diff --git a/.gitattributes b/.gitattributes index 41aef290fd..48ba61f217 100644 --- a/.gitattributes +++ b/.gitattributes @@ -8,3 +8,8 @@ upstream/** -whitespace references/copied-centers/pr29/** -whitespace references/copied-centers/pr33/** -whitespace references/semantic-bulk/** -whitespace + +# Immutable contributor archives retain original CRLF and whitespace bytes. +references/frame-compiler/pr69/** -text -whitespace +references/frame-compiler/pr70/** -text -whitespace +references/frame-compiler/pr71/** -text -whitespace diff --git a/.github/workflows/verify.yml b/.github/workflows/verify.yml index 6bd374e1ca..a897321cff 100644 --- a/.github/workflows/verify.yml +++ b/.github/workflows/verify.yml @@ -16,7 +16,7 @@ jobs: fail-fast: false matrix: python-version: ['3.11', '3.13', '3.14'] - group: [community, producers, certificates, ternary, research, tests, strips, clones, positive, joint, pair] + group: [community, producers, certificates, ternary, research, tests, strips, clones, positive, joint, pair, balanced, merged] steps: - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 with: diff --git a/Makefile b/Makefile index 84fe8290f3..9c136b3f98 100644 --- a/Makefile +++ b/Makefile @@ -23,6 +23,8 @@ verify: $(MAKE) verify-positive $(MAKE) verify-joint $(MAKE) verify-pair + $(MAKE) verify-balanced + $(MAKE) verify-merged $(MAKE) verify-tests verify-community: community-audit-check community-followup-check copied-reversed-producer copied-reversed-check copied-fixed-reversed-producer copied-fixed-reversed-check @@ -428,3 +430,26 @@ pair-assembly-verify: pair-assembly-producer pair-assembly-check .PHONY: verify-pair verify-pair: pair-assembly-verify python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify + +.PHONY: balanced-split-verify verify-balanced +balanced-split-verify: + python3 scripts/experiments/verify_balanced_split.py + python3 scripts/experiments/audit_balanced_split_completion.py + python3 scripts/experiments/audit_balanced_split_exchange.py + python3 -m unittest discover -s tests -p 'test_balanced_split*.py' -v + +verify-balanced: balanced-split-verify + +.PHONY: merged-exterior-verify verify-merged +merged-exterior-verify: + python3 scripts/experiments/verify_merged_exterior.py + python3 -m unittest discover -s tests -p 'test_merged_exterior*.py' -v + +verify-merged: merged-exterior-verify diff --git a/NOTICE b/NOTICE index b565637758..8a6bef1613 100644 --- a/NOTICE +++ b/NOTICE @@ -302,3 +302,36 @@ inherited PR #48 sources. The stacked witness in research/pair-assembly/frame uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. + +Balanced coarse split composition (2026-10-08) +--------------------------------------------- +Eumemic / @eumemic supplied PR69's balanced coarse sums, with OpenAI Codex +assistance. Alejandro Zarzuelo Urdiales / @alejandrozu supplied PR70's bounded +carry-exchange strategy with the AI disclosures retained in the source archive. +Chafik Boukhalfa / @chafreaky, with OpenAI Codex assistance, selected the row/ +half-plane coarse rules, future-compatible unit completion, exact integer-price +carry adaptation, composition and this certificate package. The PR71 anchored +split vector, schedules, arithmetic, pending controls and their contributor +chain are retained as credited above. Original PR69/70 sources, licenses and +notices and the complete published PR71 baseline are preserved under +references/frame-compiler. All earlier notices remain applicable. diff --git a/README.md b/README.md index 035c259b68..0d8b0219be 100644 --- a/README.md +++ b/README.md @@ -21,6 +21,49 @@ speedup. The model and general reduction are inherited from OpenAI's [Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · [Independent arithmetic check](docs/research/community-pair-arithmetic.json) +## Additional conditional construction: merged auxiliary exteriors + +The [merged-exterior proof and reproduction guide](research/merged-exterior/README.md) +gives **κ=55354656014473/10^18=5.5354656014473e-5**, 6.9746% above PR79. Each +auxiliary role's exterior residual is merged into its creation or retirement +edge, chosen per role. A corner-rank lemma for complementary projectors gives +the exact profiles. The largest bit child becomes 552, so the bridge uses +halving degree 17 and row stock p^2200. `make merged-exterior-verify` checks +the result. eumemic prepared it with Anthropic Claude assistance. + +## Additional conditional construction: balanced coarse split frames + +The [balanced-split proof and reproduction guide](research/balanced-split/README.md) +gives **κ=25872812736433/500000000000000000=5.1745625472866e-5**, approximately +**0.6437453019850683%** above the complete published PR71 witness. It composes +PR69 balanced coarse sums and a bounded PR70 carry exchange with PR71's +anchored split graph, future unit completion and profile-cost pending controls. +All actual words, dirty inputs, paid profiles and 47 strict assembly constraints +are checked by `make balanced-split-verify`. This finite conditional construction +retains the inherited all-size hypotheses and contributor notices. Chafik +Boukhalfa prepared the selected composition with OpenAI Codex assistance. + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + ## What changed **Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange diff --git a/certificates/balanced-split-compiler.json b/certificates/balanced-split-compiler.json new file mode 100644 index 0000000000..61295ac857 --- /dev/null +++ b/certificates/balanced-split-compiler.json @@ -0,0 +1,515 @@ +{ + "axes": { + "23": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 36432, + "baseline_pr65_roles": 27918, + "carry_exchange_passes": 0, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 30839, + "elementary_xors": 160514, + "future_unit_completion": true, + "graph_configuration": { + "anchor": true, + "carry_exchange_passes": 0, + "coarse": "half", + "future_completion": true, + "groups": [ + 1, + 1, + 2 + ], + "pending_next_use_cost": true, + "schedule": "cover-core" + }, + 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No external claimed bound is imported as a proof." + } + } +} diff --git a/certificates/balanced-split-completion-validation.json b/certificates/balanced-split-completion-validation.json new file mode 100644 index 0000000000..33d3576de1 --- /dev/null +++ b/certificates/balanced-split-completion-validation.json @@ -0,0 +1,16 @@ +{ + "baseline_source_sha256": "58f13f82ce1bb7f2b5549e17628bc6034e5e05cb24db2acb9a91c24820872f70", + "priority_fixture": "Compatible future use count first, fixed symbolic support popcount second, input index last. Backward and nonnested uses excluded.", + "proof": [ + "The desired output rows followed by selected carry rows are independent by the unchanged checks. Scanning every standard unit vector in any order and retaining it only when independent must extend that fixed prefix to a basis of the whole input-role space: otherwise all standard units would belong to a proper final span, a contradiction.", + "The new priority produces a permutation of precisely those same input indices; it never alters the already selected output/carrier rows and changes only the independent completion rows labelled retired. Rank and full-basis checks remain mandatory.", + "Gaussian elimination and its reversed literal XOR synthesis are unchanged. A square full-rank binary basis is invertible on arbitrary inputs, including dirty roles. Physical frame and clearing charges are still determined by the regenerated actual word.", + "Future-use counts are computed from fixed graph incidence and order. Popcounts use fixed symbolic linear signals already checked against graph values, not runtime input values. The word remains input-independent.", + "Matching, pending lifecycles, the two pending-frame containment checks, and next-use profile costs are byte-identical to the frozen compiler. Their prior legality argument applies unchanged." + ], + "scope": "Checks only our new completion strategy and composed finite witnesses. No mathematical optimality or all-size transfer claim.", + "source_sha256": "a6a423c49737a1f59495a6ba012ed2edcf971e56fa7f0a422b8c9e21212668e6", + "status": "PASS future-completion source delta, actual-use priority and invertible unit-basis extension", + "tested_independent_completions": 2250, + "tested_literal_xors": 34141 +} diff --git a/certificates/balanced-split-exchange-validation.json b/certificates/balanced-split-exchange-validation.json new file mode 100644 index 0000000000..b13cb60d69 --- /dev/null +++ b/certificates/balanced-split-exchange-validation.json @@ -0,0 +1,23 @@ +{ + "exercised_exchange_types": { + "different_region": 103, + "new_future_use": 582, + "same_future_use": 