PENDING_COST = True + with tempfile.TemporaryDirectory(prefix='balanced-split-compile-') as directory: + work = Path(directory) + oracle = work/'profile-oracle' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'), + str(ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/profile_oracle.cpp'), + '-o', str(oracle)], check=True) + compiler.oracles = [] + compiler.ORACLE_EXE, compiler.ORACLE_INPUT = str(oracle), str(work/'oracle-input.bin') + try: + result, word = compiler.compile_(h, matching=True, reclaim=True, dirty=True) + finally: + for process in compiler.oracles: + process.stdin.close() + assert process.wait(timeout=10) == 0, 'Discovery profile oracle failed' + finally: + compiler.graph, compiler.build = previous_graph, previous_build + for name, value in previous_runtime.items(): + if value is absent: + if hasattr(compiler, name): + delattr(compiler, name) + else: + setattr(compiler, name, value) + result.pop('seconds', None) + result['scalar'] = producer.graph(h).verify() + result['graph_configuration'] = config + result['source_pr65_head'] = source_record()['pr65']['commit'] + result['baseline_pr65_roles'] = {23: 27918, 25: 36586}[h] + result['source_pr67_head'] = source_record()['pr67']['commit'] + result['source_pr68_head'] = source_record()['pr68']['commit'] + result['reclamation_order'] = 'all eligible retired ranks, exact integer profile cost, XOR count, slot ID' + result['pending_live_controls'] = True + result['pending_cost_uses_next_use_frame'] = True + result['paid_clones'] = 0 + result['future_unit_completion'] = True + result['carry_exchange_passes'] = config['carry_exchange_passes'] + assert result['stats'].get('carry_exchanges', 0) == {23:0, 25:1000}[h] + for number in (69,70,71): + result['source_pr'+str(number)+'_head'] = source_record()['pr'+str(number)]['commit'] + return result, word + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--h', type=int, choices=(23, 25), required=True) + parser.add_argument('--output', type=Path, required=True) + parser.add_argument('--word', type=Path, required=True) + args = parser.parse_args() + result, word = compile_axis(args.h) + raw = (json.dumps(word, separators=(',', ':')) + '\n').encode() + args.word.write_bytes(gzip.compress(raw, mtime=0) if args.word.suffix == '.gz' else raw) + args.output.write_text(json.dumps(result, indent=2) + '\n') + print(json.dumps(result), flush=True) diff --git a/scripts/experiments/balanced_split_compose.py b/scripts/experiments/balanced_split_compose.py new file mode 100644 index 0000000000..9f95add5ca --- /dev/null +++ b/scripts/experiments/balanced_split_compose.py @@ -0,0 +1,182 @@ +"""Complete paid split/pair profile and PR65's exact refined balanced assembly. + +The unchanged full physical words determine every auxiliary multiplicity. +Only fixed-basis finite claims are certified; all-size transfer remains inherited. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode = True + +from copy import deepcopy +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import gzip +import json + +import binary_frame_math as arithmetic +from split_pair_arithmetic import refine, audit +from balanced_split_graph import checked_manifest +from balanced_split_compiler import source_record +from pin_balanced_split_sources import required_paths + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +OUT = ROOT / 'certificates' +INHERITED = ROOT / 'references/frame-compiler/pr48' +OLD = INHERITED / 'research/copied-fixed' +BASELINE = ROOT / 'references/frame-compiler/pr65' +BASELINE_CASE = BASELINE / 'research/reordered-rank-pair' +PROFILE_BASELINE = ROOT / 'references/frame-compiler/pr71/certificates' + + +def check_sources(): + sources = source_record() + operation = ROOT / 'references/frame-compiler/pr59-split-operation' + checked_manifest(operation) + local = json.loads((ROOT/'research/balanced-split/SOURCE.json').read_text()) + assert required_paths() <= set(local['files']), 'Incomplete source/finite-input closure' + for name, digest in local['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + engine = ROOT / 'scripts/experiments/joint_dual_reclaim_compiler.py' + assert engine.read_bytes() == (BASELINE/'scripts/experiments/rank_pair_compiler.py').read_bytes() + provenance = json.loads((ROOT/'research/balanced-split/engine-provenance.json').read_text()) + for record in provenance.values(): + assert sha256((HERE/record['portable_engine']).read_bytes()).hexdigest() == record['portable_engine_sha256'] + for name in ('binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp'): + assert (HERE/name).read_bytes() == (BASELINE/'scripts/experiments'/name).read_bytes() + return dict(sources, split_operation=checked_manifest(operation)) + + +def profile(): + parameters = json.loads((ROOT/'research/balanced-split/parameters.json').read_text()) + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + profiles = [json.loads((OUT / f'balanced-split-profiles-{h}.json').read_text()) for h in (a, b)] + words = json.loads((OUT / 'balanced-split-compiler.json').read_text()) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + receipts = [] + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + recorded = words['axes'][str(h)] + replay = recorded['replay'] + receipt = json.loads((OUT / f'balanced-split-transitions-{h}.json').read_text()) + for key in ('h', 'v', 'R'): + assert f[key] == receipt[key] + assert f['R'] == replay['roles'] == recorded['compiled']['roles'] == parameters['roles'][str(h)] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == receipt['rank_mass'] == replay['rank_mass'] + assert f['blocks'][0] == 0 and f['blocks'][h] == 0 # Positive children; copied centers already included. + assert receipt['transition_events_equal_independent_xor_word_reconstruction'] + packed = (OUT / f'balanced-split-word-{h}.json.gz').read_bytes() + assert sha256(packed).hexdigest() == recorded['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == recorded['word_sha256'] == receipt['word_sha256'] + histogram = {str(k): v for k, v in replay['histogram'].items() if int(k)} + side = replay['output_roles']-h + histogram['2'] -= side + histogram['1'] += 2*side + assert histogram == receipt['rank_histogram_with_side_growth_split_into_singletons'] + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + receipts.append(receipt) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (parameters['W'], parameters['total_rank'], 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, + maxchild=max(rows), child_multiplicities=dict(sorted(rows.items())), + parts=parts, axes=profiles, words=receipts) + + + +def finite_bridge(width): + bridge = deepcopy(json.loads((OLD/'certificate.json').read_text())['finite_bridge']) + bridge['bit']['W'] = width + bridge['bit']['wire_bits'] = width.bit_length() + bridge['rows']['coefficient'] = sum(bridge[name]['halving_degree'] * bridge[name]['wire_bits'] for name in ('bit','complex')) + bridge['rows']['degree'] = 2000 + bridge['rows']['degree_gap'] = Q(bridge['rows']['degree'])-Q(51,25)*bridge['rows']['coefficient'] + bridge['rows']['suffix_slope'] = 4*bridge['rows']['degree'] + return bridge + + +def validate_bridge(bridge, width): + expected = finite_bridge(width) + for section, key in (('bit','W'), ('bit','wire_bits'), ('rows','coefficient'), + ('rows','degree'), ('rows','degree_gap'), ('rows','suffix_slope')): + assert Q(bridge[section][key]) == Q(expected[section][key]), 'Stale finite bridge: '+section+'.'+key + assert (width,bridge['bit']['wire_bits'],bridge['rows']['coefficient'],Q(bridge['rows']['degree_gap'])) == (134126064,27,843,Q(7007,25)) + return True + + +def compose(): + sources = check_sources() + parameters = json.loads((ROOT/'research/balanced-split/parameters.json').read_text()) + bit_saving, kappa = Q(parameters['bit_saving']), Q(parameters['kappa']) + denominator = parameters['grid_denominator'] + assert type(denominator) is int and denominator == 10**18 + grid = Q(1, denominator) + assert json.loads((OUT/'balanced-split-compiler.json').read_text())['source'] == source_record() + p = profile() + exact = refine.exact_moment(p['m'], p['W'], p['child_multiplicities'], bit_saving) + excluded = refine.exact_moment(p['m'], p['W'], p['child_multiplicities'], bit_saving+grid) + assert exact['upper'] < 1 < excluded['lower'] + independent = audit.independent_moment(arithmetic.js(p), bit_saving, arithmetic.js(exact['terms'])) + independent_rejected = audit.independent_moment(arithmetic.js(p), bit_saving+grid, arithmetic.js(exact['terms'])) + assert independent[1] < 1 < independent_rejected[0] + prior71 = json.loads((PROFILE_BASELINE/'split-pair-kappa.json').read_text()) + oldbit = prior71['bit'] + previous_kappa = Q(prior71['kappa']) + previous_rows = {int(t): n for t,n in oldbit['child_multiplicities'].items()} + prior71_lower = refine.exact_moment(oldbit['m'], oldbit['W'], previous_rows, bit_saving)['lower'] + assert prior71_lower > 1 and kappa > previous_kappa + bridge = finite_bridge(p['W']) + validate_bridge(bridge, p['W']) + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/balanced-split/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113', + pr71_kappa=previous_kappa, ratio_pr71=kappa/previous_kappa, + absolute_gain_pr71=kappa-previous_kappa, + pr71_complete_profile_exclusion_lower=prior71_lower, + full_pr71_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected balanced-split partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring, PR69 balanced coarse sums, future unit completion and bounded PR70 carry exchanges; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'balanced-split-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/scripts/experiments/balanced_split_engine.py b/scripts/experiments/balanced_split_engine.py new file mode 100644 index 0000000000..e1a9883726 --- /dev/null +++ b/scripts/experiments/balanced_split_engine.py @@ -0,0 +1,278 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + _graph = _graphs[h] + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/scripts/experiments/final_frame_compiler.py b/scripts/experiments/final_frame_compiler.py new file mode 100644 index 0000000000..4d2e5cd7e5 --- /dev/null +++ b/scripts/experiments/final_frame_compiler.py @@ -0,0 +1,109 @@ +#!/usr/bin/env python3 +"""Compile the frozen final frame composition and exactly relabel coordinates. + +Chafik Boukhalfa with OpenAI Codex assistance. Uses credited PR65/67/68/69/70 +construction, Thomas DiFiore's PR74 order and relabeling, and Rohan Arun's +PR78 coordinate-flag search idea and PR82 coordinate-aware oracle pricing. Original notices and source bytes are retained. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode = True +import argparse +import gzip +from hashlib import sha256 +import json +from pathlib import Path +import os +import shlex +import subprocess +import tempfile +_previous_path = sys.path[:] +try: + import final_frame_engine as compiler +finally: + sys.path[:] = _previous_path +from final_frame_nodeops import relabel,verify_dense +import final_frame_graph as producer +ENGINES = {23: compiler, 25: compiler} +ROOT = Path(__file__).resolve().parents[2] + + +def source_record(): + paths = {f'pr{n}':ROOT/f'references/frame-compiler/pr{n}' for n in (65,67,68,69,70,71,74,78,79,82,84)} + paths.update(inherited=ROOT/'references/frame-compiler/pr48', indexed_r5=ROOT/'references/frame-compiler/indexed-r5',final_r10=ROOT/'references/frame-compiler/final-r10') + return {name:producer.checked_manifest(path) for name,path in paths.items()} + + +def compile_axis(h): + config = producer.configuration(h) + provenance = json.loads((ROOT/'research/final-frame/engine-provenance.json').read_text()) + for record in provenance.values(): + actual = ROOT/'scripts/experiments'/record['portable_engine'] + assert sha256(actual.read_bytes()).hexdigest() == record['portable_engine_sha256'], 'Selected source changed' + assert actual.read_bytes() == (ROOT/record['original']).read_bytes(), 'Portable source differs' + selection = json.loads((ROOT/'research/final-frame/discovery-selection.json').read_text())['axes'][str(h)] + binding=json.loads((ROOT/'research/final-frame/word-bindings.json').read_text())[str(h)] + previous_graph, previous_build = compiler.graph, compiler.build + absent = object() + names = ('oracles','ORACLE_EXE','ORACLE_INPUT','PENDING_COST','OUTPUT_MODE','ORACLE_COORDINATES','THREE_CYCLE_PASSES') + previous = {name:getattr(compiler,name,absent) for name in names} + try: + compiler.graph = producer.graph + compiler.PENDING_COST = True + compiler.OUTPUT_MODE = config['output_mode'] + compiler.ORACLE_COORDINATES = config['coordinate_permutation'] if config['oracle_coordinate_pricing'] else list(range(h)) + compiler.THREE_CYCLE_PASSES = config['three_cycle_passes'] + with tempfile.TemporaryDirectory(prefix='final-frame-compile-') as directory: + work=Path(directory);oracle=work/'profile-oracle' + subprocess.run([*shlex.split(os.environ.get('CXX','c++')),'-O3','-std=c++17', + '-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'), + str(ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/profile_oracle.cpp'), + '-o',str(oracle)],check=True) + compiler.oracles=[];compiler.ORACLE_EXE=str(oracle);compiler.ORACLE_INPUT=str(work/'oracle-input.bin') + try: + result,word=compiler.compile_(h,matching=True,reclaim=True,dirty=True) + finally: + for process in compiler.oracles: + process.stdin.close() + assert process.wait(timeout=10)==0,'Profile oracle failed' + finally: + compiler.graph,compiler.build=previous_graph,previous_build + for name,value in previous.items(): + if value is absent: + if hasattr(compiler,name):delattr(compiler,name) + else:setattr(compiler,name,value) + result.pop('seconds',None) + parent = json.loads((ROOT/f'research/final-frame/parent-result-{h}.json').read_text()) + parent.pop('seconds',None) + assert json.loads(json.dumps(result)) == parent, 'Frozen parent compiler receipt differs' + raw=lambda value:(json.dumps(value,separators=(',',':'))+'\n').encode() + parent_sha=sha256(raw(word)).hexdigest() + assert parent_sha == binding['parent_word_sha256'], 'Frozen parent physical word differs' + word = relabel(word,config['coordinate_permutation']) + selected_sha=sha256(raw(word)).hexdigest() + assert selected_sha == selection['word_sha256'], 'Selected relabeled physical word differs' + assert result['roles']==selection['roles'] + checked=producer.graph(h);scalar=checked.verify();scalar['dense_global_support']=verify_dense(checked) + assert scalar==json.loads((ROOT/f'research/final-frame/scalar-{h}.json').read_text()) + result.update(scalar=scalar,graph_configuration=config, + parent_word_sha256=parent_sha,selected_word_sha256=selected_sha, + coordinate_relabeling='PR74 exact bijection of sources, frames, scatter rows and output targets; ordinary and dirty columns independently replayed after relabeling', + paid_clones=0,index_order='retired descending rank then slot; pending insertion order', + future_unit_completion=True,carry_exchange_passes=3,carry_two_cycle_passes=3, + pending_cost_uses_next_use_frame=True,three_cycle_passes=config['three_cycle_passes'], + oracle_coordinate_pricing=config['oracle_coordinate_pricing'],node_order=config['node_order'], + source_r10_sha256=provenance['engine']['original_source_manifest_sha256']) + return result,word + + +if __name__ == '__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('--h',type=int,choices=(23,25),required=True) + parser.add_argument('--output',type=Path,required=True) + parser.add_argument('--word',type=Path,required=True) + args=parser.parse_args();result,word=compile_axis(args.h) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + args.word.write_bytes(gzip.compress(raw,mtime=0) if args.word.suffix=='.gz' else raw) + args.output.write_text(json.dumps(result,indent=2)+'\n') + print(json.dumps(result),flush=True) diff --git a/scripts/experiments/final_frame_compose.py b/scripts/experiments/final_frame_compose.py new file mode 100644 index 0000000000..fd4bdb263a --- /dev/null +++ b/scripts/experiments/final_frame_compose.py @@ -0,0 +1,189 @@ +"""Complete paid split/pair profile and PR65's exact refined balanced assembly. + +The unchanged full physical words determine every auxiliary multiplicity. +Only fixed-basis finite claims are certified; all-size transfer remains inherited. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode = True + +from copy import deepcopy +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import gzip +import json + +import binary_frame_math as arithmetic +from split_pair_arithmetic import refine, audit +from final_frame_graph import checked_manifest +from final_frame_compiler import source_record +from pin_final_frame_sources import required_paths + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +OUT = ROOT / 'certificates' +INHERITED = ROOT / 'references/frame-compiler/pr48' +OLD = INHERITED / 'research/copied-fixed' +BASELINE = ROOT / 'references/frame-compiler/pr65' +BASELINE_CASE = BASELINE / 'research/reordered-rank-pair' +PROFILE_BASELINE = ROOT / 'references/frame-compiler/pr84/certificates' + + +def check_sources(): + sources = source_record() + operation = ROOT / 'references/frame-compiler/pr59-split-operation' + checked_manifest(operation) + local = json.loads((ROOT/'research/final-frame/SOURCE.json').read_text()) + assert required_paths() <= set(local['files']), 'Incomplete source/finite-input closure' + for name, digest in local['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + engine = ROOT / 'scripts/experiments/joint_dual_reclaim_compiler.py' + assert engine.read_bytes() == (BASELINE/'scripts/experiments/rank_pair_compiler.py').read_bytes() + provenance = json.loads((ROOT/'research/final-frame/engine-provenance.json').read_text()) + for record in provenance.values(): + assert sha256((HERE/record['portable_engine']).read_bytes()).hexdigest() == record['portable_engine_sha256'] + for name in ('binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp'): + assert (HERE/name).read_bytes() == (BASELINE/'scripts/experiments'/name).read_bytes() + return dict(sources, split_operation=checked_manifest(operation)) + + +def profile(): + parameters = json.loads((ROOT/'research/final-frame/parameters.json').read_text()) + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + profiles = [json.loads((OUT / f'final-frame-profiles-{h}.json').read_text()) for h in (a, b)] + words = json.loads((OUT / 'final-frame-compiler.json').read_text()) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + receipts = [] + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + recorded = words['axes'][str(h)] + replay = recorded['replay'] + receipt = json.loads((OUT / f'final-frame-transitions-{h}.json').read_text()) + for key in ('h', 'v', 'R'): + assert f[key] == receipt[key] + assert f['R'] == replay['roles'] == recorded['compiled']['roles'] == parameters['roles'][str(h)] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == receipt['rank_mass'] == replay['rank_mass'] + assert f['blocks'][0] == 0 and f['blocks'][h] == 0 # Positive children; copied centers already included. + assert receipt['transition_events_equal_independent_xor_word_reconstruction'] + packed = (OUT / f'final-frame-word-{h}.json.gz').read_bytes() + assert sha256(packed).hexdigest() == recorded['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == recorded['word_sha256'] == receipt['word_sha256'] + histogram = {str(k): v for k, v in replay['histogram'].items() if int(k)} + side = replay['output_roles']-h + histogram['2'] -= side + histogram['1'] += 2*side + assert histogram == receipt['rank_histogram_with_side_growth_split_into_singletons'] + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + receipts.append(receipt) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (parameters['W'], parameters['total_rank'], 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, + maxchild=max(rows), child_multiplicities=dict(sorted(rows.items())), + parts=parts, axes=profiles, words=receipts) + + + +def finite_bridge(width): + bridge = deepcopy(json.loads((OLD/'certificate.json').read_text())['finite_bridge']) + bridge['bit']['W'] = width + bridge['bit']['wire_bits'] = width.bit_length() + bridge['rows']['coefficient'] = sum(bridge[name]['halving_degree'] * bridge[name]['wire_bits'] for name in ('bit','complex')) + bridge['rows']['degree'] = 2000 + bridge['rows']['degree_gap'] = Q(bridge['rows']['degree'])-Q(51,25)*bridge['rows']['coefficient'] + bridge['rows']['suffix_slope'] = 4*bridge['rows']['degree'] + return bridge + + +def validate_bridge(bridge, width): + expected = finite_bridge(width) + for section, key in (('bit','W'), ('bit','wire_bits'), ('rows','coefficient'), + ('rows','degree'), ('rows','degree_gap'), ('rows','suffix_slope')): + assert Q(bridge[section][key]) == Q(expected[section][key]), 'Stale finite bridge: '+section+'.'+key + assert (width,bridge['bit']['wire_bits'],bridge['rows']['coefficient'],Q(bridge['rows']['degree_gap'])) == (131503443,27,843,Q(7007,25)) + return True + + +def compose(): + sources = check_sources() + parameters = json.loads((ROOT/'research/final-frame/parameters.json').read_text()) + bit_saving, kappa = Q(parameters['bit_saving']), Q(parameters['kappa']) + denominator = parameters['grid_denominator'] + assert type(denominator) is int and denominator == 10**18 + grid = Q(1, denominator) + assert json.loads((OUT/'final-frame-compiler.json').read_text())['source'] == source_record() + p = profile() + exact = refine.exact_moment(p['m'], p['W'], p['child_multiplicities'], bit_saving) + excluded = refine.exact_moment(p['m'], p['W'], p['child_multiplicities'], bit_saving+grid) + assert exact['upper'] < 1 < excluded['lower'] + independent = audit.independent_moment(arithmetic.js(p), bit_saving, arithmetic.js(exact['terms'])) + independent_rejected = audit.independent_moment(arithmetic.js(p), bit_saving+grid, arithmetic.js(exact['terms'])) + assert independent[1] < 1 < independent_rejected[0] + prior71 = json.loads((PROFILE_BASELINE/'indexed-cycle-kappa.json').read_text()) + oldbit = prior71['bit'] + previous_kappa = Q(prior71['kappa']) + previous_rows = {int(t): n for t,n in oldbit['child_multiplicities'].items()} + prior71_lower = refine.exact_moment(oldbit['m'], oldbit['W'], previous_rows, bit_saving)['lower'] + assert prior71_lower > 1 and kappa > previous_kappa + prior74 = json.loads((ROOT/'references/frame-compiler/pr74/research/balanced-split-frames/certificate.json').read_text()) + rows74 = {int(t):n for t,n in prior74['child_multiplicities'].items()} + prior74_lower = refine.exact_moment(575, prior74['W'], rows74, bit_saving)['lower'] + reported74 = Q('10366199626713/200000000000000000') + assert prior74_lower > 1 and kappa > reported74 + bridge = finite_bridge(p['W']) + validate_bridge(bridge, p['W']) + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/final-frame/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr84_commit='88ca39571907343a49e97f328971ec7bcd26fbfd', + pr74_commit='3f78d8967c009153f2df5c6a6577b6ab1d37e2ca', reported_pr74_kappa=reported74, + ratio_reported_pr74=kappa/reported74, pr74_complete_profile_exclusion_lower=prior74_lower, + pr84_kappa=previous_kappa, ratio_pr84=kappa/previous_kappa, + absolute_gain_pr84=kappa-previous_kappa, + pr84_complete_profile_exclusion_lower=prior71_lower, + full_pr84_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected final-frame partition and point permutation, rank-preserving selected node order, natural execution, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring, PR69 balanced coarse sums, future unit completion and bounded PR70-derived single exchanges, two-cycles and selected three-donor cycles, PR82 coordinate-aware heuristic pricing, exact frame indices, late-output routing and PR74/78-inspired coordinate relabeling; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'final-frame-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/scripts/experiments/final_frame_engine.py b/scripts/experiments/final_frame_engine.py new file mode 100644 index 0000000000..5c82d20ab0 --- /dev/null +++ b/scripts/experiments/final_frame_engine.py @@ -0,0 +1,462 @@ +# Coordinate-conjugated oracle pricing adapted from Rohan Arun PR82, with OpenAI Codex assistance. +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<0 and carry_can(x,f) and carry_can(other,y): + options.append((-gain,z,x,y,other)) + if not options:continue + _,z,x,y,other=min(options) + old=(f,z,y);new=(e,x,other) + assert len(set(old))==len(set(new))==3 and not set(old)&set(new) + assert {edges[t][1] for t in old}=={edges[t][1] for t in new} + assert len({edges[t][0] for t in old})==len({edges[t][0] for t in new})==3 + for t in old: + tg,tu,ti=edges[t];chosen.remove(t);blocks[tg]['selected'].remove(t);del right[tu] + for t in new: + tg,tu,ti=edges[t];assert tu not in right;chosen.add(t);blocks[tg]['selected'].add(t);right[tu]=t + changes+=1 + return changes + + +def compile_(h,matching=True,reclaim=False,dirty=True): + t0=time.time();c,blocks,uses,value_uses,owner,signal,order,contains=build(h);v=len(c.inputs);position={g:i for i,g in enumerate(order)} + print('built',h,len(blocks),'regions',flush=True,file=sys.stderr) + mode=globals().get('OUTPUT_MODE','baseline') + edges,chosen,right,stats=match(blocks,uses,matching) + print('matched',len(chosen),'seconds',time.time()-t0,flush=True,file=sys.stderr) + slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();retired_index=RetiredIndex(h);pending={};pending_index=PendingIndex(h);stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + oracle_map=globals().get('ORACLE_COORDINATES',list(range(h))) + assert sorted(oracle_map)==list(range(h)), 'Invalid oracle coordinate permutation' + for b in blocks:stream.write(struct.pack('<2QI',*[sum(1<>i&1) for mask in b['frame']],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + for phase in range(globals().get('THREE_CYCLE_PASSES',0)): + changes=improve_three_cycles(blocks,edges,chosen,right,prices,priority,carry_can) + stats['carry_three_cycles']+=changes + print('carry three-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + first,mid,last = 0,(len(groups)-1)//2,len(groups)-1 + requested = {1:[first],2:[mid],3:[last],4:[first,mid],5:[first,last],6:[mid,last],7:[first,mid,last],8:[first,first+1],9:[last-1,last]}[choice] + chosen=[] + for k in requested: + if k not in chosen and 0<=k>common&1 and not(mask&forbidden)) + assert support[x]==expected + return {'status':'PASS all global supports, exact envelopes, disjoint additions and target outputs','nodes':len(c.active),'outputs':len(c.outputs),'sha256':digest.hexdigest()} + +# Coordinate action preserves the literal physical word under a global input relabel. +def relabel(word,permutation): + from itertools import combinations + h,v=word['h'],word['v'];assert sorted(permutation)==list(range(h)) + triples=list(combinations(range(h),3));assert len(triples)==v + index={triple:i for i,triple in enumerate(triples)} + def triple(t):return sorted(permutation[x] for x in t) + mapping={i:index[tuple(triple(t))] for i,t in enumerate(triples)} + def mask(bits):return sum(1<>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word diff --git a/scripts/experiments/indexed_cycle_compiler.py b/scripts/experiments/indexed_cycle_compiler.py new file mode 100644 index 0000000000..578e9a2fa4 --- /dev/null +++ b/scripts/experiments/indexed_cycle_compiler.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Compile the frozen indexed two-cycle pair and exactly relabel coordinates. + +Chafik Boukhalfa with OpenAI Codex assistance. Uses credited PR65/67/68/69/70 +construction, Thomas DiFiore's PR74 order and relabeling, and Rohan Arun's +PR78 coordinate-flag search idea. Original notices and source bytes are retained. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode = True +import argparse +import gzip +from hashlib import sha256 +import json +from pathlib import Path +import os +import shlex +import subprocess +import tempfile +_previous_path = sys.path[:] +try: + import indexed_cycle_engine as compiler +finally: + sys.path[:] = _previous_path +from indexed_cycle_nodeops import relabel +import indexed_cycle_graph as producer +ENGINES = {23: compiler, 25: compiler} +ROOT = Path(__file__).resolve().parents[2] + + +def source_record(): + paths = {f'pr{n}':ROOT/f'references/frame-compiler/pr{n}' for n in (65,67,68,69,70,71,74,78,79)} + paths.update(inherited=ROOT/'references/frame-compiler/pr48', indexed_r5=ROOT/'references/frame-compiler/indexed-r5') + return {name:producer.checked_manifest(path) for name,path in paths.items()} + + +def compile_axis(h): + config = producer.configuration(h) + provenance = json.loads((ROOT/'research/indexed-cycle/engine-provenance.json').read_text()) + for record in provenance.values(): + actual = ROOT/'scripts/experiments'/record['portable_engine'] + assert sha256(actual.read_bytes()).hexdigest() == record['portable_engine_sha256'], 'Selected source changed' + assert actual.read_bytes() == (ROOT/record['original']).read_bytes(), 'Portable source differs' + selection = json.loads((ROOT/'research/indexed-cycle/discovery-selection.json').read_text())['axes'][str(h)] + previous_graph, previous_build = compiler.graph, compiler.build + absent = object() + names = ('oracles','ORACLE_EXE','ORACLE_INPUT','PENDING_COST','OUTPUT_MODE') + previous = {name:getattr(compiler,name,absent) for name in names} + try: + compiler.graph = producer.graph + compiler.PENDING_COST = True + compiler.OUTPUT_MODE = config['output_mode'] + with tempfile.TemporaryDirectory(prefix='indexed-cycle-compile-') as directory: + work=Path(directory);oracle=work/'profile-oracle' + subprocess.run([*shlex.split(os.environ.get('CXX','c++')),'-O3','-std=c++17', + '-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'), + str(ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/profile_oracle.cpp'), + '-o',str(oracle)],check=True) + compiler.oracles=[];compiler.ORACLE_EXE=str(oracle);compiler.ORACLE_INPUT=str(work/'oracle-input.bin') + try: + result,word=compiler.compile_(h,matching=True,reclaim=True,dirty=True) + finally: + for process in compiler.oracles: + process.stdin.close() + assert process.wait(timeout=10)==0,'Profile oracle failed' + finally: + compiler.graph,compiler.build=previous_graph,previous_build + for name,value in previous.items(): + if value is absent: + if hasattr(compiler,name):delattr(compiler,name) + else:setattr(compiler,name,value) + result.pop('seconds',None) + parent = json.loads((ROOT/f'research/indexed-cycle/parent-result-{h}.json').read_text()) + parent.pop('seconds',None) + assert json.loads(json.dumps(result)) == parent, 'Frozen parent compiler receipt differs' + raw=lambda value:(json.dumps(value,separators=(',',':'))+'\n').encode() + parent_sha=sha256(raw(word)).hexdigest() + assert parent_sha == selection['parent_word_sha256'], 'Frozen parent physical word differs' + word = relabel(word,config['coordinate_permutation']) + selected_sha=sha256(raw(word)).hexdigest() + assert selected_sha == selection['word_sha256'], 'Selected relabeled physical word differs' + assert result['roles']==selection['roles'] + result.update(scalar=producer.graph(h).verify(),graph_configuration=config, + parent_word_sha256=parent_sha,selected_word_sha256=selected_sha, + coordinate_relabeling='PR74 exact bijection of sources, frames, scatter rows and output targets; ordinary and dirty columns independently replayed after relabeling', + paid_clones=0,index_order='retired descending rank then slot; pending insertion order', + future_unit_completion=True,carry_exchange_passes=3,carry_two_cycle_passes=3, + pending_cost_uses_next_use_frame=True,source_r5_sha256=provenance['engine']['original_R5_source_sha256']) + return result,word + + +if __name__ == '__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('--h',type=int,choices=(23,25),required=True) + parser.add_argument('--output',type=Path,required=True) + parser.add_argument('--word',type=Path,required=True) + args=parser.parse_args();result,word=compile_axis(args.h) + raw=(json.dumps(word,separators=(',',':'))+'\n').encode() + args.word.write_bytes(gzip.compress(raw,mtime=0) if args.word.suffix=='.gz' else raw) + args.output.write_text(json.dumps(result,indent=2)+'\n') + print(json.dumps(result),flush=True) diff --git a/scripts/experiments/indexed_cycle_compose.py b/scripts/experiments/indexed_cycle_compose.py new file mode 100644 index 0000000000..0ad00f6031 --- /dev/null +++ b/scripts/experiments/indexed_cycle_compose.py @@ -0,0 +1,189 @@ +"""Complete paid split/pair profile and PR65's exact refined balanced assembly. + +The unchanged full physical words determine every auxiliary multiplicity. +Only fixed-basis finite claims are certified; all-size transfer remains inherited. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode = True + +from copy import deepcopy +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import gzip +import json + +import binary_frame_math as arithmetic +from split_pair_arithmetic import refine, audit +from indexed_cycle_graph import checked_manifest +from indexed_cycle_compiler import source_record +from pin_indexed_cycle_sources import required_paths + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +OUT = ROOT / 'certificates' +INHERITED = ROOT / 'references/frame-compiler/pr48' +OLD = INHERITED / 'research/copied-fixed' +BASELINE = ROOT / 'references/frame-compiler/pr65' +BASELINE_CASE = BASELINE / 'research/reordered-rank-pair' +PROFILE_BASELINE = ROOT / 'references/frame-compiler/pr79/certificates' + + +def check_sources(): + sources = source_record() + operation = ROOT / 'references/frame-compiler/pr59-split-operation' + checked_manifest(operation) + local = json.loads((ROOT/'research/indexed-cycle/SOURCE.json').read_text()) + assert required_paths() <= set(local['files']), 'Incomplete source/finite-input closure' + for name, digest in local['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + engine = ROOT / 'scripts/experiments/joint_dual_reclaim_compiler.py' + assert engine.read_bytes() == (BASELINE/'scripts/experiments/rank_pair_compiler.py').read_bytes() + provenance = json.loads((ROOT/'research/indexed-cycle/engine-provenance.json').read_text()) + for record in provenance.values(): + assert sha256((HERE/record['portable_engine']).read_bytes()).hexdigest() == record['portable_engine_sha256'] + for name in ('binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp'): + assert (HERE/name).read_bytes() == (BASELINE/'scripts/experiments'/name).read_bytes() + return dict(sources, split_operation=checked_manifest(operation)) + + +def profile(): + parameters = json.loads((ROOT/'research/indexed-cycle/parameters.json').read_text()) + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + profiles = [json.loads((OUT / f'indexed-cycle-profiles-{h}.json').read_text()) for h in (a, b)] + words = json.loads((OUT / 'indexed-cycle-compiler.json').read_text()) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + receipts = [] + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + recorded = words['axes'][str(h)] + replay = recorded['replay'] + receipt = json.loads((OUT / f'indexed-cycle-transitions-{h}.json').read_text()) + for key in ('h', 'v', 'R'): + assert f[key] == receipt[key] + assert f['R'] == replay['roles'] == recorded['compiled']['roles'] == parameters['roles'][str(h)] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == receipt['rank_mass'] == replay['rank_mass'] + assert f['blocks'][0] == 0 and f['blocks'][h] == 0 # Positive children; copied centers already included. + assert receipt['transition_events_equal_independent_xor_word_reconstruction'] + packed = (OUT / f'indexed-cycle-word-{h}.json.gz').read_bytes() + assert sha256(packed).hexdigest() == recorded['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == recorded['word_sha256'] == receipt['word_sha256'] + histogram = {str(k): v for k, v in replay['histogram'].items() if int(k)} + side = replay['output_roles']-h + histogram['2'] -= side + histogram['1'] += 2*side + assert histogram == receipt['rank_histogram_with_side_growth_split_into_singletons'] + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + receipts.append(receipt) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (parameters['W'], parameters['total_rank'], 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, + maxchild=max(rows), child_multiplicities=dict(sorted(rows.items())), + parts=parts, axes=profiles, words=receipts) + + + +def finite_bridge(width): + bridge = deepcopy(json.loads((OLD/'certificate.json').read_text())['finite_bridge']) + bridge['bit']['W'] = width + bridge['bit']['wire_bits'] = width.bit_length() + bridge['rows']['coefficient'] = sum(bridge[name]['halving_degree'] * bridge[name]['wire_bits'] for name in ('bit','complex')) + bridge['rows']['degree'] = 2000 + bridge['rows']['degree_gap'] = Q(bridge['rows']['degree'])-Q(51,25)*bridge['rows']['coefficient'] + bridge['rows']['suffix_slope'] = 4*bridge['rows']['degree'] + return bridge + + +def validate_bridge(bridge, width): + expected = finite_bridge(width) + for section, key in (('bit','W'), ('bit','wire_bits'), ('rows','coefficient'), + ('rows','degree'), ('rows','degree_gap'), ('rows','suffix_slope')): + assert Q(bridge[section][key]) == Q(expected[section][key]), 'Stale finite bridge: '+section+'.'+key + assert (width,bridge['bit']['wire_bits'],bridge['rows']['coefficient'],Q(bridge['rows']['degree_gap'])) == (132466108,27,843,Q(7007,25)) + return True + + +def compose(): + sources = check_sources() + parameters = json.loads((ROOT/'research/indexed-cycle/parameters.json').read_text()) + bit_saving, kappa = Q(parameters['bit_saving']), Q(parameters['kappa']) + denominator = parameters['grid_denominator'] + assert type(denominator) is int and denominator == 10**18 + grid = Q(1, denominator) + assert json.loads((OUT/'indexed-cycle-compiler.json').read_text())['source'] == source_record() + p = profile() + exact = refine.exact_moment(p['m'], p['W'], p['child_multiplicities'], bit_saving) + excluded = refine.exact_moment(p['m'], p['W'], p['child_multiplicities'], bit_saving+grid) + assert exact['upper'] < 1 < excluded['lower'] + independent = audit.independent_moment(arithmetic.js(p), bit_saving, arithmetic.js(exact['terms'])) + independent_rejected = audit.independent_moment(arithmetic.js(p), bit_saving+grid, arithmetic.js(exact['terms'])) + assert independent[1] < 1 < independent_rejected[0] + prior71 = json.loads((PROFILE_BASELINE/'balanced-split-kappa.json').read_text()) + oldbit = prior71['bit'] + previous_kappa = Q(prior71['kappa']) + previous_rows = {int(t): n for t,n in oldbit['child_multiplicities'].items()} + prior71_lower = refine.exact_moment(oldbit['m'], oldbit['W'], previous_rows, bit_saving)['lower'] + assert prior71_lower > 1 and kappa > previous_kappa + prior74 = json.loads((ROOT/'references/frame-compiler/pr74/research/balanced-split-frames/certificate.json').read_text()) + rows74 = {int(t):n for t,n in prior74['child_multiplicities'].items()} + prior74_lower = refine.exact_moment(575, prior74['W'], rows74, bit_saving)['lower'] + reported74 = Q('10366199626713/200000000000000000') + assert prior74_lower > 1 and kappa > reported74 + bridge = finite_bridge(p['W']) + validate_bridge(bridge, p['W']) + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/indexed-cycle/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr79_commit='9a58e62cf9e8954a4dde3c9b1372d733c276a6d1', + pr74_commit='3f78d8967c009153f2df5c6a6577b6ab1d37e2ca', reported_pr74_kappa=reported74, + ratio_reported_pr74=kappa/reported74, pr74_complete_profile_exclusion_lower=prior74_lower, + pr79_kappa=previous_kappa, ratio_pr79=kappa/previous_kappa, + absolute_gain_pr79=kappa-previous_kappa, + pr79_complete_profile_exclusion_lower=prior71_lower, + full_pr79_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected indexed-cycle partition and point permutation, PR74 node order, natural execution, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring, PR69 balanced coarse sums, future unit completion and bounded PR70-derived single exchanges and two-cycles, exact frame indices, late-output routing and PR74/78-inspired coordinate relabeling; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'indexed-cycle-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/scripts/experiments/indexed_cycle_engine.py b/scripts/experiments/indexed_cycle_engine.py new file mode 100644 index 0000000000..beb64af862 --- /dev/null +++ b/scripts/experiments/indexed_cycle_engine.py @@ -0,0 +1,407 @@ +# Bounded carry exchanges adapted from Alejandro Zarzuelo Urdiales PR70. +# Exact integer entropy discovery scores replace floating moment prices. +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']) + if s in retired: + retired_index.remove(s,blocks[old]['frame'],blocks[old]['rank']);retired_index.insert(s,blocks[g]['frame'],blocks[g]['rank']) + if s in pending:pending_index.move(s,blocks[old]['frame'],blocks[g]['frame']) + hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]0 and carry_can(e,z) and carry_can(other,f):options.append((-gain,z,other)) + if not options:continue + _,z,other=min(options) + for old in (f,z): + og,ou,oi=edges[old];chosen.remove(old);blocks[og]['selected'].remove(old);del right[ou] + for new_edge in (e,other): + ng,nu,ni=edges[new_edge];assert nu not in right;chosen.add(new_edge);blocks[ng]['selected'].add(new_edge);right[nu]=new_edge + changes+=1 + stats['carry_two_cycles']+=changes + print('carry two-cycles',phase,changes,flush=True,file=sys.stderr) + if not changes:break + assert len(chosen)==len(right)==initial_count + assert sum(prices[e] for e in chosen)<=initial_price + for b in blocks:assert len(basis(b['outbasis']+[1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1];pending_index.insert(s,blocks[frames[s]]['frame'],blocks[pending[s]]['frame']) + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + first,mid,last = 0,(len(groups)-1)//2,len(groups)-1 + requested = {1:[first],2:[mid],3:[last],4:[first,mid],5:[first,last],6:[mid,last],7:[first,mid,last],8:[first,first+1],9:[last-1,last]}[choice] + chosen=[] + for k in requested: + if k not in chosen and 0<=k>i&1) + word['frames']=[[mask(c),mask(u)] for c,u in word['frames']] + word['sources']={str(mapping[int(i)]):slot for i,slot in word['sources'].items()} + scatter=[] + for a,b in word['scatter']: + assert v<=a<2*v and b>=2*v + scatter.append([v+mapping[a-v],b]) + word['scatter']=scatter + word['outputs']=[[s,g,permutation[common],triple(t)] for s,g,common,t in word['outputs']] + return word + + diff --git a/scripts/experiments/pin_aligned_composition_sources.py b/scripts/experiments/pin_aligned_composition_sources.py new file mode 100644 index 0000000000..828c6355f2 --- /dev/null +++ b/scripts/experiments/pin_aligned_composition_sources.py @@ -0,0 +1,43 @@ +#!/usr/bin/env python3 +"""Explicit immutable source and finite-input closure for the aligned-composition witness.""" +from hashlib import sha256 +import json +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2] +NAMES=('aligned_composition_graph.py','aligned_composition_compiler.py','aligned_composition_engine.py', + 'aligned_composition_nodeops.py','aligned_composition_compose.py','verify_aligned_composition.py', + 'pin_aligned_composition_sources.py','split_pair_arithmetic.py','joint_dual_reclaim_compiler.py', + 'binary_frame_math.py','binary_frame_replay.py','binary_frame_profile_prepare.py','binary_frame_profiles.cpp', + 'audit_aligned_composition_completion.py','audit_aligned_composition_exchange.py','audit_aligned_composition_cycles.py', + 'audit_aligned_composition_retired.py','audit_aligned_composition_pending.py','audit_aligned_composition_three_cycles.py','audit_aligned_composition_pricing.py','audit_aligned_composition_lean.py') + +def required_paths(): + names={'scripts/experiments/'+n for n in NAMES} + names.update(('.gitattributes','Makefile','README.md','NOTICE','.github/workflows/verify.yml', + 'tests/test_aligned_composition.py','tests/test_aligned_composition_coordinates.py','tests/test_aligned_composition_order.py','tests/test_aligned_composition_partitions.py', + 'research/aligned-composition/README.md','research/aligned-composition/PROOF.md', + 'research/aligned-composition/parameters.json','research/aligned-composition/engine-provenance.json', + 'research/aligned-composition/discovery-selection.json','research/aligned-composition/word-bindings.json','research/aligned-composition/discovery-source-audit.json','research/aligned-composition/selected-discovery-clearance.json', + 'research/aligned-composition/reported-comparisons.json','certificates/aligned-composition-compiler.json')) + for h in (23,25): + names.update((f'research/aligned-composition/config-{h}.json',f'research/aligned-composition/parent-result-{h}.json',f'research/aligned-composition/scalar-{h}.json')) + names.update(f'certificates/aligned-composition-{kind}-{h}.{ext}' for kind,ext in (('word','json.gz'),('profiles','json'),('transitions','json'))) + for prior in ('pr48','pr59-split-operation','pr65','pr67','pr68','pr69','pr70','pr71','pr74','pr78','pr79','pr82','pr84','pr88','pr74-aligned','indexed-r5','final-r10','aligned-r11'): + path=Path('references/frame-compiler')/prior + manifest=json.loads((ROOT/path/'SOURCE.json').read_text()) + names.add(str(path/'SOURCE.json'));names.update(str(path/name) for name in manifest['files']) + names.update(str(p.relative_to(ROOT)) for p in (ROOT/'research/aligned-composition/lean').rglob('*') if p.is_file()) + names.update(('formal/lean/KappaCheck/AlignedFrameComposition.lean','formal/lean/KappaCheck.lean','formal/lean/AuditAll.lean','formal/lean/sources.py','formal/lean/SOURCES.md','scripts/check_lean_axioms.py','tests/test_lean_axiom_output.py')) + return names + +def run(): + manifest=dict(author='Chafik Boukhalfa with OpenAI Codex assistance', + pr88_construction='3ffd9b1dc7ef2978fa1831fe3850cd4f534aea70', + pr74_aligned_partition='428b5c167686b42a83f1abf7003c6d17aec561ea', + pr78_coordinate_flags='1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf', + discovery_selection_sha256='43a762adf17b2338b2d7ec486fd6eb17d00d1d221e7f1e4041711cbce9964ea7', + scope='Exact source and finite-input freeze; all original contributor archives remain immutable; derived arithmetic and validation receipts excluded.', + files={name:sha256((ROOT/name).read_bytes()).hexdigest() for name in sorted(required_paths())}) + (ROOT/'research/aligned-composition/SOURCE.json').write_text(json.dumps(manifest,indent=2,sort_keys=True)+'\n') + print('Pinned',len(manifest['files']),'sources and finite inputs') +if __name__=='__main__':run() diff --git a/scripts/experiments/pin_balanced_split_sources.py b/scripts/experiments/pin_balanced_split_sources.py new file mode 100644 index 0000000000..a4bc483ecc --- /dev/null +++ b/scripts/experiments/pin_balanced_split_sources.py @@ -0,0 +1,53 @@ +#!/usr/bin/env python3 +"""Explicit source and finite-input freeze for the selected split/pair witness.""" +from hashlib import sha256 +import json +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +NAMES = ('balanced_split_graph.py', 'balanced_split_compiler.py', 'split_pair_arithmetic.py', + 'balanced_split_engine.py', 'balanced_split_exchange_engine.py', + 'balanced_split_compose.py', 'audit_balanced_split_completion.py', 'audit_balanced_split_exchange.py', + 'split_pair_engine.py', 'verify_balanced_split.py', 'pin_balanced_split_sources.py', + 'joint_dual_reclaim_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp') + + +def required_paths(): + names = {'scripts/experiments/'+name for name in NAMES} + names.update(('.gitattributes', 'Makefile', 'README.md', 'NOTICE', '.github/workflows/verify.yml', 'research/balanced-split/README.md', + 'research/balanced-split/PROOF.md', 'research/balanced-split/parameters.json', + 'research/balanced-split/engine-provenance.json', 'research/balanced-split/engine-relocation-23.patch', + 'research/balanced-split/engine-relocation-25.patch', + 'tests/test_balanced_split.py', 'tests/test_balanced_split_pending.py', + 'certificates/balanced-split-compiler.json')) + for h in (23,25): + names.add(f'research/balanced-split/config-{h}.json') + names.update(f'certificates/balanced-split-{kind}-{h}.{extension}' + for kind,extension in (('word','json.gz'),('profiles','json'),('transitions','json'))) + for prior in ('48', '59-split-operation', '65', '67', '68', '69', '70', '71'): + relative = Path('references/frame-compiler/pr'+prior) + manifest = json.loads((ROOT/relative/'SOURCE.json').read_text()) + names.add(str(relative/'SOURCE.json')) + names.update(str(relative/name) for name in manifest['files']) + return names + + +def run(): + result = dict( + baseline_pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113', + coarse_pr69_commit='91aa1f17e6e3fc063241686a41a34ddd0dc24c50', + exchange_pr70_commit='98147912b80a2656da0416487be53f1f5e8dfdcc', + baseline_pr65_commit='49e84f939d15b618b50714eb039cabf97c74256a', + profile_cost_pr67_commit='b3745601e947a94316bf25c2c6263d93c06e3364', + pending_live_pr68_commit='734c58e225e9d2254570c3b50296ed96943f62ea', + split_operation_pr59_commit='641f22e52913db784f3b6ff1176b0c2945aae45b', + author='Chafik Boukhalfa with OpenAI Codex assistance', + scope='Explicit source and finite-input freeze. Credited contributor originals and complete published PR71 physical/arithmetic baseline are preserved. Exact composition and validation receipts are derived.', + files={name:sha256((ROOT/name).read_bytes()).hexdigest() for name in sorted(required_paths())}) + (ROOT/'research/balanced-split/SOURCE.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + return len(result['files']) + + +if __name__ == '__main__': + print('Pinned',run(),'sources and finite inputs') diff --git a/scripts/experiments/pin_final_frame_sources.py b/scripts/experiments/pin_final_frame_sources.py new file mode 100644 index 0000000000..9d29bab4b9 --- /dev/null +++ b/scripts/experiments/pin_final_frame_sources.py @@ -0,0 +1,41 @@ +#!