205, + "same_region": 684 + }, + "only_executable_change": "The inserted fixed-price carry-exchange segment; all graph synthesis, future completion, pending controls and physical charging unchanged.", + "proof": [ + "Every candidate edge retains the pre-existing temporal and envelope eligibility. The source changes no candidate construction. Prices are fixed deterministic integers and only rank legal candidates; they are not acceptance bounds for the final moment.", + "If a candidate has an already occupied future use, removing that use owner preserves partition uniqueness. Its destination region either drops the same carrier before the independence test or must support the additional independent row. A different old region only loses a row, which preserves independence.", + "For an unoccupied future use, the code drops one selected edge from the same region and explicitly checks independence with that edge removed. The old future use becomes free and the new use is assigned once. Both cases preserve cardinality.", + "Each accepted exchange strictly reduces the fixed integer price. Only three passes over a finite deterministic priority order are allowed. Final assertions check matching cardinality and every output/carrier row independence; no maximality or final-moment optimality is claimed.", + "After the legal selection changes, the unchanged invertible physical synthesis constructs a fresh word. Selected candidate acceptance must still use full arbitrary-dirty replay, actual frame profiles and exact arithmetic." + ], + "random_matroid_cases": 800, + "scope": "Audits our composition/adaptation only. External PR70 baseline claims are accepted working inputs, not independently reverified.", + "source_sha256": "b80879652ffd52abfc09efe91151cd8613c0cc75bc8c32f46e7edc1ac0ca8bd3", + "status": "PASS our integer-price bounded carry exchange integration", + "targeted_cases": 5, + "total_exchanges_checked": 787, + "unchanged_compiler_sha256": "a6a423c49737a1f59495a6ba012ed2edcf971e56fa7f0a422b8c9e21212668e6" +} diff --git a/certificates/balanced-split-kappa.json b/certificates/balanced-split-kappa.json new file mode 100644 index 0000000000..d95322f078 --- /dev/null +++ b/certificates/balanced-split-kappa.json @@ -0,0 +1,1698 @@ +{ + "assembly": { + "absorption_gap": "103183197446126114632137843787/250012937075805308875848389330500000000000000000", + "constraints": { + "K_dominates_log": "25874151735591877545043043248303221339/500025874151610617751696778661000000000000", + "K_geometry": "375025874151735617751696778661/500025874151610617751696778661000000000000", + "a_below_b": 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"6706303200000000002296594794432615674559610063567/6706303200000000000000000000000000000000000000000", + "rejected_upper": "6706303200000000002296594794432615674560951292087/6706303200000000000000000000000000000000000000000" + }, + "kappa": "55354656014473/1000000000000000000", + "next_kappa": "27677328007237/500000000000000000", + "next_kappa_rejection": "{'g3_above_kappa': '-1477394562229356330270409409/5952710462620964852884281878500000000000000000'}", + "selection_sha256": "83699da476f78fa7af0f31447d427ff34e690fca54ead09a9d9d812f0de7fa44", + "status": "Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed" +} diff --git a/certificates/merged-exterior-selection.json b/certificates/merged-exterior-selection.json new file mode 100644 index 0000000000..5c94129198 --- /dev/null +++ b/certificates/merged-exterior-selection.json @@ -0,0 +1 @@ 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These files document the adapted grouping operation; they are not imported by this producer. Actual imported source closure is PR65 plus shared PR48." + } + }, + "status": "Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed" +} diff --git a/certificates/split-pair-profiles-23.json b/certificates/split-pair-profiles-23.json new file mode 100644 index 0000000000..bf40dc76b4 --- /dev/null +++ b/certificates/split-pair-profiles-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27455,"loss":506,"rank_sum":631971,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38745,"crt_matrices":5750,"crt_disagreements":0,"blocks":[0,357148,21253,8022,5466,4156,3835,3250,2612,2109,1750,1529,1008,863,555,461,234,149,40,9,0,23,0,0]} diff --git a/certificates/split-pair-profiles-25.json b/certificates/split-pair-profiles-25.json new file mode 100644 index 0000000000..2f4bb6b9e9 --- /dev/null +++ b/certificates/split-pair-profiles-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":36015,"loss":600,"rank_sum":900975,"field_prime":2305843009213693951,"frames":84845,"distinct_matrices":52075,"crt_matrices":7444,"crt_disagreements":0,"blocks":[0,492698,27869,10467,7897,5674,5027,4110,3809,3047,2490,2047,1814,1443,1151,898,567,470,271,163,47,13,0,25,0,0]} diff --git a/certificates/split-pair-repository-validation.json b/certificates/split-pair-repository-validation.json new file mode 100644 index 0000000000..5d54439696 --- /dev/null +++ b/certificates/split-pair-repository-validation.json @@ -0,0 +1,20 @@ +{ + "base_commit": "fc74109a6978cb1849547e0dcb9d9df995ddaac5", + "construction": "Anchored split frames with profile-cost pending live reclamation", + "focused_verification": { + "certificate_sha256": "0fcb53fa374273efab6370953c966e8fa065dbfdba43691843a4788cb2cda42e", + "command": "make -j1 split-pair-verify", + "completed_at": "2026-10-08T19:06:05.451986+00:00", + "exit_code": 0, + "full_repository": "PENDING", + "independent_source_receipt_sha256": "89a3b9123f908acf2c877c1c676abfaf44a986db9366c6d675b5e129bc4fcab9", + "independent_tests_receipt_sha256": "db7c44f82fba9f585617438c059088a7991accbe9d48be5c78ef969d73cd504f", + "log_sha256": "076411072dd88e92b155c39a5223bffc846a205f76379ad509790f8cbfeb89c3", + "source_sha256": "9d5a4a7c4cf459f4c5731809de93cfb4b873cb8c9ea95a1be9239733a9a93c72", + "status": "PASS deterministic selected-word regeneration, both physical replays/profiles, exact moment/assembly and 23 focused tests" + }, + "full_repository_command": "make -j1 verify", + "independent_audit": "PASS frozen source/proof/physical/arithmetic integration; receipts bound in focused result", + "scope": "Only finite conditional construction; inherited all-size hypotheses remain.", + "status": "PENDING expanded full repository verification" +} diff --git a/certificates/split-pair-transitions-23.json b/certificates/split-pair-transitions-23.json new file mode 100644 index 0000000000..1a389c32fd --- /dev/null +++ b/certificates/split-pair-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27455, + "frames": 59803, + "distinct_transitions": 152272, + "singles": 15939, + "rank_mass": 631971, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69190, + "2": 73632, + "3": 10224, + "4": 15382, + "5": 6461, + "6": 1593, + "7": 694, + "8": 1229, + "9": 411, + "10": 539, + "11": 98, + "12": 671, + "13": 254, + "14": 1927, + "15": 439, + "16": 440, + "17": 487, + "18": 3417, + "19": 6882, + "21": 171, + "22": 23 + }, + "word_sha256": "b0379d99fd6c10307da0d0fc526ed6171f19105a47bae61730fc3745ef60bd9e", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/certificates/split-pair-transitions-25.json b/certificates/split-pair-transitions-25.json new file mode 100644 index 0000000000..e5864300a1 --- /dev/null +++ b/certificates/split-pair-transitions-25.json @@ -0,0 +1,37 @@ +{ + "h": 25, + "v": 2300, + "R": 36015, + "frames": 84845, + "distinct_transitions": 212584, + "singles": 20700, + "rank_mass": 900975, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 91026, + "2": 108047, + "3": 13560, + "4": 19874, + "5": 8387, + "6": 2967, + "7": 1127, + "8": 1443, + "9": 664, + "10": 791, + "11": 38, + "12": 758, + "13": 149, + "14": 681, + "15": 167, + "16": 2265, + "17": 680, + "18": 566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "word_sha256": "4c956749f0ec72c61875c51099afdf23e69ccea268a9b43b8d46da2ffdb24903", + "copied_centers": 25, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/certificates/split-pair-validation.json b/certificates/split-pair-validation.json new file mode 100644 index 0000000000..80c788033e --- /dev/null +++ b/certificates/split-pair-validation.json @@ -0,0 +1,237 @@ +{ + "axes": { + "23": { + "profile": { + "R": 27455, + "blocks": [ + 0, + 357148, + 21253, + 8022, + 5466, + 4156, + 3835, + 3250, + 2612, + 2109, + 1750, + 1529, + 1008, + 863, + 555, + 461, + 234, + 149, + 40, + 9, + 0, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 5750, + "distinct_matrices": 38745, + "field_prime": 2305843009213693951, + "frames": 59803, + "h": 23, + "loss": 506, + "rank_sum": 631971, + "v": 1771 + }, + "replay": { + "elementary_xors": 162103, + "full_basis_vectors": 30997, + "h": 