/usr/bin/env python3 +"""Explicit immutable source and finite-input closure for the final-frame witness.""" +from hashlib import sha256 +import json +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2] +NAMES=('final_frame_graph.py','final_frame_compiler.py','final_frame_engine.py', + 'final_frame_nodeops.py','final_frame_compose.py','verify_final_frame.py', + 'pin_final_frame_sources.py','split_pair_arithmetic.py','joint_dual_reclaim_compiler.py', + 'binary_frame_math.py','binary_frame_replay.py','binary_frame_profile_prepare.py','binary_frame_profiles.cpp', + 'audit_final_frame_completion.py','audit_final_frame_exchange.py','audit_final_frame_cycles.py', + 'audit_final_frame_retired.py','audit_final_frame_pending.py','audit_final_frame_three_cycles.py','audit_final_frame_pricing.py') + +def required_paths(): + names={'scripts/experiments/'+n for n in NAMES} + names.update(('.gitattributes','Makefile','README.md','NOTICE','.github/workflows/verify.yml', + 'tests/test_final_frame.py','tests/test_final_frame_coordinates.py','tests/test_final_frame_order.py', + 'research/final-frame/README.md','research/final-frame/PROOF.md', + 'research/final-frame/parameters.json','research/final-frame/engine-provenance.json', + 'research/final-frame/discovery-selection.json','research/final-frame/word-bindings.json','research/final-frame/discovery-source-audit.json','research/final-frame/selected-discovery-clearance.json', + 'research/final-frame/reported-comparisons.json','certificates/final-frame-compiler.json')) + for h in (23,25): + names.update((f'research/final-frame/config-{h}.json',f'research/final-frame/parent-result-{h}.json',f'research/final-frame/scalar-{h}.json')) + names.update(f'certificates/final-frame-{kind}-{h}.{ext}' for kind,ext in (('word','json.gz'),('profiles','json'),('transitions','json'))) + for prior in ('pr48','pr59-split-operation','pr65','pr67','pr68','pr69','pr70','pr71','pr74','pr78','pr79','pr82','pr84','indexed-r5','final-r10'): + path=Path('references/frame-compiler')/prior + manifest=json.loads((ROOT/path/'SOURCE.json').read_text()) + names.add(str(path/'SOURCE.json'));names.update(str(path/name) for name in manifest['files']) + return names + +def run(): + manifest=dict(author='Chafik Boukhalfa with OpenAI Codex assistance', + pr84_construction='88ca39571907343a49e97f328971ec7bcd26fbfd', + pr74_node_order='3f78d8967c009153f2df5c6a6577b6ab1d37e2ca', + pr78_coordinate_flags='1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf', + discovery_selection_sha256='c05715807ad48d2c292f6e3431c338c39d4e7ae80b9758a8c3f8ace520178e23', + scope='Exact source and finite-input freeze; all original contributor archives remain immutable; derived arithmetic and validation receipts excluded.', + files={name:sha256((ROOT/name).read_bytes()).hexdigest() for name in sorted(required_paths())}) + (ROOT/'research/final-frame/SOURCE.json').write_text(json.dumps(manifest,indent=2,sort_keys=True)+'\n') + print('Pinned',len(manifest['files']),'sources and finite inputs') +if __name__=='__main__':run() diff --git a/scripts/experiments/pin_indexed_cycle_sources.py b/scripts/experiments/pin_indexed_cycle_sources.py new file mode 100644 index 0000000000..bd6d24e93b --- /dev/null +++ b/scripts/experiments/pin_indexed_cycle_sources.py @@ -0,0 +1,41 @@ +#!/usr/bin/env python3 +"""Explicit immutable source and finite-input closure for the indexed-cycle witness.""" +from hashlib import sha256 +import json +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2] +NAMES=('indexed_cycle_graph.py','indexed_cycle_compiler.py','indexed_cycle_engine.py', + 'indexed_cycle_nodeops.py','indexed_cycle_compose.py','verify_indexed_cycle.py', + 'pin_indexed_cycle_sources.py','split_pair_arithmetic.py','joint_dual_reclaim_compiler.py', + 'binary_frame_math.py','binary_frame_replay.py','binary_frame_profile_prepare.py','binary_frame_profiles.cpp', + 'audit_indexed_cycle_completion.py','audit_indexed_cycle_exchange.py','audit_indexed_cycle_cycles.py', + 'audit_indexed_cycle_retired.py','audit_indexed_cycle_pending.py') + +def required_paths(): + names={'scripts/experiments/'+n for n in NAMES} + names.update(('.gitattributes','Makefile','README.md','NOTICE','.github/workflows/verify.yml', + 'tests/test_indexed_cycle.py','tests/test_indexed_cycle_coordinates.py', + 'research/indexed-cycle/README.md','research/indexed-cycle/PROOF.md', + 'research/indexed-cycle/parameters.json','research/indexed-cycle/engine-provenance.json', + 'research/indexed-cycle/discovery-selection.json','research/indexed-cycle/coordinate-search.py', + 'research/indexed-cycle/reported-comparisons.json','certificates/indexed-cycle-compiler.json')) + for h in (23,25): + names.update((f'research/indexed-cycle/config-{h}.json',f'research/indexed-cycle/parent-result-{h}.json')) + names.update(f'certificates/indexed-cycle-{kind}-{h}.{ext}' for kind,ext in (('word','json.gz'),('profiles','json'),('transitions','json'))) + for prior in ('pr48','pr59-split-operation','pr65','pr67','pr68','pr69','pr70','pr71','pr74','pr78','pr79','indexed-r5'): + path=Path('references/frame-compiler')/prior + manifest=json.loads((ROOT/path/'SOURCE.json').read_text()) + names.add(str(path/'SOURCE.json'));names.update(str(path/name) for name in manifest['files']) + return names + +def run(): + manifest=dict(author='Chafik Boukhalfa with OpenAI Codex assistance', + pr79_construction='9a58e62cf9e8954a4dde3c9b1372d733c276a6d1', + pr74_node_order='3f78d8967c009153f2df5c6a6577b6ab1d37e2ca', + pr78_coordinate_flags='1c1f1e4ee87a6895eaea622e1a33dcd4b0aa62cf', + discovery_selection_sha256='7bfb5b01851f3f80cb1946bb691383d0861f9801043ceb866ed43c86b45bac8a', + scope='Exact source and finite-input freeze; all original contributor archives remain immutable; derived arithmetic and validation receipts excluded.', + files={name:sha256((ROOT/name).read_bytes()).hexdigest() for name in sorted(required_paths())}) + (ROOT/'research/indexed-cycle/SOURCE.json').write_text(json.dumps(manifest,indent=2,sort_keys=True)+'\n') + print('Pinned',len(manifest['files']),'sources and finite inputs') +if __name__=='__main__':run() diff --git a/scripts/experiments/pin_split_pair_sources.py b/scripts/experiments/pin_split_pair_sources.py new file mode 100644 index 0000000000..879d6699dc --- /dev/null +++ b/scripts/experiments/pin_split_pair_sources.py @@ -0,0 +1,48 @@ +#!/usr/bin/env python3 +"""Explicit source and finite-input freeze for the selected split/pair witness.""" +from hashlib import sha256 +import json +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +NAMES = ('split_pair_graph.py', 'split_pair_compiler.py', 'split_pair_arithmetic.py', + 'split_pair_engine.py', + 'split_pair_compose.py', 'verify_split_pair.py', 'pin_split_pair_sources.py', + 'joint_dual_reclaim_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp') + + +def required_paths(): + names = {'scripts/experiments/'+name for name in NAMES} + names.update(('Makefile', 'README.md', 'NOTICE', 'research/split-pair/README.md', + 'research/split-pair/PROOF.md', 'research/split-pair/parameters.json', + 'research/split-pair/engine-provenance.json', 'research/split-pair/engine-changes.patch', + 'tests/test_split_pair.py', 'tests/test_split_pair_pending.py', + 'certificates/split-pair-compiler.json')) + for h in (23,25): + names.add(f'research/split-pair/config-{h}.json') + names.update(f'certificates/split-pair-{kind}-{h}.{extension}' + for kind,extension in (('word','json.gz'),('profiles','json'),('transitions','json'))) + for prior in ('48', '59-split-operation', '65', '67', '68'): + relative = Path('references/frame-compiler/pr'+prior) + manifest = json.loads((ROOT/relative/'SOURCE.json').read_text()) + names.add(str(relative/'SOURCE.json')) + names.update(str(relative/name) for name in manifest['files']) + return names + + +def run(): + result = dict( + baseline_pr65_commit='49e84f939d15b618b50714eb039cabf97c74256a', + profile_cost_pr67_commit='b3745601e947a94316bf25c2c6263d93c06e3364', + pending_live_pr68_commit='734c58e225e9d2254570c3b50296ed96943f62ea', + split_operation_pr59_commit='641f22e52913db784f3b6ff1176b0c2945aae45b', + author='Chafik Boukhalfa with OpenAI Codex assistance', + scope='Explicit source and finite-input freeze. Credited contributor originals and complete published PR65 physical/arithmetic baseline are preserved. Exact composition and validation receipts are derived.', + files={name:sha256((ROOT/name).read_bytes()).hexdigest() for name in sorted(required_paths())}) + (ROOT/'research/split-pair/SOURCE.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + return len(result['files']) + + +if __name__ == '__main__': + print('Pinned',run(),'sources and finite inputs') diff --git a/scripts/experiments/split_pair_arithmetic.py b/scripts/experiments/split_pair_arithmetic.py new file mode 100644 index 0000000000..a34aeb543b --- /dev/null +++ b/scripts/experiments/split_pair_arithmetic.py @@ -0,0 +1,39 @@ +"""Private adapters for the unchanged PR65 directed arithmetic and audit.""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode = True + +import importlib.util +from pathlib import Path + +BASELINE = Path(__file__).resolve().parents[2] / 'references/frame-compiler/pr65' + + +def _load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + module = importlib.util.module_from_spec(spec) + spec.loader.exec_module(module) + return module + + +def private_arithmetic(): + here = BASELINE / 'research/reordered-rank-pair/arithmetic' + previous_path = sys.path[:] + absent = object() + previous_refine = sys.modules.get('refine', absent) + try: + refine = _load('split_pair_private_refine', here / 'refine.py') + sys.modules['refine'] = refine + audit = _load('split_pair_private_arithmetic_audit', here / 'audit.py') + assert audit.refine is refine + return refine, audit + finally: + sys.path[:] = previous_path + if previous_refine is absent: + sys.modules.pop('refine', None) + else: + sys.modules['refine'] = previous_refine + + +refine, audit = private_arithmetic() diff --git a/scripts/experiments/split_pair_compiler.py b/scripts/experiments/split_pair_compiler.py new file mode 100644 index 0000000000..1ebfc5c752 --- /dev/null +++ b/scripts/experiments/split_pair_compiler.py @@ -0,0 +1,90 @@ +#!/usr/bin/env python3 +"""Compile aligned split frames with profile-cost pending live reclamation.""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode = True + +import argparse +import gzip +from hashlib import sha256 +import json +from pathlib import Path +import os +import shlex +import subprocess +import tempfile + +import split_pair_engine as compiler +import split_pair_graph as producer + +ROOT = Path(__file__).resolve().parents[2] + + +def source_record(): + return dict(pr65=producer.checked_manifest(producer.BASELINE), + pr67=producer.checked_manifest(ROOT / 'references/frame-compiler/pr67'), + pr68=producer.checked_manifest(ROOT / 'references/frame-compiler/pr68'), + inherited=producer.checked_manifest(ROOT / 'references/frame-compiler/pr48')) + + +def compile_axis(h): + config = producer.configuration(h) + provenance = json.loads((ROOT/'research/split-pair/engine-provenance.json').read_text()) + assert sha256(Path(compiler.__file__).read_bytes()).hexdigest() == provenance['portable_engine_sha256'], 'Selected engine changed' + previous_graph, previous_build = compiler.graph, compiler.build + absent = object() + runtime_names = ('oracles', 'ORACLE_EXE', 'ORACLE_INPUT', 'PENDING_COST') + previous_runtime = {name:getattr(compiler, name, absent) for name in runtime_names} + try: + compiler.graph = producer.graph + compiler.build = producer.ordered_build(previous_build, h) + compiler.PENDING_COST = True + with tempfile.TemporaryDirectory(prefix='split-pair-compile-') as directory: + work = Path(directory) + oracle = work/'profile-oracle' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'), + str(ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/profile_oracle.cpp'), + '-o', str(oracle)], check=True) + compiler.oracles = [] + compiler.ORACLE_EXE, compiler.ORACLE_INPUT = str(oracle), str(work/'oracle-input.bin') + try: + result, word = compiler.compile_(h, matching=True, reclaim=True, dirty=True) + finally: + for process in compiler.oracles: + process.stdin.close() + assert process.wait(timeout=10) == 0, 'Discovery profile oracle failed' + finally: + compiler.graph, compiler.build = previous_graph, previous_build + for name, value in previous_runtime.items(): + if value is absent: + if hasattr(compiler, name): + delattr(compiler, name) + else: + setattr(compiler, name, value) + result.pop('seconds', None) + result['scalar'] = producer.graph(h).verify() + result['graph_configuration'] = config + result['source_pr65_head'] = source_record()['pr65']['commit'] + result['baseline_pr65_roles'] = {23: 27918, 25: 36586}[h] + result['source_pr67_head'] = source_record()['pr67']['commit'] + result['source_pr68_head'] = source_record()['pr68']['commit'] + result['reclamation_order'] = 'all eligible retired ranks, exact integer profile cost, XOR count, slot ID' + result['pending_live_controls'] = True + result['pending_cost_uses_next_use_frame'] = True + result['paid_clones'] = 0 + return result, word + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--h', type=int, choices=(23, 25), required=True) + parser.add_argument('--output', type=Path, required=True) + parser.add_argument('--word', type=Path, required=True) + args = parser.parse_args() + result, word = compile_axis(args.h) + raw = (json.dumps(word, separators=(',', ':')) + '\n').encode() + args.word.write_bytes(gzip.compress(raw, mtime=0) if args.word.suffix == '.gz' else raw) + args.output.write_text(json.dumps(result, indent=2) + '\n') + print(json.dumps(result), flush=True) diff --git a/scripts/experiments/split_pair_compose.py b/scripts/experiments/split_pair_compose.py new file mode 100644 index 0000000000..e08ce74f33 --- /dev/null +++ b/scripts/experiments/split_pair_compose.py @@ -0,0 +1,161 @@ +"""Complete paid split/pair profile and PR65's exact refined balanced assembly. + +The unchanged full physical words determine every auxiliary multiplicity. +Only fixed-basis finite claims are certified; all-size transfer remains inherited. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode = True + +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import gzip +import json + +import binary_frame_math as arithmetic +from split_pair_arithmetic import refine, audit +from split_pair_graph import checked_manifest +from split_pair_compiler import source_record +from pin_split_pair_sources import required_paths + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +OUT = ROOT / 'certificates' +INHERITED = ROOT / 'references/frame-compiler/pr48' +OLD = INHERITED / 'research/copied-fixed' +BASELINE = ROOT / 'references/frame-compiler/pr65' +BASELINE_CASE = BASELINE / 'research/reordered-rank-pair' +PROFILE_BASELINE = ROOT / 'references/frame-compiler/pr67/research/slot-cost-rank-pair' + + +def check_sources(): + sources = source_record() + operation = ROOT / 'references/frame-compiler/pr59-split-operation' + checked_manifest(operation) + local = json.loads((ROOT/'research/split-pair/SOURCE.json').read_text()) + assert required_paths() <= set(local['files']), 'Incomplete source/finite-input closure' + for name, digest in local['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + engine = ROOT / 'scripts/experiments/joint_dual_reclaim_compiler.py' + assert engine.read_bytes() == (BASELINE/'scripts/experiments/rank_pair_compiler.py').read_bytes() + provenance = json.loads((ROOT/'research/split-pair/engine-provenance.json').read_text()) + assert sha256((HERE/'split_pair_engine.py').read_bytes()).hexdigest() == provenance['portable_engine_sha256'] + for name in ('binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp'): + assert (HERE/name).read_bytes() == (BASELINE/'scripts/experiments'/name).read_bytes() + return dict(sources, split_operation=checked_manifest(operation)) + + +def profile(): + parameters = json.loads((ROOT/'research/split-pair/parameters.json').read_text()) + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + profiles = [json.loads((OUT / f'split-pair-profiles-{h}.json').read_text()) for h in (a, b)] + words = json.loads((OUT / 'split-pair-compiler.json').read_text()) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + receipts = [] + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + recorded = words['axes'][str(h)] + replay = recorded['replay'] + receipt = json.loads((OUT / f'split-pair-transitions-{h}.json').read_text()) + for key in ('h', 'v', 'R'): + assert f[key] == receipt[key] + assert f['R'] == replay['roles'] == recorded['compiled']['roles'] == parameters['roles'][str(h)] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == receipt['rank_mass'] == replay['rank_mass'] + assert f['blocks'][0] == 0 and f['blocks'][h] == 0 # Positive children; copied centers already included. + assert receipt['transition_events_equal_independent_xor_word_reconstruction'] + packed = (OUT / f'split-pair-word-{h}.json.gz').read_bytes() + assert sha256(packed).hexdigest() == recorded['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == recorded['word_sha256'] == receipt['word_sha256'] + histogram = {str(k): v for k, v in replay['histogram'].items() if int(k)} + side = replay['output_roles']-h + histogram['2'] -= side + histogram['1'] += 2*side + assert histogram == receipt['rank_histogram_with_side_growth_split_into_singletons'] + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + receipts.append(receipt) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (parameters['W'], parameters['total_rank'], 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, + maxchild=max(rows), child_multiplicities=dict(sorted(rows.items())), + parts=parts, axes=profiles, words=receipts) + + +def compose(): + sources = check_sources() + parameters = json.loads((ROOT/'research/split-pair/parameters.json').read_text()) + bit_saving, kappa = Q(parameters['bit_saving']), Q(parameters['kappa']) + denominator = parameters['grid_denominator'] + assert type(denominator) is int and denominator == 10**18 + grid = Q(1, denominator) + assert json.loads((OUT/'split-pair-compiler.json').read_text())['source'] == source_record() + p = profile() + exact = refine.exact_moment(p['m'], p['W'], p['child_multiplicities'], bit_saving) + excluded = refine.exact_moment(p['m'], p['W'], p['child_multiplicities'], bit_saving+grid) + assert exact['upper'] < 1 < excluded['lower'] + independent = audit.independent_moment(arithmetic.js(p), bit_saving, arithmetic.js(exact['terms'])) + independent_rejected = audit.independent_moment(arithmetic.js(p), bit_saving+grid, arithmetic.js(exact['terms'])) + assert independent[1] < 1 < independent_rejected[0] + prior65 = json.loads((PROFILE_BASELINE/'arithmetic/certificate.json').read_text()) + oldprofile = json.loads((PROFILE_BASELINE/'paired-candidate.json').read_text()) + oldbit = oldprofile['bit'] + previous_kappa = Q(prior65['preferred']['kappa']) + previous_rows = {int(t): n for t,n in oldbit['child_multiplicities'].items()} + prior65_lower = refine.exact_moment(oldbit['m'], oldbit['W'], previous_rows, bit_saving)['lower'] + assert prior65_lower > 1 and kappa > previous_kappa + bridge = json.loads((OLD/'certificate.json').read_text())['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/split-pair/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr67_commit='b3745601e947a94316bf25c2c6263d93c06e3364', + pr67_kappa=previous_kappa, ratio_pr67=kappa/previous_kappa, + absolute_gain_pr67=kappa-previous_kappa, + pr67_complete_profile_exclusion_lower=prior65_lower, + full_pr67_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected split-pair partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'split-pair-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/scripts/experiments/split_pair_engine.py b/scripts/experiments/split_pair_engine.py new file mode 100644 index 0000000000..1290ef2eb8 --- /dev/null +++ b/scripts/experiments/split_pair_engine.py @@ -0,0 +1,275 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/scripts/experiments/verify_aligned_composition.py b/scripts/experiments/verify_aligned_composition.py new file mode 100644 index 0000000000..0fb9b6bd37 --- /dev/null +++ b/scripts/experiments/verify_aligned_composition.py @@ -0,0 +1,80 @@ +#!/usr/bin/env python3 +"""Replay the aligned aligned-composition/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import os +import shlex +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from aligned_composition_compose import compose, check_sources +from aligned_composition_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'aligned-composition-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='aligned-composition-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + *shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'aligned-composition-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'aligned-composition-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'aligned-composition-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'aligned-composition-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'aligned-composition-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/scripts/experiments/verify_balanced_split.py b/scripts/experiments/verify_balanced_split.py new file mode 100644 index 0000000000..67e084e583 --- /dev/null +++ b/scripts/experiments/verify_balanced_split.py @@ -0,0 +1,80 @@ +#!/usr/bin/env python3 +"""Replay the aligned balanced-split/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import os +import shlex +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from balanced_split_compose import compose, check_sources +from balanced_split_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'balanced-split-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='balanced-split-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + *shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'balanced-split-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'balanced-split-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'balanced-split-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'balanced-split-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'balanced-split-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/scripts/experiments/verify_final_frame.py b/scripts/experiments/verify_final_frame.py new file mode 100644 index 0000000000..53da533237 --- /dev/null +++ b/scripts/experiments/verify_final_frame.py @@ -0,0 +1,80 @@ +#!/usr/bin/env python3 +"""Replay the aligned final-frame/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import os +import shlex +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from final_frame_compose import compose, check_sources +from final_frame_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'final-frame-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='final-frame-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + *shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'final-frame-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'final-frame-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'final-frame-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'final-frame-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'final-frame-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/scripts/experiments/verify_indexed_cycle.py b/scripts/experiments/verify_indexed_cycle.py new file mode 100644 index 0000000000..89ea4fa992 --- /dev/null +++ b/scripts/experiments/verify_indexed_cycle.py @@ -0,0 +1,80 @@ +#!/usr/bin/env python3 +"""Replay the aligned indexed-cycle/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import os +import shlex +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from indexed_cycle_compose import compose, check_sources +from indexed_cycle_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'indexed-cycle-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='indexed-cycle-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + *shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'indexed-cycle-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'indexed-cycle-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'indexed-cycle-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'indexed-cycle-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'indexed-cycle-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/scripts/experiments/verify_split_pair.py b/scripts/experiments/verify_split_pair.py new file mode 100644 index 0000000000..7908c963a4 --- /dev/null +++ b/scripts/experiments/verify_split_pair.py @@ -0,0 +1,78 @@ +#!/usr/bin/env python3 +"""Replay the aligned split-pair/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from split_pair_compose import compose, check_sources +from split_pair_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'split-pair-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='split-pair-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + 'c++', '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'split-pair-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'split-pair-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'split-pair-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'split-pair-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'split-pair-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/tests/test_aligned_composition.py b/tests/test_aligned_composition.py new file mode 100644 index 0000000000..e5d78d1703 --- /dev/null +++ b/tests/test_aligned_composition.py @@ -0,0 +1,248 @@ +"""Physical and exact-arithmetic controls for the aligned split/pair witness.""" +from copy import deepcopy +from fractions import Fraction +from itertools import combinations +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile +import unittest +from unittest.mock import patch + +ROOT = Path(__file__).resolve().parents[1] +EXPERIMENTS = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXPERIMENTS)) +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from binary_frame_math import moment + + +class SplitPairControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.words = {h: json.loads(gzip.decompress((ROOT/f'certificates/aligned-composition-word-{h}.json.gz').read_bytes())) + for h in (23,25)} + + def reject_mutation(self, mutate, checker='both'): + for h, original in self.words.items(): + with self.subTest(h=h), tempfile.TemporaryDirectory() as directory: + changed = deepcopy(original) + mutate(changed) + path = Path(directory)/'word.json' + path.write_text(json.dumps(changed, separators=(',', ':'))+'\n') + with self.assertRaises((AssertionError, ValueError, IndexError, KeyError)): + if checker != 'transitions': + replay(path) + if checker != 'replay': + prepare(path, Path(directory)/'transitions.bin') + + def test_selected_words_pass_independent_replay(self): + recorded = json.loads((ROOT/'certificates/aligned-composition-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + actual = replay(ROOT/f'certificates/aligned-composition-word-{h}.json.gz') + self.assertEqual(json.loads(json.dumps(actual)), recorded['axes'][str(h)]['replay']) + + def test_omitted_literal_xor_is_rejected(self): + self.reject_mutation(lambda word: word['ops'].pop(0)) + + def test_self_xor_is_rejected(self): + def mutate(word): + word['ops'][0][1] = word['ops'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_non_nested_operation_frame_is_rejected(self): + def mutate(word): + narrow = next(i for i,(core,cover) in enumerate(word['frames']) if core == cover) + operation = next(op for op in word['ops'] if word['frames'][op[2]][0] != word['frames'][op[2]][1]) + operation[2] = narrow + self.reject_mutation(mutate) + + def test_aliased_terminal_role_is_rejected(self): + def mutate(word): + word['outputs'][1][0] = word['outputs'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_missing_copied_center_is_rejected(self): + def mutate(word): + index = next(i for i,(_,_,_,target) in enumerate(word['outputs']) if len(target) == 1) + word['outputs'].pop(index) + self.reject_mutation(mutate) + + def test_omitted_transition_cannot_reduce_paid_profile(self): + self.reject_mutation(lambda word: word['events'].pop(0), 'transitions') + + def test_understated_physical_width_is_rejected(self): + def mutate(word): + word['R'] -= 1 + self.reject_mutation(mutate) + + def test_complete_pr88_profile_fails_new_bit_saving(self): + from split_pair_arithmetic import refine + previous = json.loads((ROOT/'references/frame-compiler/pr88/certificates/final-frame-kappa.json').read_text())['bit'] + current = json.loads((ROOT/'certificates/aligned-composition-kappa.json').read_text()) + result = refine.exact_moment(previous['m'], previous['W'], {int(t): n for t,n in previous['child_multiplicities'].items()}, Fraction(current['bit_saving'])) + self.assertGreater(result['lower'], 1) + self.assertGreater(Fraction(current['kappa']), Fraction(current['comparison']['pr88_kappa'])) + + def test_private_import_preserves_path_and_arithmetic_module(self): + import aligned_composition_graph as provider + import split_pair_arithmetic as arithmetic + sentinel = object() + existing = sys.modules.get('refine', sentinel) + previous_path = sys.path[:] + graph, schedule = provider._private_modules() + refine, audit = arithmetic.private_arithmetic() + self.assertIs(audit.refine, refine) + self.assertIs(sys.modules.get('refine', sentinel), existing) + self.assertEqual(sys.path, previous_path) + + def test_failed_graph_build_restores_original_providers(self): + import aligned_composition_graph as provider + previous_class, previous_points = provider._graph.circuit_class, provider._graph.alternating_points + with patch.object(provider._graph, 'graph', side_effect=RuntimeError('deliberate graph failure')): + with self.assertRaises(RuntimeError): + provider.graph(23) + self.assertIs(provider._graph.circuit_class, previous_class) + self.assertIs(provider._graph.alternating_points, previous_points) + + def test_failed_compilation_restores_engine_graph_and_schedule(self): + import aligned_composition_compiler as producer + previous_graph, previous_build = producer.ENGINES[23].graph, producer.ENGINES[23].build + missing = object() + runtime = {name:getattr(producer.ENGINES[23],name,missing) for name in ('PENDING_COST','ORACLE_EXE','ORACLE_INPUT','oracles','OUTPUT_MODE','ORACLE_COORDINATES','THREE_CYCLE_PASSES')} + with patch.object(producer.ENGINES[23], 'compile_', side_effect=RuntimeError('deliberate compiler failure')): + with self.assertRaises(RuntimeError): + producer.compile_axis(23) + self.assertIs(producer.ENGINES[23].graph, previous_graph) + self.assertIs(producer.ENGINES[23].build, previous_build) + for name,value in runtime.items(): + self.assertIs(getattr(producer.ENGINES[23],name,missing),value) + + def test_uncertified_configurations_are_rejected(self): + import aligned_composition_graph as provider + wrong_anchor = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_anchor['anchor'] = False + boolean_group = deepcopy(provider.EXPECTED_CONFIGS[23]); boolean_group['groups'][0] = True + changed_schedule = deepcopy(provider.EXPECTED_CONFIGS[23]); changed_schedule['schedule'] = 'reverse-node' + wrong_coarse = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_coarse['coarse'] = 'row' + omitted_completion = deepcopy(provider.EXPECTED_CONFIGS[23]); omitted_completion['future_completion'] = False + extra_exchanges = deepcopy(provider.EXPECTED_CONFIGS[23]); extra_exchanges['carry_exchange_passes'] = 4 + wrong_route = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_route['output_mode'] = 'route-late' + wrong_permutation = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_permutation['coordinate_permutation'][0] = True + extra_cycles = deepcopy(provider.EXPECTED_CONFIGS[23]); extra_cycles['carry_two_cycle_passes'] = 4 + wrong_order=deepcopy(provider.EXPECTED_CONFIGS[23]);wrong_order['node_order']='cover-minus-core-minus' + wrong_price=deepcopy(provider.EXPECTED_CONFIGS[23]);wrong_price['oracle_coordinate_pricing']=0 + wrong_three=deepcopy(provider.EXPECTED_CONFIGS[23]);wrong_three['three_cycle_passes']=False + for changed in (wrong_anchor, boolean_group, changed_schedule, wrong_coarse, omitted_completion, extra_exchanges,wrong_route,wrong_permutation,extra_cycles,wrong_order,wrong_price,wrong_three): + with self.subTest(configuration=changed), patch.object(provider.json, 'loads', return_value=changed): + with self.assertRaises(ValueError): + provider.configuration(23) + for dimension in (True, 22, 24, '23'): + with self.subTest(dimension=dimension), self.assertRaises(ValueError): + provider.configuration(dimension) + + def test_recursive_weighted_exclusions_and_contraction(self): + import aligned_composition_graph as provider + for h in (23,25): + block_sizes = [] + parent = provider._graphs[h].circuit_class(h) + selected = provider.split_class(parent, provider.configuration(h)['groups']) + case = self + class Audited(selected): + def grouping(self, points): + groups = super().grouping(points) + case.assertEqual([x for group in groups for x in group], list(points)) + case.assertLess(len(groups), len(points)) + return groups + + def _block(self, points, edges, weights, level): + def expected(omitted): + values = [value for pair,value in edges.items() if not set(pair) & omitted] + values += [value for point,value in weights.items() if point not in omitted] + support = 0 + for value in values: + case.assertEqual(support & self.support[value], 0) + support |= self.support[value] + return support + total, single, pairs = super()._block(points, edges, weights, level) + case.assertEqual(self.support[total], expected(set())) + case.assertEqual(set(single), set(points)) + for a in points: + case.assertEqual(self.support[single[a]], expected({a})) + case.assertEqual(set(pairs), set(combinations(points,2))) + for a,b in combinations(points,2): + case.assertEqual(self.support[pairs[a,b]], expected({a,b})) + block_sizes.append(len(points)) + return total, single, pairs + local = Audited(h-1) + block_sizes.clear() + local.pair(list(range(h-1))) + self.assertEqual(max(block_sizes), h-1) + self.assertIn(2,block_sizes) + self.assertTrue(all(2<=n<=h-1 for n in block_sizes)) + + def test_next_fine_grid_points_and_old_assembly_controls_reject(self): + from split_pair_arithmetic import refine + current = json.loads((ROOT/'certificates/aligned-composition-kappa.json').read_text()) + bit = current['bit']; saving = Fraction(current['bit_saving']); kappa = Fraction(current['kappa']) + grid = Fraction(1,10**18) + rows = {int(t): n for t,n in bit['child_multiplicities'].items()} + self.assertLess(refine.exact_moment(bit['m'],bit['W'],rows,saving)['upper'], 1) + self.assertGreater(refine.exact_moment(bit['m'],bit['W'],rows,saving+grid)['lower'], 1) + for label, variant in ( + ('next_kappa', dict(kappa=kappa+grid)), + ('zero_backoff', dict(h=Fraction())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))): + call = dict(a_bit=saving, kappa=kappa, h=Fraction(1,10**12));call.update(variant) + with self.subTest(control=label), self.assertRaises(refine.balanced.InvalidAssembly): + refine.balanced.assembly(current['finite_bridge'], **call) + + def test_mass_preserving_profile_mutation_is_rejected(self): + from aligned_composition_compose import check_sources + profile_path = ROOT/'certificates/aligned-composition-profiles-23.json' + changed = json.loads(profile_path.read_text()) + before = sum(t*n for t,n in enumerate(changed['blocks'])) + changed['blocks'][2] += 3; changed['blocks'][3] -= 2 + self.assertTrue(all(n >= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'aligned-composition-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from aligned_composition_compose import check_sources + manifest_path = ROOT/'research/aligned-composition/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/aligned-composition-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_all_threshold_dependent_bridge_fields_are_checked(self): + from aligned_composition_compose import finite_bridge, validate_bridge + expected = finite_bridge(130417912) + self.assertTrue(validate_bridge(expected, 130417912)) + for section,key in (('bit','wire_bits'),('rows','coefficient'),('rows','degree'),('rows','degree_gap'),('rows','suffix_slope')): + changed = deepcopy(expected) + changed[section][key] = Fraction(changed[section][key])+1 + with self.subTest(field=section+'.'