23, + "histogram": { + "0": 175253, + "1": 58564, + "2": 78945, + "3": 10224, + "4": 15382, + "5": 6461, + "6": 1593, + "7": 694, + "8": 1229, + "9": 411, + "10": 539, + "11": 98, + "12": 671, + "13": 254, + "14": 1927, + "15": 439, + "16": 440, + "17": 487, + "18": 3417, + "19": 6882, + "21": 171, + "22": 23 + }, + "output_roles": 5336, + "rank_mass": 631971, + "roles": 27455, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 673206 + }, + "transitions": { + "R": 27455, + "copied_centers": 23, + "distinct_transitions": 152272, + "frames": 59803, + "h": 23, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69190, + "2": 73632, + "3": 10224, + "4": 15382, + "5": 6461, + "6": 1593, + "7": 694, + "8": 1229, + "9": 411, + "10": 539, + "11": 98, + "12": 671, + "13": 254, + "14": 1927, + "15": 439, + "16": 440, + "17": 487, + "18": 3417, + "19": 6882, + "21": 171, + "22": 23 + }, + "rank_mass": 631971, + "singles": 15939, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 1771, + "word_sha256": "b0379d99fd6c10307da0d0fc526ed6171f19105a47bae61730fc3745ef60bd9e" + } + }, + "25": { + "profile": { + "R": 36015, + "blocks": [ + 0, + 492698, + 27869, + 10467, + 7897, + 5674, + 5027, + 4110, + 3809, + 3047, + 2490, + 2047, + 1814, + 1443, + 1151, + 898, + 567, + 470, + 271, + 163, + 47, + 13, + 0, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 7444, + "distinct_matrices": 52075, + "field_prime": 2305843009213693951, + "frames": 84845, + "h": 25, + "loss": 600, + "rank_sum": 900975, + "v": 2300 + }, + "replay": { + "elementary_xors": 225757, + "full_basis_vectors": 40615, + "h": 25, + "histogram": { + "0": 242882, + "1": 77226, + "2": 114947, + "3": 13560, + "4": 19874, + "5": 8387, + "6": 2967, + "7": 1127, + "8": 1443, + "9": 664, + "10": 791, + "11": 38, + "12": 758, + "13": 149, + "14": 681, + "15": 167, + "16": 2265, + "17": 680, + "18": 566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "output_roles": 6925, + "rank_mass": 900975, + "roles": 36015, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 935228 + }, + "transitions": { + "R": 36015, + "copied_centers": 25, + "distinct_transitions": 212584, + "frames": 84845, + "h": 25, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 91026, + "2": 108047, + "3": 13560, + "4": 19874, + "5": 8387, + "6": 2967, + "7": 1127, + "8": 1443, + "9": 664, + "10": 791, + "11": 38, + "12": 758, + "13": 149, + "14": 681, + "15": 167, + "16": 2265, + "17": 680, + "18": 566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "rank_mass": 900975, + "singles": 20700, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 2300, + "word_sha256": "4c956749f0ec72c61875c51099afdf23e69ccea268a9b43b8d46da2ffdb24903" + } + } + }, + "bit_saving": "12854322426487/250000000000000000", + "certificate_sha256": "97441a432af2301773ec1d729ae7445b9e9d56d6051941a5e0b2e7b617e3e99f", + "kappa": "51414646104039/1000000000000000000", + "margins": 7, + "producer_words_regenerated_and_matched": true, + "scope": "Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.", + "source_binding": "Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.", + "status": "PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly", + "strict_constraints": 47 +} diff --git a/certificates/split-pair-word-23.json.gz b/certificates/split-pair-word-23.json.gz new file mode 100644 index 0000000000..38b82cbb3d Binary files /dev/null and b/certificates/split-pair-word-23.json.gz differ diff --git a/certificates/split-pair-word-25.json.gz b/certificates/split-pair-word-25.json.gz new file mode 100644 index 0000000000..da9935d15a Binary files /dev/null and b/certificates/split-pair-word-25.json.gz differ diff --git a/references/frame-compiler/pr59-split-operation/LICENSE b/references/frame-compiler/pr59-split-operation/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/references/frame-compiler/pr59-split-operation/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. diff --git a/references/frame-compiler/pr59-split-operation/SOURCE.json b/references/frame-compiler/pr59-split-operation/SOURCE.json new file mode 100644 index 0000000000..280e096342 --- /dev/null +++ b/references/frame-compiler/pr59-split-operation/SOURCE.json @@ -0,0 +1,12 @@ +{ + "author": "Rohan Garg / rohangar1 with OpenAI Codex assistance", + "commit": "641f22e52913db784f3b6ff1176b0c2945aae45b", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "f85437ee441f2a028660dd5e8dbdc0ec7b52bb55c04ea34fa4829c154bfd0ac1", + "research/split-skip/SOURCE.json": "7c2b4646a3ecfef6f881da5c43e4bd0fa9a4d1b00548b8ab458d897e16735134", + "research/split-skip/split_graph.py": "9b16ba907cbd58611fb64bfb9211be7809d54822d44c78fc6167cf4ba79eb905" + }, + "repo": "CrocSwap/integer-mult-bounds", + "scope": "Preserved original split-pair operation and attribution. These files document the adapted grouping operation; they are not imported by this producer. Actual imported source closure is PR65 plus shared PR48." +} diff --git a/references/frame-compiler/pr59-split-operation/research/split-skip/SOURCE.json b/references/frame-compiler/pr59-split-operation/research/split-skip/SOURCE.json new file mode 100644 index 0000000000..2ab610b6ea --- /dev/null +++ b/references/frame-compiler/pr59-split-operation/research/split-skip/SOURCE.json @@ -0,0 +1,189 @@ +{ + "PR54": { + "consumed_commit": "7210de7d0f9ccaeb64c3f60f188419e02be08d95", + "contribution": "Chafik Boukhalfa original-envelope paid-clone replay, deriving from RaD / hipotures PR51", + "difference": "Only validation.json changed; claim and replay sources unchanged", + "latest_observed_commit": "84eb0b067741dc2690da837743fda06d133da865" + }, + "files": { + "research/skip-strips/PROOF.md": "0fad3bfbd7062e1607fc95430170d12f9613cc6d850a18871f1cbc8c27434934", + "research/skip-strips/SOURCE.json": "d6819476cb69ad731db2c809844d672a8c8f367fb120ffe43467ac471dc8574d", + 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OpenAI Codex assistance. +Apache-2.0; retained predecessor source notices apply. +""" +from itertools import combinations +import sys, json +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2] +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/skip-strips')] +import skip_graph as base +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + +def reorder(c, values, mode): + order=list(range(len(values))) + if mode=='reverse': order.reverse() + elif mode=='desc': order.sort(key=lambda i:(c.support[values[i]].bit_count(),c.support[values[i]]),reverse=True) + elif mode=='asc': order.sort(key=lambda i:(c.support[values[i]].bit_count(),c.support[values[i]])) + elif mode=='size_desc': order.sort(key=lambda i:(-c.support[values[i]].bit_count(),c.support[values[i]])) + elif mode=='support_desc': order.sort(key=lambda i:(c.support[values[i]].bit_count(),-c.support[values[i]])) + elif mode=='odd_even': order=order[1::2]+order[::2] + elif mode=='even_odd': order=order[::2]+order[1::2] + elif mode=='ends': order=[x for pair in zip(order[:len(order)//2],order[::-1][:len(order)//2]) for x in pair]+([len(order)//2] if len(order)%2 else []) + elif mode!='input': raise ValueError(mode) + return order + +def graph(h,config=None,record=None): + if config is None: + config=json.loads((Path(__file__).resolve().parent/f"config-{h}.json").read_text()) + cfg=config or {}; recording=record if record is not None else {} + totals=cfg.get('totals',{});strips=cfg.get('strips',{}) + class Circuit(base.circuit_class(h)): + def grouping(self,points): + groups=super().grouping(points) + choices=cfg.get('groups',[0,0,0,0,0]) + choice=choices[self._level] if self._level3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": 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0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + 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Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + } + }, + "gzip_sha256": "4629d45d5074f87706db46be3aa3cd369071cd215bc6560d641115aadcce54a0", + "word_sha256": "bd0cbf73756f2e4f8d3879ec6c7a194990eb9ec40aaf3580bdded6994798d920" + }, + "25": { + "compiled": { + "h": 25, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 36586, + "baseline_pr48_roles": 48329, + "histogram": { + "1": 55478, + "0": 416276, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + }, + "rank_mass": 915250, + "elementary_xors": 205650, + "stats": { + "augmentations": 286, + "regions": 73695, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json b/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json new file mode 100644 index 0000000000..346cf87ea3 --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json @@ -0,0 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b/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json 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"transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz b/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz new file mode 100644 index 0000000000..3a7c7c41c1 Binary files /dev/null and b/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz differ diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz b/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz new file mode 100644 index 0000000000..6a239a3e9f Binary files /dev/null and b/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz differ diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 64793806 + }, + "internal_23": { + "1": 790852700, + "10": 4149200, + "11": 3946800, + "12": 2902600, + "13": 2477100, + "14": 1635300, + "15": 1354700, + "16": 809600, + "17": 443900, + "18": 262200, + "2": 38771100, + "20": 103500, + "21": 52900, + "3": 24242000, + "4": 13298600, + "5": 9558800, + "6": 8995300, + "7": 8360500, + "8": 6573400, + "9": 5253200 + }, + "internal_25": { + "1": 840587440, + "10": 4772845, + "11": 4691379, + "12": 3375526, + "13": 2945173, + "14": 2380224, + "15": 1995917, + "16": 1259181, + "17": 1036035, + "18": 672980, + "19": 320551, + "2": 44554818, + "20": 200123, + "22": 97405, + "23": 44275, + "3": 21423787, + "4": 12000296, + "5": 10156685, + "6": 9740500, + "7": 8633625, + "8": 6701464, + "9": 5683139 + }, + "paid_endpoint_copy": { + "1": 4073300 + } + }, + "total_rank": 78860441550 + }, + "bit_saving": "2551509/50000000000", + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + "exponent": 5333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5715743812, + "rhs": 1792000000313576, + "rhs_bits": 51 + }, + "rows": { + "exponent": 5715743812, + "rhs": 896000000156824000, + "rhs_bits": 60 + } + } + }, + { + "log2_input": 224000000000000, + "powers": { + "alpha": { + "exponent": 11431487624, + "rhs": 1792000000156824, + "rhs_bits": 51 + }, + "compact": { + "exponent": 11431487624, + "rhs": 7168000000627232, + "rhs_bits": 53 + }, + "leaf": { + "exponent": 10666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11431487624, + "rhs": 3584000000313576, + "rhs_bits": 52 + }, + "rows": { + "exponent": 11431487624, + "rhs": 1792000000156824000, + "rhs_bits": 61 + } + } + }, + { + "log2_input": 448000000000000, + "powers": { + "alpha": { + "exponent": 22862975248, + "rhs": 3584000000156824, + "rhs_bits": 52 + }, + "compact": { + "exponent": 22862975248, + "rhs": 14336000000627232, + "rhs_bits": 54 + }, + "leaf": { + "exponent": 21333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 22862975248, + "rhs": 7168000000313576, + "rhs_bits": 53 + }, + "rows": { + "exponent": 22862975248, + "rhs": 3584000000156824000, + "rhs_bits": 62 + } + } + } + ], + "practical_runtime_claim": false + }, + "kappa": "40827/800000000", + "next_kappa": "318961/6250000000", + "next_kappa_rejection": "{'g1_above_kappa': '-25408022593116799041/7102635201420453820506250000000', 'g3_above_kappa': '-5201705247125960457841/1136421632227272611281000000000000', 'g5_above_kappa': '-7640875416065173165777/1818274611563636178049600000000000', 'g6_above_kappa': '-33658690551416775383761/9091373057818180890248000000000000'}", + "original_enclosure_control": { + "accepted_upper": "427922022655051425592169455669348999419009338821677321501934579031509793316011927849852932699225587520480274623290826519124585131702799274967695430254567113650998884459986946222692530282749027853246814000572815342011972280832203653626757194588235745687874105909336892415629002940540277569675953192803096179140323199169875932058482212840371519373866332987776983981442275480629595879092440778438065834410270423292532877965451564571150969903518733283745770147929604915103094966966240445718551419238205360172260389165815355293860586787487668007987689744585745259297708409486845374929838902410526770296527117452860612190765279746966315757114757646249443956020657651637850471083396567352186238660458491615294604389003317389825219053116168473153626947262543915434579501546193988862612230828605213616950127673267971569642351835151332191639228898384399684069201926146521990048728093044781289653532998958679374426311189560250341590145887508815021337226982815008224357898461730107482372032845888428476273500999760300211786400006201411895378711403441679516543048925021677151249124774565210588951830515783148269750340702961227551/427922022656065148722015624802653702889498564421131911283499341667573520226931037010841800905471906532344178836996138043716400845851217866305783744362952178488692163617667760947934446961428764096857095662125776648371730944750850740376437391609342381012534311915175448066736517476339673099556706774420618964194148648273392198066357729130169733561134843302857240883248026154958104699812690626052696940220399106081385425042375485602542555097186568052507330835744941604979041042724146442866160606543845260686788873587136675704407457814823973491248098778928607362558510538701395621352496475077156310639504247824069338077266718928997258973439362819271794470658904562860362470215133491491305622841328989108583065554731667738937158958161399293136952726957825424616696098290625805073806865420810062253320746566043770582998650738545122821954094593047815197564256009823257422725379706679933315631514838786135447434356419391187561619401952168548631044553632502869921434523792993783307013326156305798890689568359302672301544894715282222433613932715358768884516049207059704442128612279932500000000000000000000000000000000000000000", + "next_bit_lower": "374050380000830479912607937870818083834173718615907103079616878943322706260497332605534066060136407627149268792108716494485294881071/374050380000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + } + }, + "comparison": { + "additional_precision_gain": "2116843/200000000000000000", + "difference": "1238116843/200000000000000000", + "difference_pr65": "59693903/12500000000000000", + "kappa": "10206752116843/200000000000000000", + "pr63_kappa": "5102757/100000000000", + "pr65_kappa": "2041159402879/40000000000000000", + "structural_gain_on_original_grid": "309/50000000000" + }, + "grid_denominator": 1000000000000000000, + "next_bit_saving": "5103636516201/100000000000000000", + "preferred": { + "assembly": { + "absorption_gap": "12957517239351787231794417587/100005103636516190692726967598200000000000000000", + "constraints": { + "K_dominates_log": "25518182705927945452132037536365162009/500025518182580953463634837991000000000000", + "K_geometry": "375025518182705953463634837991/500025518182580953463634837991000000000000", + "a_below_b": "20663634837991/1000000000000000000", + "a_positive": "51036365162009/1000000000000000000", + "alpha_below_one": "999999999999500025518182580953463634837991/1000051036365161906927269675982000000000000", + "alpha_below_one_fourth": "249961722725628595322730323966963634837991/1000051036365161906927269675982000000000000", + "alpha_positive": "51036365661881409087095028536365162009/1000051036365161906927269675982000000000000", + "artificial_boundary": "28001633163690681098227177374284390904513973/4000204145460647627709078703928000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "499974481817294046536365162009/500000000000000000000000000000", + "c_positive": "25518182705953463634837991/500000000000000000000000000000", + "cell_above_band": "999999999998499974481817419046536365162009/2000102072730323813854539351964000000000000", + "compact_leaf": "8539317419046536365162009/500000000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "25518183080953463634837991/500025518182580953463634837991", + "epsilon_positive": "499999999999500000000000000000/500025518182580953463634837991", + "g1_above_kappa": "100005116594033430044514199392617587/100005103636516190692726967598200000000000000000", + "g2_above_kappa": "1302288897/500000000000000000", + "g3_above_kappa": "12957517239351787231794417587/100005103636516190692726967598200000000000000000", + "g4_above_kappa": "1302288897/500000000000000000", + "g5_above_kappa": "37501926821210810861559844643742587/100005103636516190692726967598200000000000000000", + "g6_above_kappa": "87504478639468906207923328442842587/100005103636516190692726967598200000000000000000", + "g7_above_kappa": "99994896363383814423867065831844514199392617587/100005103636516190692726967598200000000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "25518183080953463634837991/500025518182580953463634837991", + "lambda_above_internal": "51036365162009/1000000000000000000000000000000", + "lambda_above_sigma": "20663634838042036365162009/1000000000000000000000000000000", + "lambda_above_tau": "51036365162009/1000000000000000000000000000000", + "lambda_prime_above_lambda": "51036365162009/1000000000000000000000000000000", + "lambda_prime_below_one": "25518182580953463634837991/500000000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "40829092429500023633159832136365162009/800040829092129525541815740785600000000000", + "phase_leaf_above_bit": "17078634837991/1000000000000000000", + "phase_local": "204145464147602190896122974536365162009/4000204145460647627709078703928000000000000", + "prime_interval_packing": "25518183080953463634837991/500025518182580953463634837991", + "q_below_internal": "51036365162009/500000000000000000000000000000", + "q_below_leaf": "8539317419046536365162009/500000000000000000000000000000", + "q_below_reservations": "1/4000000000000", + "q_positive": "25518182580953463634837991/500000000000000000000000000000", + "record_suffix": "25518183080953463634837991/500025518182580953463634837991", + "row_product_gap": "6548/25", + "short_record_fallback": "499974480514563711027641740160491885440816916081/500025518182580953463634837991000000000000000000", + "small_field_exposure": "1/1000000000000" + }, + "finite_bridge": { + "bit": { + "W": 