+key), self.assertRaisesRegex(AssertionError, 'Stale finite bridge'): + validate_bridge(changed, 130417912) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('aligned_composition_graph.py', 'aligned_composition_engine.py', 'aligned_composition_compiler.py', 'split_pair_arithmetic.py', 'aligned_composition_compose.py', 'verify_aligned_composition.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/tests/test_aligned_composition_coordinates.py b/tests/test_aligned_composition_coordinates.py new file mode 100644 index 0000000000..c9e80b4b33 --- /dev/null +++ b/tests/test_aligned_composition_coordinates.py @@ -0,0 +1,49 @@ +"""Bijection and adverse-coordinate controls for the actual PR74 relabel functions.""" +from pathlib import Path +from itertools import combinations +from copy import deepcopy +from hashlib import sha256 +import gzip,json,sys,unittest +ROOT=Path(__file__).resolve().parents[1];sys.path.insert(0,str(ROOT/'scripts/experiments')) +from aligned_composition_nodeops import relabel +from aligned_composition_graph import configuration + +class CoordinateControls(unittest.TestCase): + def test_selected_permutations_are_exact_integer_bijections(self): + for h in (23,25): + perm=configuration(h)['coordinate_permutation'] + self.assertEqual(sorted(perm),list(range(h))) + self.assertTrue(all(type(x) is int for x in perm)) + self.assertEqual(configuration(23)['coordinate_permutation'],[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 17, 19, 20, 21, 22, 0, 1, 3, 2, 4]) + + def test_every_selected_word_roundtrips_full_coordinate_inverse(self): + for h in (23,25): + word=json.loads(gzip.decompress((ROOT/f'certificates/aligned-composition-word-{h}.json.gz').read_bytes())) + perm=configuration(h)['coordinate_permutation'];inverse=[perm.index(i) for i in range(h)] + parent=relabel(deepcopy(word),inverse) + # Dict iteration and scatter order are deliberately retained by the actual function. + raw=(json.dumps(parent,separators=(',',':'))+'\n').encode() + selection=json.loads((ROOT/'research/aligned-composition/word-bindings.json').read_text())[str(h)] + self.assertEqual(sha256(raw).hexdigest(),selection['parent_word_sha256']) + self.assertEqual(relabel(parent,perm),word) + + def test_relabel_preserves_physical_operations_and_frame_inclusions(self): + h=5;triples=list(combinations(range(h),3));v=len(triples);perm=[4,0,2,1,3] + word=dict(h=h,v=v,frames=[[3,7],[1,31]],sources={str(i):i for i in range(v)}, + scatter=[[v+i,2*v+i] for i in reversed(range(v))],outputs=[[2*v+i,0,0,list(t)] for i,t in enumerate(triples)], + ops=[[2*v,2*v+1,0]],events=[[2*v,0,1]]) + changed=relabel(deepcopy(word),perm) + self.assertEqual(changed['ops'],word['ops']);self.assertEqual(changed['events'],word['events']) + self.assertEqual(set(map(int,changed['sources'])),set(range(v))) + self.assertEqual([b for a,b in changed['scatter']],[b for a,b in word['scatter']]) + self.assertEqual(set(a for a,b in changed['scatter']),set(range(v,2*v))) + (a,b),(c,d)=changed['frames'];self.assertEqual(c&~a,0);self.assertEqual(b&~d,0) + + def test_invalid_permutation_and_scatter_source_are_rejected(self): + word=dict(h=3,v=1,frames=[[1,7]],sources={'0':0},scatter=[[1,2]],outputs=[[2,0,0,[0,1,2]]]) + for permutation in ([0,1,1],[0,1],[0,1,3]): + with self.subTest(permutation=permutation),self.assertRaises(AssertionError):relabel(deepcopy(word),permutation) + word['scatter'][0][0]=0 + with self.assertRaises(AssertionError):relabel(word,[0,1,2]) + +if __name__=='__main__':unittest.main() diff --git a/tests/test_aligned_composition_order.py b/tests/test_aligned_composition_order.py new file mode 100644 index 0000000000..347b1c824f --- /dev/null +++ b/tests/test_aligned_composition_order.py @@ -0,0 +1,45 @@ +from pathlib import Path +from itertools import combinations +from copy import deepcopy +import importlib.util,json,unittest +import sys +sys.path.insert(0,str(Path(__file__).resolve().parents[1]/'scripts/experiments')) +from aligned_composition_nodeops import order_key,reorder,verify_dense,relabel +ROOT=Path(__file__).resolve().parents[1] +spec=importlib.util.spec_from_file_location('original',ROOT/'scripts/experiments/indexed_cycle_nodeops.py');original=importlib.util.module_from_spec(spec);spec.loader.exec_module(original) +KEYS=['pr74','cover-minus-core-minus'] +class Fake: + def __init__(self): + self.h=5;self.inputs=list(combinations(range(5),3));self.args=[None]*11;self.core=[0]+[sum(1<3 else [] + expected=[piece for i,g in enumerate(groups) for piece in ([[x] for x in g] if i in chosen else [g])] + actual=obj.grouping(points);self.assertEqual(actual,expected);self.assertLess(len(actual),n);self.assertEqual([x for g in actual for x in g],points) + def test_absent_depth_uses_original_partition(self): + class Parent: + def grouping(self,unused):return [[0,1],[2,3],[4]] + obj=provider.split_class(Parent,['first6'])();obj._level=10 + self.assertEqual(obj.grouping(list(range(5))),[[0,1],[2,3],[4]]) + def test_new_depth_and_anchor_settings_are_certified(self): + for h in (23,25): + for key,value in (('anchor_pairs',True),('anchor_pairs',0),('coarse_word','hhh'+'c'),('coarse_word','ccc')): + changed=deepcopy(provider.EXPECTED_CONFIGS[h]);changed[key]=value + with self.subTest(h=h,key=key,value=value),patch.object(provider.json,'loads',return_value=changed),self.assertRaises(ValueError):provider.configuration(h) +if __name__=='__main__':unittest.main() diff --git a/tests/test_balanced_split.py b/tests/test_balanced_split.py new file mode 100644 index 0000000000..175e7af890 --- /dev/null +++ b/tests/test_balanced_split.py @@ -0,0 +1,251 @@ +"""Physical and exact-arithmetic controls for the aligned split/pair witness.""" +from copy import deepcopy +from fractions import Fraction +from itertools import combinations +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile +import unittest +from unittest.mock import patch + +ROOT = Path(__file__).resolve().parents[1] +EXPERIMENTS = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXPERIMENTS)) +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from binary_frame_math import moment + + +class SplitPairControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.words = {h: json.loads(gzip.decompress((ROOT/f'certificates/balanced-split-word-{h}.json.gz').read_bytes())) + for h in (23,25)} + + def reject_mutation(self, mutate, checker='both'): + for h, original in self.words.items(): + with self.subTest(h=h), tempfile.TemporaryDirectory() as directory: + changed = deepcopy(original) + mutate(changed) + path = Path(directory)/'word.json' + path.write_text(json.dumps(changed, separators=(',', ':'))+'\n') + with self.assertRaises((AssertionError, ValueError, IndexError, KeyError)): + if checker != 'transitions': + replay(path) + if checker != 'replay': + prepare(path, Path(directory)/'transitions.bin') + + def test_selected_words_pass_independent_replay(self): + recorded = json.loads((ROOT/'certificates/balanced-split-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + actual = replay(ROOT/f'certificates/balanced-split-word-{h}.json.gz') + self.assertEqual(json.loads(json.dumps(actual)), recorded['axes'][str(h)]['replay']) + + def test_omitted_literal_xor_is_rejected(self): + self.reject_mutation(lambda word: word['ops'].pop(0)) + + def test_self_xor_is_rejected(self): + def mutate(word): + word['ops'][0][1] = word['ops'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_non_nested_operation_frame_is_rejected(self): + def mutate(word): + narrow = next(i for i,(core,cover) in enumerate(word['frames']) if core == cover) + operation = next(op for op in word['ops'] if word['frames'][op[2]][0] != word['frames'][op[2]][1]) + operation[2] = narrow + self.reject_mutation(mutate) + + def test_aliased_terminal_role_is_rejected(self): + def mutate(word): + word['outputs'][1][0] = word['outputs'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_missing_copied_center_is_rejected(self): + def mutate(word): + index = next(i for i,(_,_,_,target) in enumerate(word['outputs']) if len(target) == 1) + word['outputs'].pop(index) + self.reject_mutation(mutate) + + def test_omitted_transition_cannot_reduce_paid_profile(self): + self.reject_mutation(lambda word: word['events'].pop(0), 'transitions') + + def test_understated_physical_width_is_rejected(self): + def mutate(word): + word['R'] -= 1 + self.reject_mutation(mutate) + + def test_complete_pr71_profile_fails_new_bit_saving(self): + from split_pair_arithmetic import refine + previous = json.loads((ROOT/'references/frame-compiler/pr71/certificates/split-pair-kappa.json').read_text())['bit'] + current = json.loads((ROOT/'certificates/balanced-split-kappa.json').read_text()) + result = refine.exact_moment(previous['m'], previous['W'], {int(t): n for t,n in previous['child_multiplicities'].items()}, Fraction(current['bit_saving'])) + self.assertGreater(result['lower'], 1) + self.assertGreater(Fraction(current['kappa']), Fraction(current['comparison']['pr71_kappa'])) + + def test_private_import_preserves_path_and_arithmetic_module(self): + import balanced_split_graph as provider + import split_pair_arithmetic as arithmetic + sentinel = object() + existing = sys.modules.get('refine', sentinel) + previous_path = sys.path[:] + graph, schedule = provider._private_modules() + refine, audit = arithmetic.private_arithmetic() + self.assertIs(audit.refine, refine) + self.assertIs(sys.modules.get('refine', sentinel), existing) + self.assertEqual(sys.path, previous_path) + + def test_failed_graph_build_restores_original_providers(self): + import balanced_split_graph as provider + previous_class, previous_points = provider._graph.circuit_class, provider._graph.alternating_points + with patch.object(provider._graph, 'graph', side_effect=RuntimeError('deliberate graph failure')): + with self.assertRaises(RuntimeError): + provider.graph(23) + self.assertIs(provider._graph.circuit_class, previous_class) + self.assertIs(provider._graph.alternating_points, previous_points) + + def test_failed_compilation_restores_engine_graph_and_schedule(self): + import balanced_split_compiler as producer + previous_graph, previous_build = producer.ENGINES[23].graph, producer.ENGINES[23].build + missing = object() + runtime = {name:getattr(producer.ENGINES[23],name,missing) for name in ('PENDING_COST','ORACLE_EXE','ORACLE_INPUT','oracles')} + with patch.object(producer.ENGINES[23], 'compile_', side_effect=RuntimeError('deliberate compiler failure')): + with self.assertRaises(RuntimeError): + producer.compile_axis(23) + self.assertIs(producer.ENGINES[23].graph, previous_graph) + self.assertIs(producer.ENGINES[23].build, previous_build) + for name,value in runtime.items(): + self.assertIs(getattr(producer.ENGINES[23],name,missing),value) + + def test_uncertified_configurations_are_rejected(self): + import balanced_split_graph as provider + wrong_anchor = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_anchor['anchor'] = False + boolean_group = deepcopy(provider.EXPECTED_CONFIGS[23]); boolean_group['groups'][0] = True + changed_schedule = deepcopy(provider.EXPECTED_CONFIGS[23]); changed_schedule['schedule'] = 'reverse-node' + wrong_coarse = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_coarse['coarse'] = 'row' + omitted_completion = deepcopy(provider.EXPECTED_CONFIGS[23]); omitted_completion['future_completion'] = False + extra_exchanges = deepcopy(provider.EXPECTED_CONFIGS[23]); extra_exchanges['carry_exchange_passes'] = 3 + for changed in (wrong_anchor, boolean_group, changed_schedule, wrong_coarse, omitted_completion, extra_exchanges): + with self.subTest(configuration=changed), patch.object(provider.json, 'loads', return_value=changed): + with self.assertRaises(ValueError): + provider.configuration(23) + for dimension in (True, 22, 24, '23'): + with self.subTest(dimension=dimension), self.assertRaises(ValueError): + provider.configuration(dimension) + + def test_recursive_weighted_exclusions_and_contraction(self): + import balanced_split_graph as provider + for h in (23,25): + block_sizes = [] + parent = provider._graphs[h].circuit_class(h) + selected = provider.split_class(parent, provider.configuration(h)['groups']) + case = self + class Audited(selected): + def grouping(self, points): + groups = super().grouping(points) + case.assertEqual([x for group in groups for x in group], list(points)) + case.assertLess(len(groups), len(points)) + return groups + + def _block(self, points, edges, weights, level): + def expected(omitted): + values = [value for pair,value in edges.items() if not set(pair) & omitted] + values += [value for point,value in weights.items() if point not in omitted] + support = 0 + for value in values: + case.assertEqual(support & self.support[value], 0) + support |= self.support[value] + return support + total, single, pairs = super()._block(points, edges, weights, level) + case.assertEqual(self.support[total], expected(set())) + case.assertEqual(set(single), set(points)) + for a in points: + case.assertEqual(self.support[single[a]], expected({a})) + case.assertEqual(set(pairs), set(combinations(points,2))) + for a,b in combinations(points,2): + case.assertEqual(self.support[pairs[a,b]], expected({a,b})) + block_sizes.append(len(points)) + return total, single, pairs + local = Audited(h-1) + block_sizes.clear() + local.pair(list(range(h-1))) + self.assertEqual(sorted(block_sizes, reverse=True), [h-1, 12 if h==23 else 13, 7 if h==23 else 8, 5, 3, 2]) + + def test_next_fine_grid_points_and_old_assembly_controls_reject(self): + from split_pair_arithmetic import refine + current = json.loads((ROOT/'certificates/balanced-split-kappa.json').read_text()) + bit = current['bit']; saving = Fraction(current['bit_saving']); kappa = Fraction(current['kappa']) + grid = Fraction(1,10**18) + rows = {int(t): n for t,n in bit['child_multiplicities'].items()} + self.assertLess(refine.exact_moment(bit['m'],bit['W'],rows,saving)['upper'], 1) + self.assertGreater(refine.exact_moment(bit['m'],bit['W'],rows,saving+grid)['lower'], 1) + for label, variant in ( + ('next_kappa', dict(kappa=kappa+grid)), + ('zero_backoff', dict(h=Fraction())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))): + call = dict(a_bit=saving, kappa=kappa, h=Fraction(1,10**12));call.update(variant) + with self.subTest(control=label), self.assertRaises(refine.balanced.InvalidAssembly): + refine.balanced.assembly(current['finite_bridge'], **call) + + def test_mass_preserving_profile_mutation_is_rejected(self): + from balanced_split_compose import check_sources + profile_path = ROOT/'certificates/balanced-split-profiles-23.json' + changed = json.loads(profile_path.read_text()) + before = sum(t*n for t,n in enumerate(changed['blocks'])) + changed['blocks'][2] += 3; changed['blocks'][3] -= 2 + self.assertTrue(all(n >= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'balanced-split-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from balanced_split_compose import check_sources + manifest_path = ROOT/'research/balanced-split/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/balanced-split-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import balanced_split_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_all_threshold_dependent_bridge_fields_are_checked(self): + from balanced_split_compose import finite_bridge, validate_bridge + expected = finite_bridge(134126064) + self.assertTrue(validate_bridge(expected, 134126064)) + for section,key in (('bit','wire_bits'),('rows','coefficient'),('rows','degree'),('rows','degree_gap'),('rows','suffix_slope')): + changed = deepcopy(expected) + changed[section][key] = Fraction(changed[section][key])+1 + with self.subTest(field=section+'.'+key), self.assertRaisesRegex(AssertionError, 'Stale finite bridge'): + validate_bridge(changed, 134126064) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('balanced_split_graph.py', 'balanced_split_engine.py', 'balanced_split_compiler.py', 'split_pair_arithmetic.py', 'balanced_split_exchange_engine.py', 'balanced_split_compose.py', 'verify_balanced_split.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/tests/test_balanced_split_pending.py b/tests/test_balanced_split_pending.py new file mode 100644 index 0000000000..cce267112e --- /dev/null +++ b/tests/test_balanced_split_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/balanced_split_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/balanced-split-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main() diff --git a/tests/test_final_frame.py b/tests/test_final_frame.py new file mode 100644 index 0000000000..b789b5863a --- /dev/null +++ b/tests/test_final_frame.py @@ -0,0 +1,248 @@ +"""Physical and exact-arithmetic controls for the aligned split/pair witness.""" +from copy import deepcopy +from fractions import Fraction +from itertools import combinations +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile +import unittest +from unittest.mock import patch + +ROOT = Path(__file__).resolve().parents[1] +EXPERIMENTS = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXPERIMENTS)) +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from binary_frame_math import moment + + +class SplitPairControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.words = {h: json.loads(gzip.decompress((ROOT/f'certificates/final-frame-word-{h}.json.gz').read_bytes())) + for h in (23,25)} + + def reject_mutation(self, mutate, checker='both'): + for h, original in self.words.items(): + with self.subTest(h=h), tempfile.TemporaryDirectory() as directory: + changed = deepcopy(original) + mutate(changed) + path = Path(directory)/'word.json' + path.write_text(json.dumps(changed, separators=(',', ':'))+'\n') + with self.assertRaises((AssertionError, ValueError, IndexError, KeyError)): + if checker != 'transitions': + replay(path) + if checker != 'replay': + prepare(path, Path(directory)/'transitions.bin') + + def test_selected_words_pass_independent_replay(self): + recorded = json.loads((ROOT/'certificates/final-frame-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + actual = replay(ROOT/f'certificates/final-frame-word-{h}.json.gz') + self.assertEqual(json.loads(json.dumps(actual)), recorded['axes'][str(h)]['replay']) + + def test_omitted_literal_xor_is_rejected(self): + self.reject_mutation(lambda word: word['ops'].pop(0)) + + def test_self_xor_is_rejected(self): + def mutate(word): + word['ops'][0][1] = word['ops'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_non_nested_operation_frame_is_rejected(self): + def mutate(word): + narrow = next(i for i,(core,cover) in enumerate(word['frames']) if core == cover) + operation = next(op for op in word['ops'] if word['frames'][op[2]][0] != word['frames'][op[2]][1]) + operation[2] = narrow + self.reject_mutation(mutate) + + def test_aliased_terminal_role_is_rejected(self): + def mutate(word): + word['outputs'][1][0] = word['outputs'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_missing_copied_center_is_rejected(self): + def mutate(word): + index = next(i for i,(_,_,_,target) in enumerate(word['outputs']) if len(target) == 1) + word['outputs'].pop(index) + self.reject_mutation(mutate) + + def test_omitted_transition_cannot_reduce_paid_profile(self): + self.reject_mutation(lambda word: word['events'].pop(0), 'transitions') + + def test_understated_physical_width_is_rejected(self): + def mutate(word): + word['R'] -= 1 + self.reject_mutation(mutate) + + def test_complete_pr84_profile_fails_new_bit_saving(self): + from split_pair_arithmetic import refine + previous = json.loads((ROOT/'references/frame-compiler/pr84/certificates/indexed-cycle-kappa.json').read_text())['bit'] + current = json.loads((ROOT/'certificates/final-frame-kappa.json').read_text()) + result = refine.exact_moment(previous['m'], previous['W'], {int(t): n for t,n in previous['child_multiplicities'].items()}, Fraction(current['bit_saving'])) + self.assertGreater(result['lower'], 1) + self.assertGreater(Fraction(current['kappa']), Fraction(current['comparison']['pr84_kappa'])) + + def test_private_import_preserves_path_and_arithmetic_module(self): + import final_frame_graph as provider + import split_pair_arithmetic as arithmetic + sentinel = object() + existing = sys.modules.get('refine', sentinel) + previous_path = sys.path[:] + graph, schedule = provider._private_modules() + refine, audit = arithmetic.private_arithmetic() + self.assertIs(audit.refine, refine) + self.assertIs(sys.modules.get('refine', sentinel), existing) + self.assertEqual(sys.path, previous_path) + + def test_failed_graph_build_restores_original_providers(self): + import final_frame_graph as provider + previous_class, previous_points = provider._graph.circuit_class, provider._graph.alternating_points + with patch.object(provider._graph, 'graph', side_effect=RuntimeError('deliberate graph failure')): + with self.assertRaises(RuntimeError): + provider.graph(23) + self.assertIs(provider._graph.circuit_class, previous_class) + self.assertIs(provider._graph.alternating_points, previous_points) + + def test_failed_compilation_restores_engine_graph_and_schedule(self): + import final_frame_compiler as producer + previous_graph, previous_build = producer.ENGINES[23].graph, producer.ENGINES[23].build + missing = object() + runtime = {name:getattr(producer.ENGINES[23],name,missing) for name in ('PENDING_COST','ORACLE_EXE','ORACLE_INPUT','oracles','OUTPUT_MODE','ORACLE_COORDINATES','THREE_CYCLE_PASSES')} + with patch.object(producer.ENGINES[23], 'compile_', side_effect=RuntimeError('deliberate compiler failure')): + with self.assertRaises(RuntimeError): + producer.compile_axis(23) + self.assertIs(producer.ENGINES[23].graph, previous_graph) + self.assertIs(producer.ENGINES[23].build, previous_build) + for name,value in runtime.items(): + self.assertIs(getattr(producer.ENGINES[23],name,missing),value) + + def test_uncertified_configurations_are_rejected(self): + import final_frame_graph as provider + wrong_anchor = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_anchor['anchor'] = False + boolean_group = deepcopy(provider.EXPECTED_CONFIGS[23]); boolean_group['groups'][0] = True + changed_schedule = deepcopy(provider.EXPECTED_CONFIGS[23]); changed_schedule['schedule'] = 'reverse-node' + wrong_coarse = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_coarse['coarse'] = 'row' + omitted_completion = deepcopy(provider.EXPECTED_CONFIGS[23]); omitted_completion['future_completion'] = False + extra_exchanges = deepcopy(provider.EXPECTED_CONFIGS[23]); extra_exchanges['carry_exchange_passes'] = 4 + wrong_route = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_route['output_mode'] = 'route-late' + wrong_permutation = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_permutation['coordinate_permutation'][0] = True + extra_cycles = deepcopy(provider.EXPECTED_CONFIGS[23]); extra_cycles['carry_two_cycle_passes'] = 4 + wrong_order=deepcopy(provider.EXPECTED_CONFIGS[23]);wrong_order['node_order']='pr74' + wrong_price=deepcopy(provider.EXPECTED_CONFIGS[23]);wrong_price['oracle_coordinate_pricing']=0 + wrong_three=deepcopy(provider.EXPECTED_CONFIGS[23]);wrong_three['three_cycle_passes']=False + for changed in (wrong_anchor, boolean_group, changed_schedule, wrong_coarse, omitted_completion, extra_exchanges,wrong_route,wrong_permutation,extra_cycles,wrong_order,wrong_price,wrong_three): + with self.subTest(configuration=changed), patch.object(provider.json, 'loads', return_value=changed): + with self.assertRaises(ValueError): + provider.configuration(23) + for dimension in (True, 22, 24, '23'): + with self.subTest(dimension=dimension), self.assertRaises(ValueError): + provider.configuration(dimension) + + def test_recursive_weighted_exclusions_and_contraction(self): + import final_frame_graph as provider + for h in (23,25): + block_sizes = [] + parent = provider._graphs[h].circuit_class(h) + selected = provider.split_class(parent, provider.configuration(h)['groups']) + case = self + class Audited(selected): + def grouping(self, points): + groups = super().grouping(points) + case.assertEqual([x for group in groups for x in group], list(points)) + case.assertLess(len(groups), len(points)) + return groups + + def _block(self, points, edges, weights, level): + def expected(omitted): + values = [value for pair,value in edges.items() if not set(pair) & omitted] + values += [value for point,value in weights.items() if point not in omitted] + support = 0 + for value in values: + case.assertEqual(support & self.support[value], 0) + support |= self.support[value] + return support + total, single, pairs = super()._block(points, edges, weights, level) + case.assertEqual(self.support[total], expected(set())) + case.assertEqual(set(single), set(points)) + for a in points: + case.assertEqual(self.support[single[a]], expected({a})) + case.assertEqual(set(pairs), set(combinations(points,2))) + for a,b in combinations(points,2): + case.assertEqual(self.support[pairs[a,b]], expected({a,b})) + block_sizes.append(len(points)) + return total, single, pairs + local = Audited(h-1) + block_sizes.clear() + local.pair(list(range(h-1))) + self.assertEqual(max(block_sizes), h-1) + self.assertIn(2,block_sizes) + self.assertTrue(all(2<=n<=h-1 for n in block_sizes)) + + def test_next_fine_grid_points_and_old_assembly_controls_reject(self): + from split_pair_arithmetic import refine + current = json.loads((ROOT/'certificates/final-frame-kappa.json').read_text()) + bit = current['bit']; saving = Fraction(current['bit_saving']); kappa = Fraction(current['kappa']) + grid = Fraction(1,10**18) + rows = {int(t): n for t,n in bit['child_multiplicities'].items()} + self.assertLess(refine.exact_moment(bit['m'],bit['W'],rows,saving)['upper'], 1) + self.assertGreater(refine.exact_moment(bit['m'],bit['W'],rows,saving+grid)['lower'], 1) + for label, variant in ( + ('next_kappa', dict(kappa=kappa+grid)), + ('zero_backoff', dict(h=Fraction())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))): + call = dict(a_bit=saving, kappa=kappa, h=Fraction(1,10**12));call.update(variant) + with self.subTest(control=label), self.assertRaises(refine.balanced.InvalidAssembly): + refine.balanced.assembly(current['finite_bridge'], **call) + + def test_mass_preserving_profile_mutation_is_rejected(self): + from final_frame_compose import check_sources + profile_path = ROOT/'certificates/final-frame-profiles-23.json' + changed = json.loads(profile_path.read_text()) + before = sum(t*n for t,n in enumerate(changed['blocks'])) + changed['blocks'][2] += 3; changed['blocks'][3] -= 2 + self.assertTrue(all(n >= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'final-frame-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from final_frame_compose import check_sources + manifest_path = ROOT/'research/final-frame/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/final-frame-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_all_threshold_dependent_bridge_fields_are_checked(self): + from final_frame_compose import finite_bridge, validate_bridge + expected = finite_bridge(131503443) + self.assertTrue(validate_bridge(expected, 131503443)) + for section,key in (('bit','wire_bits'),('rows','coefficient'),('rows','degree'),('rows','degree_gap'),('rows','suffix_slope')): + changed = deepcopy(expected) + changed[section][key] = Fraction(changed[section][key])+1 + with self.subTest(field=section+'.'+key), self.assertRaisesRegex(AssertionError, 'Stale finite bridge'): + validate_bridge(changed, 131503443) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('final_frame_graph.py', 'final_frame_engine.py', 'final_frame_compiler.py', 'split_pair_arithmetic.py', 'final_frame_compose.py', 'verify_final_frame.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/tests/test_final_frame_coordinates.py b/tests/test_final_frame_coordinates.py new file mode 100644 index 0000000000..ef68ff7675 --- /dev/null +++ b/tests/test_final_frame_coordinates.py @@ -0,0 +1,49 @@ +"""Bijection and adverse-coordinate controls for the actual PR74 relabel functions.""" +from pathlib import Path +from itertools import combinations +from copy import deepcopy +from hashlib import sha256 +import gzip,json,sys,unittest +ROOT=Path(__file__).resolve().parents[1];sys.path.insert(0,str(ROOT/'scripts/experiments')) +from final_frame_nodeops import relabel +from final_frame_graph import configuration + +class CoordinateControls(unittest.TestCase): + def test_selected_permutations_are_exact_integer_bijections(self): + for h in (23,25): + perm=configuration(h)['coordinate_permutation'] + self.assertEqual(sorted(perm),list(range(h))) + self.assertTrue(all(type(x) is int for x in perm)) + self.assertEqual(configuration(23)['coordinate_permutation'],[1, 2, 4, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 19, 21, 22, 0]) + + def test_every_selected_word_roundtrips_full_coordinate_inverse(self): + for h in (23,25): + word=json.loads(gzip.decompress((ROOT/f'certificates/final-frame-word-{h}.json.gz').read_bytes())) + perm=configuration(h)['coordinate_permutation'];inverse=[perm.index(i) for i in range(h)] + parent=relabel(deepcopy(word),inverse) + # Dict iteration and scatter order are deliberately retained by the actual function. + raw=(json.dumps(parent,separators=(',',':'))+'\n').encode() + selection=json.loads((ROOT/'research/final-frame/word-bindings.json').read_text())[str(h)] + self.assertEqual(sha256(raw).hexdigest(),selection['parent_word_sha256']) + self.assertEqual(relabel(parent,perm),word) + + def test_relabel_preserves_physical_operations_and_frame_inclusions(self): + h=5;triples=list(combinations(range(h),3));v=len(triples);perm=[4,0,2,1,3] + word=dict(h=h,v=v,frames=[[3,7],[1,31]],sources={str(i):i for i in range(v)}, + scatter=[[v+i,2*v+i] for i in reversed(range(v))],outputs=[[2*v+i,0,0,list(t)] for i,t in enumerate(triples)], + ops=[[2*v,2*v+1,0]],events=[[2*v,0,1]]) + changed=relabel(deepcopy(word),perm) + self.assertEqual(changed['ops'],word['ops']);self.assertEqual(changed['events'],word['events']) + self.assertEqual(set(map(int,changed['sources'])),set(range(v))) + self.assertEqual([b for a,b in changed['scatter']],[b for a,b in word['scatter']]) + self.assertEqual(set(a for a,b in changed['scatter']),set(range(v,2*v))) + (a,b),(c,d)=changed['frames'];self.assertEqual(c&~a,0);self.assertEqual(b&~d,0) + + def test_invalid_permutation_and_scatter_source_are_rejected(self): + word=dict(h=3,v=1,frames=[[1,7]],sources={'0':0},scatter=[[1,2]],outputs=[[2,0,0,[0,1,2]]]) + for permutation in ([0,1,1],[0,1],[0,1,3]): + with self.subTest(permutation=permutation),self.assertRaises(AssertionError):relabel(deepcopy(word),permutation) + word['scatter'][0][0]=0 + with self.assertRaises(AssertionError):relabel(word,[0,1,2]) + +if __name__=='__main__':unittest.main() diff --git a/tests/test_final_frame_order.py b/tests/test_final_frame_order.py new file mode 100644 index 0000000000..43e0832103 --- /dev/null +++ b/tests/test_final_frame_order.py @@ -0,0 +1,45 @@ +from pathlib import Path +from itertools import combinations +from copy import deepcopy +import importlib.util,json,unittest +import sys +sys.path.insert(0,str(Path(__file__).resolve().parents[1]/'scripts/experiments')) +from final_frame_nodeops import order_key,reorder,verify_dense,relabel +ROOT=Path(__file__).resolve().parents[1] +spec=importlib.util.spec_from_file_location('original',ROOT/'scripts/experiments/indexed_cycle_nodeops.py');original=importlib.util.module_from_spec(spec);spec.loader.exec_module(original) +KEYS=['pr74','cover-minus-core-minus'] +class Fake: + def __init__(self): + self.h=5;self.inputs=list(combinations(range(5),3));self.args=[None]*11;self.core=[0]+[sum(1<= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'indexed-cycle-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from indexed_cycle_compose import check_sources + manifest_path = ROOT/'research/indexed-cycle/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/indexed-cycle-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_all_threshold_dependent_bridge_fields_are_checked(self): + from indexed_cycle_compose import finite_bridge, validate_bridge + expected = finite_bridge(132466108) + self.assertTrue(validate_bridge(expected, 132466108)) + for section,key in (('bit','wire_bits'),('rows','coefficient'),('rows','degree'),('rows','degree_gap'),('rows','suffix_slope')): + changed = deepcopy(expected) + changed[section][key] = Fraction(changed[section][key])+1 + with self.subTest(field=section+'.'