137151806, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "margins": { + "g1": "25518183080953463634837991/500025518182580953463634837991", + "g2": "51036365162009/1000000000000000000", + "g3": "25518182580927945452257037536365162009/500025518182580953463634837991000000000000", + "g4": "51036365162009/1000000000000000000", + "g5": "40829092429500023633159832136365162009/800040829092129525541815740785600000000000", + "g6": "204145464147602190896122974536365162009/4000204145460647627709078703928000000000000", + "g7": "499999999999500000000000000000/500025518182580953463634837991" + }, + "minimum_margin": "25518182580927945452257037536365162009/500025518182580953463634837991000000000000", + "parameters": { + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": "1", + "a_bit": "51036365162009/1000000000000000000", + "a_complex": "717/10000000", + "alpha_squared_power": "51036365661881409087095028536365162009/1000051036365161906927269675982000000000000", + "beta": "1/20", + "c": "25518182705953463634837991/500000000000000000000000000000", + "delta": "1/8000000000000", + "epsilon": "499999999999500000000000000000/500025518182580953463634837991", + "h": "1/1000000000000", + "kappa": "10206752116843/200000000000000000", + "lambda_": "999948963634838042036365162009/1000000000000000000000000000000", + "lambda_prime": "499974481817419046536365162009/500000000000000000000000000000", + "q": "25518182580953463634837991/500000000000000000000000000000", + "sigma": "9999283/10000000", + "tau": "999948963634837991/1000000000000000000" + }, + "recurrence": { + "internal": "999948963634837991/1000000000000000000", + "leaf": "199986377/200000000", + "reservations": "499974481817294046536365162009/500000000000000000000000000000" + }, + "scoped_limit": "51036365162009/1000051036365162009" + }, + "eventual_bounds": { + "additional_eventual_conditions": [ + "BHP prime threshold and distinct-prime packing", + "Fixed rational basis, eligible common prime and native table setup", + "Catalogue/descriptor domination, logarithm absorption, exact recovery" + ], + "all_interval_argument": "For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). Successive intervals double LHS; the positive affine RHS grows at most linearly, so 2^j >= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956143, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + "exponent": 5333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 5715743812, + "rhs": 1792000000313576, + "rhs_bits": 51 + }, + "rows": { + "exponent": 5715743812, + "rhs": 896000000156824000, + "rhs_bits": 60 + } + } + }, + { + "log2_input": 224000000000000, + "powers": { + "alpha": { + "exponent": 11431487624, + "rhs": 1792000000156824, + "rhs_bits": 51 + }, + "compact": { + "exponent": 11431487624, + "rhs": 7168000000627232, + "rhs_bits": 53 + }, + "leaf": { + "exponent": 10666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 11431487624, + "rhs": 3584000000313576, + "rhs_bits": 52 + }, + "rows": { + "exponent": 11431487624, + "rhs": 1792000000156824000, + "rhs_bits": 61 + } + } + }, + { + "log2_input": 448000000000000, + "powers": { + "alpha": { + "exponent": 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b/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 at the new bit saving, +and the new complete profile has exact upper moment <1. All47 strict assembly +conditions and seven margins pass. **53 Lean endpoints** pass:34 new universal, +15 concrete,4 reused rational-helper lemmas. No omitted proof, project axiom or +native decision shortcut. The math scope includes dirty-word/complement safety, +coordinate conjugacy, fresh-kernel clearing, actual finite rounding and old-profile +rejection. It does not formalize the Python/C++ compiler or the all-size theorem. + +## Reproduce the accepted words + +Use an external checkout of frozen PR62 commit +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No newer sources are consumed. +See `verification/README.md` to compile its exact C++17 profiler, then run: + +``` +python verification/verify_words.py --upstream UPSTREAM --profiler PROFILER --word23 words/word-23.json.gz --word25 words/word-25.json.gz --output work/recheck +python verification/check_guards.py words/word-23.json.gz +python verification/check_guards.py words/word-25.json.gz +cd math +lake build Frozen62Research +``` + +The verifier checks immutable sources and its own adapter hashes, full input/dirty +bases in both orientations, exact source/scatter inventory, every literal frame +transition and all fixed-I+J profiles with bounded-minor and CRT checks. It rejects +optimized Python assertion mode. Use the supplied words for authoritative replay; +floating discovery prices propose candidates and have no trusted-proof role. +Discovery source snapshots, exact oracle fixtures (gzip-compressed) and matching +seeds retain original byte hashes. `discovery/SEARCH.md` explains the algorithms, +heuristic boundary and experimental commands. Historical workspace paths in the +source-generation receipts identify the original run; the accepted-word replay +uses the explicit upstream argument and needs no private directory layout. +Portable discovery regeneration: + +``` +python discovery/regenerate_portable.py --upstream UPSTREAM --work work/regenerate +``` + +This rewrites workspace paths only and checks both raw words and deterministic +gzip against the accepted words. Floating discovery is outside the trusted +certificate; the independent word/profile verifier establishes acceptance. + +The one-hour session froze information through #62. The unchanged data geometry +and its rational recovery are inherited; selected physical words/profile checks +are fresh. All-size analytic, compiler/frame transfer, finite-alphabet tape, +routing, prime selection/recovery and eventual-threshold contracts remain +conditional. No practical runtime or global-optimality claim is made. + +Alejandro Zarzuelo Urdiales is the human author/developer, following earlier +Archivara and personal July/October matrix/parity work developed with multiple +AI tools. This synthesis involved substantial OpenAI Codex assistance. Known +linear algebra, matroid exchange, dirty uncomputation and concavity principles +retain prior-work status. The finite construction credits Avi Eisenberg/ikeboy +(#62 interval/core-aware graph), eumemic (#57 frame compiler), Chafik Boukhalfa +(#60 ranking and earlier exact profiling), Rohan Arun and other retained notices. +The prior matrix/parity source is in `../matrix-exponent-synthesis/` and prior +Gaussian work in PR45. Its product counts retain their separate arithmetic scope. +The paper is supplied as LaTeX source; no newly compiled PDF is claimed. diff --git a/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md b/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md new file mode 100644 index 0000000000..b8dd669634 --- /dev/null +++ b/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/SEARCH.md @@ -0,0 +1,136 @@ +# Local frame-compiler search, frozen through PR62 + +All experiments in this directory use the pinned PR62 pair graph at +`ad0f25ff7b23cff7f08ad237c2254e6ecf74257e`. No later community source is consumed. +The original checkout is unchanged. Each emitted word and compiler copy has +a SHA256 recorded in its `compiled.json`; changed words are sent separately +to the independent literal replay and profile verifier. + +## New dependency-circuit choices + +The inherited compiler reduces retired fresh-signal rows against the current +live anchors and an echelon basis of compatible retired rows. Instead of +accepting the first dependent retired row, the new selectors collect the +available fundamental dependency circuits and choose a circuit by one of: + +- total charged target/provider rank growth (`all_growth`); +- number and rank growth of other retired providers (`all_collateral`); +- anchor-only dependence before general retired dependence (`anchor_first`); +- actual physical transition child-profile moment cost (`profile_cost*`). + +Every clearing XOR and every target/provider frame promotion is still emitted +and charged. A zero fresh-signal row can contain arbitrary physical dirty state; +its reuse is justified by the complete reversible word, not by claiming that +the physical register is initialized to zero. The compiler runs both complete +dirty-basis orientations, and the independent verifier repeats them. + +For the last selector let `C(A,B) = sum_t n_t(A,B) F_t`, where the `n_t` are +the exact inherited fixed-I+J pivot-run profile of the physical frame transition +and `F_t = t exp(a log(m/t))`. A candidate target `s` at old frame `A_s`, cleared +into frame `G` with providers `z`, is priced by + +``` +C(A_s,G) - C(A_s,I) + + sum_z [C(A_z,G) + C(G,I) - C(A_z,I)]. +``` + +This accounts for immediate promotions and the change in deferred cleanup, +assuming each other retired provider remains retired until cleanup. Future +reuse couples decisions, so this is a discovery heuristic, not an additive +global optimality certificate. Linear rank mass cancels between candidates; +`t*expm1(a*log(m/t))` avoids cancellation in floating discovery prices. +Missing transition profiles are recorded and collected for the next iteration. +Once a run has zero missing pairs, every local price uses an actual transition +profile. The final saving is accepted only through exact rational whole-profile +moment bounds and all assembly gates. + +`build_pair_oracle.py` is a local adaptation of the frozen C++ profiler that +additionally exports each transition histogram. It preserves the projector, +pivot, bounded-minor and three-prime CRT routines. Its synthetic transition-list +input is an oracle request, not a physical executable word. Each immutable +profile dump and the source/header hashes are recorded. + +## Moment-ordered carry selection + +The `--weighted` experiment orders the inherited linear/partition-matroid +candidate edges by their physical transition moment change before the original +greedy initialization and augmenting paths. For a value produced at `P`, +preserved through donor frame `G`, and carried to future target `T`, its +no-reclamation child-cost change is + +``` +C(G,T) - C(G,I) - C(0,P) - C(P,T). +``` + +At fixed cardinality, role and external-volume corrections are common to all +edge choices in the same axis. The inherited augmenting algorithm still seeks +maximum cardinality; it does not optimize the weights globally. Reclamation +adds coupling, so only the changed whole-word profile can establish an actual +improvement. This experiment makes no minimum-cost matroid claim. + +The `--exchange` variant starts from the frozen original maximum-cardinality +matching and tries bounded improving one-edge exchanges. A new edge may replace +the old donor of the same use when its donor block stays linearly independent; +or it may replace a selected edge in the same donor block and serve an unused +use. Both preserve cardinality and distinct-use constraints. The `--cycle` +variant additionally tests two-edge donor/use cycles, checking the independence +of both changed blocks. No improving two-edge cycle was found in the tested +native-price instance; this is not a proof that longer cycles cannot improve it. + +## Joint basis and schedule search + +`--basis shift1` profiles all candidate physical transitions after the point +permutation `i -> (i+1) mod h`, while preserving their original frame IDs. +Matching and reclamation are then priced in that basis. The emitted word is +renamed by `relabel_word.py`: all frame masks, canonical source/output triples, +common points and scatter port indices change together. Scratch slots and +literal XOR instructions are retained. The complete triple family and the +permutation-invariant `I+J` basis are inherited; every final renamed word still +gets fresh full-basis and actual physical-profile verification. + +This joint search differs from merely relabeling an already selected schedule: +the selected carries and clearing circuits are optimized under the new ordered +pivot-run prices. It remains a bounded discovery heuristic. + +## Regeneration + +The frozen graph/matching setup and a moment-cost exchange run are generated by: + +``` +python -S collect_matching_pairs.py --h 23 +python -S build_pair_oracle.py --h 23 --strategy matching_collect +python -S run_strategy.py --h 23 --strategy profile_cost --exchange +``` + +Repeat at `h=25`. For joint search, add `--basis shift1` to the oracle and +strategy commands. Reclamation may encounter transitions absent from the +initial carry-edge inventory. Run the oracle again on the emitted strategy +directory with `--incremental`, then run a new strategy label. The new label +must start with `profile_cost`; output directories are never overwritten. +`compiled.json` records the exact oracle dump hash, missing-pair count, word +hashes and source pin. Immutable earlier oracle dumps are retained by SHA256. +Use `--oracle path/to/the-immutable-dump.jsonl` to reproduce the prices of a +specific recorded run instead of consuming the subsequently enlarged cache. +The initial compiler matching cache is accepted only if its complete candidate +edge list matches the current frozen graph and every restored selected block +passes the same linear-independence check. + +The runner saves an immutable source copy and its hash for later runs. Floating +`expm1` prices at discovery saving `a=0.00005103` select proposals only. Neither +those prices nor their reported local gains are used as an arithmetic witness. + +## Acceptance boundary + +The independent verifier checks all input and dirty basis vectors in both +orientations, exact literal-scatter incidences, causal nested physical frames, +event equality reconstructed from the actual XOR word, rank mass, actual child +profiles and CRT agreement. It then computes the whole mixed-axis recurrence +and exact rational moment/assembly witnesses. Existing all-size geometry, +analytic envelopes, compiler/tape arguments and the surrounding reduction are +inherited from frozen PR62. A finite profile improvement does not by itself +formally prove those inherited hypotheses. + +Reduced XOR count alone is not accepted as an exponent improvement. In this +search `all_collateral` and `anchor_first` reduced clearing XORs but worsened +the certified characteristic. Actual child-size distributions decide the +saving, even when both physical-role counts and total rank mass are unchanged. diff --git a/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py b/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py new file mode 100644 index 0000000000..7c154b1a29 --- /dev/null +++ b/references/frame-compiler/pr70/research/profile-aware-frame-search/discovery/compiler_profile_cost4_exchange_3d3d6f5c9a0b.py @@ -0,0 +1,275 @@ +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +import sys;sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'matrix-synthesis/bridge/pr62/references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s,add=True): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<>s&1;e^=1<=prices[f]-1e-14:continue + if not can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:-prices[z])if prices[e] /dev/null + python3 scripts/batched_network.py --output certificates/batched-network.json --summary + +batched-patch: + python3 scripts/make_batched_patch.py + +batched-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex +endif + +.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note +partial-swap-producer: + python3 scripts/partial_swap_producer.py + +partial-swap-certificate: + python3 scripts/partial_swap_network.py + +partial-swap-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex +endif + +.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note +endpoint-gauge-producer: + python3 scripts/endpoint_gauge_producer.py + +endpoint-gauge-certificate: + python3 scripts/endpoint_gauge_network.py + +endpoint-gauge-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex +endif + +.PHONY: endpoint-gauge-verify +endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate + python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v + +.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note +structured-bulk-producer: + python3 scripts/structured_bulk_producer.py + +structured-bulk-certificate: + python3 scripts/structured_bulk_network.py + +structured-bulk-verify: structured-bulk-producer structured-bulk-certificate + +structured-bulk-note: + mkdir -p artifacts +ifeq ($(TEX_ENGINE),tectonic) + $(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex +else + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex + $(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex +endif + +.