+key), self.assertRaisesRegex(AssertionError, 'Stale finite bridge'): + validate_bridge(changed, 132466108) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('indexed_cycle_graph.py', 'indexed_cycle_engine.py', 'indexed_cycle_compiler.py', 'split_pair_arithmetic.py', 'indexed_cycle_compose.py', 'verify_indexed_cycle.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/tests/test_indexed_cycle_coordinates.py b/tests/test_indexed_cycle_coordinates.py new file mode 100644 index 0000000000..12fedd3b90 --- /dev/null +++ b/tests/test_indexed_cycle_coordinates.py @@ -0,0 +1,49 @@ +"""Bijection and adverse-coordinate controls for the actual PR74 relabel functions.""" +from pathlib import Path +from itertools import combinations +from copy import deepcopy +from hashlib import sha256 +import gzip,json,sys,unittest +ROOT=Path(__file__).resolve().parents[1];sys.path.insert(0,str(ROOT/'scripts/experiments')) +from indexed_cycle_nodeops import relabel +from indexed_cycle_graph import configuration + +class CoordinateControls(unittest.TestCase): + def test_selected_permutations_are_exact_integer_bijections(self): + for h in (23,25): + perm=configuration(h)['coordinate_permutation'] + self.assertEqual(sorted(perm),list(range(h))) + self.assertTrue(all(type(x) is int for x in perm)) + self.assertEqual(configuration(23)['coordinate_permutation'],list(range(1,23))+[0]) + + def test_every_selected_word_roundtrips_full_coordinate_inverse(self): + for h in (23,25): + word=json.loads(gzip.decompress((ROOT/f'certificates/indexed-cycle-word-{h}.json.gz').read_bytes())) + perm=configuration(h)['coordinate_permutation'];inverse=[perm.index(i) for i in range(h)] + parent=relabel(deepcopy(word),inverse) + # Dict iteration and scatter order are deliberately retained by the actual function. + raw=(json.dumps(parent,separators=(',',':'))+'\n').encode() + selection=json.loads((ROOT/'research/indexed-cycle/discovery-selection.json').read_text())['axes'][str(h)] + self.assertEqual(sha256(raw).hexdigest(),selection['parent_word_sha256']) + self.assertEqual(relabel(parent,perm),word) + + def test_relabel_preserves_physical_operations_and_frame_inclusions(self): + h=5;triples=list(combinations(range(h),3));v=len(triples);perm=[4,0,2,1,3] + word=dict(h=h,v=v,frames=[[3,7],[1,31]],sources={str(i):i for i in range(v)}, + scatter=[[v+i,2*v+i] for i in reversed(range(v))],outputs=[[2*v+i,0,0,list(t)] for i,t in enumerate(triples)], + ops=[[2*v,2*v+1,0]],events=[[2*v,0,1]]) + changed=relabel(deepcopy(word),perm) + self.assertEqual(changed['ops'],word['ops']);self.assertEqual(changed['events'],word['events']) + self.assertEqual(set(map(int,changed['sources'])),set(range(v))) + self.assertEqual([b for a,b in changed['scatter']],[b for a,b in word['scatter']]) + self.assertEqual(set(a for a,b in changed['scatter']),set(range(v,2*v))) + (a,b),(c,d)=changed['frames'];self.assertEqual(c&~a,0);self.assertEqual(b&~d,0) + + def test_invalid_permutation_and_scatter_source_are_rejected(self): + word=dict(h=3,v=1,frames=[[1,7]],sources={'0':0},scatter=[[1,2]],outputs=[[2,0,0,[0,1,2]]]) + for permutation in ([0,1,1],[0,1],[0,1,3]): + with self.subTest(permutation=permutation),self.assertRaises(AssertionError):relabel(deepcopy(word),permutation) + word['scatter'][0][0]=0 + with self.assertRaises(AssertionError):relabel(word,[0,1,2]) + +if __name__=='__main__':unittest.main() diff --git a/tests/test_lean_axiom_output.py b/tests/test_lean_axiom_output.py new file mode 100644 index 0000000000..a5f7fa21b2 --- /dev/null +++ b/tests/test_lean_axiom_output.py @@ -0,0 +1,28 @@ +"""Parser controls using preserved real Lean output; these do not simulate proof compilation.""" +from pathlib import Path +import os,re,subprocess,sys,tempfile,unittest +ROOT=Path(__file__).resolve().parents[1] +class LeanAxiomOutput(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.output=(ROOT/'research/aligned-composition/lean/receipts/compile/output.log').read_text() + source=(ROOT/'formal/lean/KappaCheck/AlignedFrameComposition.lean').read_text() + cls.audit='\n'.join(line for line in source.splitlines() if line.startswith('#print axioms '))+'\n' + def check_output(self,output): + with tempfile.TemporaryDirectory() as temp: + directory=Path(temp);(directory/'Audit.lean').write_text(self.audit);(directory/'output.txt').write_text(output) + # Stand in only for the subprocess transport, replaying immutable real output. + (directory/'lake').write_text('#!'+sys.executable+'\nfrom pathlib import Path\nprint(Path(__file__).with_name("output.txt").read_text(),end="")\n');(directory/'lake').chmod(0o755) + env=os.environ.copy();env['PATH']=str(directory)+os.pathsep+env.get('PATH','') + return subprocess.run([sys.executable,str(ROOT/'scripts/check_lean_axioms.py'),'--project',temp,'--audit',str(directory/'Audit.lean')],capture_output=True,text=True,env=env) + def test_real_197_theorem_output_with_wrapped_lists_passes(self): + self.assertIn('propext,\n Classical.choice,\n Quot.sound',self.output) + result=self.check_output(self.output);self.assertEqual(result.returncode,0,result.stdout+result.stderr);self.assertIn('PASS 197 declarations',result.stdout) + def test_forbidden_axiom_in_wrapped_list_is_rejected(self): + output=self.output.replace('propext,\n Classical.choice,\n Quot.sound','propext,\n forbidden_axiom,\n Quot.sound',1) + result=self.check_output(output);self.assertNotEqual(result.returncode,0);self.assertIn('forbidden_axiom',result.stdout+result.stderr) + def test_missing_expected_theorem_is_rejected(self): + output=self.output.split('\n',1)[1];result=self.check_output(output);self.assertNotEqual(result.returncode,0);self.assertIn('196/197',result.stdout+result.stderr) + def test_duplicate_output_is_rejected(self): + output=self.output+'\n'+self.output.split('\n',1)[0]+'\n';result=self.check_output(output);self.assertNotEqual(result.returncode,0);self.assertIn('198/197',result.stdout+result.stderr) +if __name__=='__main__':unittest.main() diff --git a/tests/test_split_pair.py b/tests/test_split_pair.py new file mode 100644 index 0000000000..5088cff133 --- /dev/null +++ b/tests/test_split_pair.py @@ -0,0 +1,238 @@ +"""Physical and exact-arithmetic controls for the aligned split/pair witness.""" +from copy import deepcopy +from fractions import Fraction +from itertools import combinations +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile +import unittest +from unittest.mock import patch + +ROOT = Path(__file__).resolve().parents[1] +EXPERIMENTS = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXPERIMENTS)) +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from binary_frame_math import moment + + +class SplitPairControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.words = {h: json.loads(gzip.decompress((ROOT/f'certificates/split-pair-word-{h}.json.gz').read_bytes())) + for h in (23,25)} + + def reject_mutation(self, mutate, checker='both'): + for h, original in self.words.items(): + with self.subTest(h=h), tempfile.TemporaryDirectory() as directory: + changed = deepcopy(original) + mutate(changed) + path = Path(directory)/'word.json' + path.write_text(json.dumps(changed, separators=(',', ':'))+'\n') + with self.assertRaises((AssertionError, ValueError, IndexError, KeyError)): + if checker != 'transitions': + replay(path) + if checker != 'replay': + prepare(path, Path(directory)/'transitions.bin') + + def test_selected_words_pass_independent_replay(self): + recorded = json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + actual = replay(ROOT/f'certificates/split-pair-word-{h}.json.gz') + self.assertEqual(json.loads(json.dumps(actual)), recorded['axes'][str(h)]['replay']) + + def test_omitted_literal_xor_is_rejected(self): + self.reject_mutation(lambda word: word['ops'].pop(0)) + + def test_self_xor_is_rejected(self): + def mutate(word): + word['ops'][0][1] = word['ops'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_non_nested_operation_frame_is_rejected(self): + def mutate(word): + narrow = next(i for i,(core,cover) in enumerate(word['frames']) if core == cover) + operation = next(op for op in word['ops'] if word['frames'][op[2]][0] != word['frames'][op[2]][1]) + operation[2] = narrow + self.reject_mutation(mutate) + + def test_aliased_terminal_role_is_rejected(self): + def mutate(word): + word['outputs'][1][0] = word['outputs'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_missing_copied_center_is_rejected(self): + def mutate(word): + index = next(i for i,(_,_,_,target) in enumerate(word['outputs']) if len(target) == 1) + word['outputs'].pop(index) + self.reject_mutation(mutate) + + def test_omitted_transition_cannot_reduce_paid_profile(self): + self.reject_mutation(lambda word: word['events'].pop(0), 'transitions') + + def test_understated_physical_width_is_rejected(self): + def mutate(word): + word['R'] -= 1 + self.reject_mutation(mutate) + + def test_complete_pr67_profile_fails_new_bit_saving(self): + from split_pair_arithmetic import refine + previous = json.loads((ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/paired-candidate.json').read_text())['bit'] + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + result = refine.exact_moment(previous['m'], previous['W'], {int(t): n for t,n in previous['child_multiplicities'].items()}, Fraction(current['bit_saving'])) + self.assertGreater(result['lower'], 1) + self.assertGreater(Fraction(current['kappa']), Fraction(current['comparison']['pr67_kappa'])) + + def test_private_import_preserves_path_and_arithmetic_module(self): + import split_pair_graph as provider + import split_pair_arithmetic as arithmetic + sentinel = object() + existing = sys.modules.get('refine', sentinel) + previous_path = sys.path[:] + graph, schedule = provider._private_modules() + refine, audit = arithmetic.private_arithmetic() + self.assertIs(audit.refine, refine) + self.assertIs(sys.modules.get('refine', sentinel), existing) + self.assertEqual(sys.path, previous_path) + + def test_failed_graph_build_restores_original_providers(self): + import split_pair_graph as provider + previous_class, previous_points = provider._graph.circuit_class, provider._graph.alternating_points + with patch.object(provider._graph, 'graph', side_effect=RuntimeError('deliberate graph failure')): + with self.assertRaises(RuntimeError): + provider.graph(23) + self.assertIs(provider._graph.circuit_class, previous_class) + self.assertIs(provider._graph.alternating_points, previous_points) + + def test_failed_compilation_restores_engine_graph_and_schedule(self): + import split_pair_compiler as producer + previous_graph, previous_build = producer.compiler.graph, producer.compiler.build + missing = object() + runtime = {name:getattr(producer.compiler,name,missing) for name in ('PENDING_COST','ORACLE_EXE','ORACLE_INPUT','oracles')} + with patch.object(producer.compiler, 'compile_', side_effect=RuntimeError('deliberate compiler failure')): + with self.assertRaises(RuntimeError): + producer.compile_axis(23) + self.assertIs(producer.compiler.graph, previous_graph) + self.assertIs(producer.compiler.build, previous_build) + for name,value in runtime.items(): + self.assertIs(getattr(producer.compiler,name,missing),value) + + def test_uncertified_configurations_are_rejected(self): + import split_pair_graph as provider + wrong_anchor = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_anchor['anchor'] = False + boolean_group = deepcopy(provider.EXPECTED_CONFIGS[23]); boolean_group['groups'][0] = True + changed_schedule = deepcopy(provider.EXPECTED_CONFIGS[23]); changed_schedule['schedule'] = 'reverse-node' + for changed in (wrong_anchor, boolean_group, changed_schedule): + with self.subTest(configuration=changed), patch.object(provider.json, 'loads', return_value=changed): + with self.assertRaises(ValueError): + provider.configuration(23) + for dimension in (True, 22, 24, '23'): + with self.subTest(dimension=dimension), self.assertRaises(ValueError): + provider.configuration(dimension) + + def test_recursive_weighted_exclusions_and_contraction(self): + import split_pair_graph as provider + for h in (23,25): + block_sizes = [] + parent = provider._graph.circuit_class(h) + selected = provider.split_class(parent, provider.configuration(h)['groups']) + case = self + class Audited(selected): + def grouping(self, points): + groups = super().grouping(points) + case.assertEqual([x for group in groups for x in group], list(points)) + case.assertLess(len(groups), len(points)) + return groups + + def _block(self, points, edges, weights, level): + def expected(omitted): + values = [value for pair,value in edges.items() if not set(pair) & omitted] + values += [value for point,value in weights.items() if point not in omitted] + support = 0 + for value in values: + case.assertEqual(support & self.support[value], 0) + support |= self.support[value] + return support + total, single, pairs = super()._block(points, edges, weights, level) + case.assertEqual(self.support[total], expected(set())) + case.assertEqual(set(single), set(points)) + for a in points: + case.assertEqual(self.support[single[a]], expected({a})) + case.assertEqual(set(pairs), set(combinations(points,2))) + for a,b in combinations(points,2): + case.assertEqual(self.support[pairs[a,b]], expected({a,b})) + block_sizes.append(len(points)) + return total, single, pairs + local = Audited(h-1) + block_sizes.clear() + local.pair(list(range(h-1))) + self.assertEqual(sorted(block_sizes, reverse=True), [h-1, 12 if h==23 else 13, 7 if h==23 else 8, 5, 3, 2]) + + def test_next_fine_grid_points_and_old_assembly_controls_reject(self): + from split_pair_arithmetic import refine + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + bit = current['bit']; saving = Fraction(current['bit_saving']); kappa = Fraction(current['kappa']) + grid = Fraction(1,10**18) + rows = {int(t): n for t,n in bit['child_multiplicities'].items()} + self.assertLess(refine.exact_moment(bit['m'],bit['W'],rows,saving)['upper'], 1) + self.assertGreater(refine.exact_moment(bit['m'],bit['W'],rows,saving+grid)['lower'], 1) + for label, variant in ( + ('next_kappa', dict(kappa=kappa+grid)), + ('zero_backoff', dict(h=Fraction())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))): + call = dict(a_bit=saving, kappa=kappa, h=Fraction(1,10**12));call.update(variant) + with self.subTest(control=label), self.assertRaises(refine.balanced.InvalidAssembly): + refine.balanced.assembly(current['finite_bridge'], **call) + + def test_mass_preserving_profile_mutation_is_rejected(self): + from split_pair_compose import check_sources + profile_path = ROOT/'certificates/split-pair-profiles-23.json' + changed = json.loads(profile_path.read_text()) + before = sum(t*n for t,n in enumerate(changed['blocks'])) + changed['blocks'][2] += 3; changed['blocks'][3] -= 2 + self.assertTrue(all(n >= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'split-pair-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from split_pair_compose import check_sources + manifest_path = ROOT/'research/split-pair/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/split-pair-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import split_pair_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('split_pair_graph.py', 'split_pair_engine.py', 'split_pair_compiler.py', 'split_pair_arithmetic.py', 'split_pair_compose.py', 'verify_split_pair.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/tests/test_split_pair_pending.py b/tests/test_split_pair_pending.py new file mode 100644 index 0000000000..e6d63f72a4 --- /dev/null +++ b/tests/test_split_pair_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/split_pair_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main()