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify +copied-centers-producer: + python3 scripts/copied_centers_producer.py + +copied-centers-certificate: + python3 scripts/copied_centers_network.py + +copied-centers-verify: copied-centers-producer copied-centers-certificate + +.PHONY: copied-reversed-check copied-reversed-producer +copied-reversed-check: + python3 research/copied-reversed/geometry.py + python3 research/copied-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_reversed.py' -v + +copied-reversed-producer: + mkdir -p build/copied-reversed/producer + python3 scripts/copied_centers_producer.py --work-dir build/copied-reversed/producer --output build/copied-reversed/producer.json + + +.PHONY: copied-fixed-reversed-check copied-fixed-reversed-producer +copied-fixed-reversed-check: + python3 research/copied-fixed-reversed/geometry.py --full + python3 research/copied-fixed-reversed/witness.py + python3 -m unittest discover -s tests -p 'test_copied_fixed_reversed.py' + +copied-fixed-reversed-producer: + mkdir -p build/copied-fixed-reversed/producer + python3 research/copied-fixed-reversed/producer.py --work-dir build/copied-fixed-reversed/producer --output build/copied-fixed-reversed/producer.json + python3 research/copied-fixed-reversed/review/fixed25_copied_crt_audit.py --work-dir build/copied-fixed-reversed/producer --record build/copied-fixed-reversed/producer.json --profiler-source research/copied-fixed-reversed/full_profiles25.cpp --output build/copied-fixed-reversed/crt-audit.json + + +.PHONY: copied-fixed-verify copied-fixed-producer copied-fixed-check +copied-fixed-producer: + python3 research/copied-fixed/producer.py + +copied-fixed-check: + python3 research/copied-fixed/audit.py + python3 research/copied-fixed/verify.py --output research/copied-fixed/certificate.json + python3 -m unittest discover -s tests -p 'test_copied_fixed.py' -v + +copied-fixed-verify: copied-fixed-producer copied-fixed-check + +.PHONY: climbed-48-verify climbed-48-producer climbed-48-check +climbed-48-producer: + python3 research/climbed-48/producer.py + +climbed-48-check: + python3 research/climbed-48/witness.py --output research/climbed-48/certificate.json + python3 -m unittest discover -s tests -p 'test_climbed_48.py' -v + +climbed-48-verify: climbed-48-producer climbed-48-check + +.PHONY: formal-verify formal-historical-verify formal-gaussian-verify +formal-verify: formal-historical-verify formal-gaussian-verify + +formal-historical-verify: + cd formal/lean && lake build + python3 scripts/check_lean_axioms.py --project formal/lean --audit formal/lean/AuditAll.lean + python3 formal/lean/sources.py + python3 formal/open-prs/drift_A.py + python3 formal/open-prs/drift_B.py --selftest + python3 formal/open-prs/drift_C.py + mkdir -p build/formal + python3 formal/circuit/export_paired.py build/formal/paired50.json + python3 -I formal/circuit/check_paired.py build/formal/paired50.json + +formal-gaussian-verify: + $(MAKE) -C research/gaussian-parity-synthesis verify + python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean + +.PHONY: verify-research +# Historical finite searches; no current witness or production certificates change. +verify-research: + python3 scripts/audit_bit_compression.py + python3 scripts/audit_mixed_point.py + python3 scripts/audit_early_sharing.py + python3 scripts/audit_split_centers.py + python3 scripts/audit_stage_pair.py + python3 scripts/audit_block_carry.py + python3 scripts/audit_joint_return.py + python3 scripts/audit_cyclic_topology.py + python3 scripts/audit_fano_completion.py + python3 scripts/audit_fano_permutation.py + python3 scripts/audit_rank_product_core.py + python3 scripts/audit_stronger_screens.py + python3 scripts/audit_subset_cores.py + python3 scripts/audit_cube_cores.py + python3 scripts/audit_single_intersection.py + python3 scripts/audit_shared_core.py + python3 scripts/audit_general_guard.py + python3 scripts/audit_disjoint_tensor.py + python3 scripts/audit_core_limits.py + python3 scripts/audit_affine_vectors.py + python3 scripts/audit_block_core.py + python3 scripts/audit_complex_centers.py + python3 scripts/audit_inplace_side.py + python3 scripts/audit_quadratic_affine.py + python3 scripts/audit_signed_sparse.py + python3 scripts/audit_positive_side.py + python3 scripts/audit_parity_side.py + python3 scripts/audit_prime_subset_limits.py +.PHONY: skip-frame-verify +skip-frame-verify: + python3 scripts/experiments/verify_skip_frame.py + + +.PHONY: joint-dual-verify +joint-dual-verify: + python3 scripts/experiments/verify_joint_dual.py + python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v + + +.PHONY: skip-strips-verify skip-strips-producer skip-strips-check +skip-strips-producer: + python3 research/skip-strips/producer.py + +skip-strips-check: + python3 research/skip-strips/audit.py + python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json + cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v + +skip-strips-verify: skip-strips-producer skip-strips-check + +.PHONY: positive-skip-verify positive-skip-build positive-skip-check +positive-skip-build: + python3 scripts/audit_positive_skip_exact.py + +positive-skip-check: + python3 research/positive-skip/witness.py --output research/positive-skip/certificate.json + python3 -m unittest discover -s tests -p 'test_positive_skip.py' -v + +positive-skip-verify: positive-skip-build positive-skip-check + +.PHONY: split-skip-producer split-skip-check split-skip-verify +split-skip-producer: + python3 research/split-skip/producer.py --work-dir build/split-skip --output build/split-skip-receipt.json + +split-skip-check: + python3 research/split-skip/witness.py + python3 research/split-skip/independent_arithmetic.py + python3 -m unittest discover -s tests -p 'test_split_skip.py' -v + +split-skip-verify: split-skip-producer split-skip-check + +.PHONY: skip-suffix-verify skip-suffix-producer skip-suffix-check +skip-suffix-producer: + python3 research/skip-suffix/producer.py + +skip-suffix-check: + python3 research/skip-suffix/audit.py + python3 research/skip-suffix/verify.py --output research/skip-suffix/certificate.json + cd research/skip-suffix && python3 -m unittest discover -s ../../tests -p 'test_skip_suffix.py' -v + +skip-suffix-verify: skip-suffix-producer skip-suffix-check + +.PHONY: skip-clones-verify skip-clones-producer skip-clones-check +skip-clones-producer: + python3 research/skip-clones/producer.py + +skip-clones-check: + python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json + python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v + +skip-clones-verify: skip-clones-producer skip-clones-check + +.PHONY: verify-strips verify-clones verify-positive verify-joint formal-matrix-verify +verify-strips: skip-strips-verify skip-suffix-verify +verify-clones: skip-clones-verify split-skip-verify +verify-positive: positive-skip-verify +verify-joint: skip-frame-verify joint-dual-verify + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + +formal-verify: formal-matrix-verify +formal-matrix-verify: + mkdir -p build + cd research/matrix-exponent-synthesis && lake build + python3 scripts/check_lean_axioms.py --project research/matrix-exponent-synthesis --audit research/matrix-exponent-synthesis/AuditAll.lean + python3 research/matrix-exponent-synthesis/run_checks.py --work "$$(mktemp -d build/matrix-synthesis.XXXXXX)" + python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: pair-assembly-verify pair-assembly-producer pair-assembly-check +pair-assembly-producer: + python3 research/pair-assembly/producer.py + +pair-assembly-check: + python3 research/pair-assembly/audit.py + python3 research/pair-assembly/verify.py --output research/pair-assembly/certificate.json + python3 research/pair-assembly/frame/frame_verify.py + cd research/pair-assembly && python3 -m unittest discover -s ../../tests -p 'test_pair_assembly.py' -v + +pair-assembly-verify: pair-assembly-producer pair-assembly-check + +.PHONY: verify-pair +verify-pair: pair-assembly-verify + python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: split-pair-verify +split-pair-verify: + python3 scripts/experiments/verify_split_pair.py + python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v + +verify-joint: split-pair-verify diff --git a/references/frame-compiler/pr71/NOTICE b/references/frame-compiler/pr71/NOTICE new file mode 100644 index 0000000000..8adab44ba3 --- /dev/null +++ b/references/frame-compiler/pr71/NOTICE @@ -0,0 +1,324 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Aligned split-pair composition (2026-10-08) +------------------------------------------ +Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik +Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending +live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules +and refined exact arithmetic, and PR67 all-rank profile-cost selection and +its profile oracle. Rohan Garg / rohangar1 +with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic +with substantial OpenAI Codex assistance: PR57 joint reversible compiler and +independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex +assistance: PR60 ranked reclamation and this selected [1,1,2] split vector, +aligned common-point permutation, next-use profile score, composition and +certification package. +The complete PR65 baseline words, profiles and arithmetic, plus 43 original +source/provenance files, are preserved under references/frame-compiler/pr65. +The original PR59 split operation and notices are separately preserved. +PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof, +retain their original bytes, licenses and notices in their own archives. +All previous notices and mathematical dependencies remain applicable. diff --git a/references/frame-compiler/pr71/README.md b/references/frame-compiler/pr71/README.md new file mode 100644 index 0000000000..4a9b481aa3 --- /dev/null +++ b/references/frame-compiler/pr71/README.md @@ -0,0 +1,172 @@ +# A sharper exponent for integer multiplication + +**Community research maintained by Douglas Colkitt — conditional on the original +OpenAI #109 framework.** + +The reviewed community witness gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\boxed{\kappa=\frac{25508460085039}{500000000000000000} +=5.1016920170078\times10^{-5}>2^{-15}}. +$$ + +This is **23.71% above the preceding PR #49 release** and remains below 2^-14. +It is an improvement in the asymptotic exponent saving, not a measured runtime +speedup. The model and general reduction are inherited from OpenAI's +[*Integer multiplication below n log n*](https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Integer-multiplication-below-n-log-n-September-23-2026). + +**[Maintainer review and contribution ledger](docs/research/community-round2-review.md)** · +[Finite circuit proof](research/pair-assembly/PROOF.md) · +[Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) · +[Independent arithmetic check](docs/research/community-pair-arithmetic.json) + +## Additional conditional construction: anchored split frames with live reclamation + +The [split-pair proof and reproduction guide](research/split-pair/README.md) +gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately +**0.7463402960%** above the complete pinned PR67 witness. It combines +the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules +and exact arithmetic, PR67's profile-cost selection, and PR68's pending live +controls on the PR60/57 reversible frame compiler. +The new selection uses split vector `[1,1,2]` and aligns the first intact +global pair across common-point permutations. A new integer score uses each +live control's known next-use frame. Actual roles are R23=27455 +and R25=36015, with W=135075665. + +`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch +and actual fixed-I+J profiles, and certifies the complete recursive child +list and strict assembly inequalities. This separately submitted finite +conditional witness retains the inherited all-size hypotheses. Its namespace, +sources and comparison remain distinct from the maintainer-reviewed statement +above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor +credits and original notices are retained in the package. + +## What changed + +**Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange +additions to allow more physical wire reuse. Combined with **eumemic's joint +frame compiler (#57)**, this yields the strongest finite network in this batch. +**Alejandro Zarzuelo Urdiales's exact parameter refinement and scoped Lean +certificate (#61)** supply the selected numerical value. + +The bit network has m=575 and 137,151,806 physical roles; its certified recursive +saving is 102039046058023/2000000000000000000. The complex network retains saving +717/10^7. All recursive children, workspace restoration, copied centers and +endpoint costs remain charged. The seven final exponent margins are strictly positive. + +The preceding combination of Avi's skip-prefix strips (#53), **Rohan Gupta's +dual-suffix layout (#55)**, eumemic's compiler and **Chafik Boukhalfa's composition +and ranked reclamation (#58/#60)** is also fully retained and reviewed. + +Other reviewed contributions are retained even when their numerical witnesses +are superseded: **RaD's enlarged-frame and clone machinery (#51)**, **Rohan Arun's +positive-frame composition and order searches (#52/#56)**, **Rohan Gupta's parallel +order search (#50)**, **Chafik's original-envelope clones (#54)**, and **Rohan Garg's +split-pair recursion (#59)**. The review records the exact validation scope of each. + +## Attribution + +The names below identify GitHub contributors; they are not verified Twitter handles. + +- **[Avi Eisenberg (ikeboy)](https://github.com/ikeboy):** skip-prefix and interval strips, core-aware pair assembly ([#53](https://github.com/CrocSwap/integer-mult-bounds/pull/53), [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62)). +- **[Rohan Gupta (gupt1156)](https://github.com/gupt1156):** dual-suffix strips and parallel order improvements ([#50](https://github.com/CrocSwap/integer-mult-bounds/pull/50), [#55](https://github.com/CrocSwap/integer-mult-bounds/pull/55)). +- **[eumemic](https://github.com/eumemic):** joint frame compilation and paid reclamation ([#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57)); earlier complex circuits, Gaussian resampling and source frames. +- **[Chafik Boukhalfa (chafreaky)](https://github.com/chafreaky):** exact recovery, independent checkers, reordered sums, paid clones and joint-compiler composition/refinement ([#43/#46/#48/#54/#58/#60](docs/research/community-round2-review.md)). +- **[Rohan Arun (rohanarun)](https://github.com/rohanarun):** corner geometry, fixed-basis composition, weighted matching, order searches and positive-frame composition ([#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49), [#52](https://github.com/CrocSwap/integer-mult-bounds/pull/52), [#56](https://github.com/CrocSwap/integer-mult-bounds/pull/56)). +- **[Rohan Garg (rohangar1)](https://github.com/rohangar1):** split-pair recursion, order refinement and paid-clone composition ([#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59)). +- **[Alejandro Zarzuelo Urdiales (alejandrozu)](https://github.com/alejandrozu):** Gaussian parity and finite tensor proofs, matrix/search tools, exact refinement and scoped Lean arithmetic ([#45](https://github.com/CrocSwap/integer-mult-bounds/pull/45), [#61](https://github.com/CrocSwap/integer-mult-bounds/pull/61)). +- **[RaD project (hipotures)](https://github.com/hipotures):** semantic precision, routing, phase-cell inversion, bulk resampling, alternating producers, physical compiler and enlarged-frame/clone machinery ([#41](https://github.com/CrocSwap/integer-mult-bounds/pull/41), [#51](https://github.com/CrocSwap/integer-mult-bounds/pull/51)). +- **icekylinx:** recursive batching, partial swaps, fixed projector profiles, copied retained centers and the selected complex construction. +- **Zhihao Chen (jacklightChen):** controlled bases, translated frames, semantic/bulk compatibility and two-stage integration. +- **James Chang (jamesyc):** reversed two-stage geometry and exact controls. +- **Aurel Prosz (Paureel) and Swapnil Jain:** attributed two-stage development and paid copied-stream endpoints. +- **Dominik Scholz:** dimension, parameter and fixed-basis refinements. +- **Ryan S (princezuda):** historical Lean certificates, algebraic contracts and independent circuit checks ([#26](https://github.com/CrocSwap/integer-mult-bounds/pull/26)). +- **Andrew Barnes (Bortlesboat) and David Leen (dleen):** aligned pairing, retained totals and sharing. + +The [full contribution record](CONTRIBUTORS.md) credits incorporated, parallel, +superseded and pending work separately. Douglas Colkitt maintains the project, +original research, review and integration, with OpenAI Codex assistance. +OpenAI's original manuscript and Harvey–van der Hoeven's analytic work retain +their attribution. Contributor-specific AI disclosures remain in [NOTICE](NOTICE). + +## Evidence and limits + +The [round-two review](docs/research/community-round2-review.md) extends the +[previous follow-up audit](docs/research/community-followup-review.md) and +[PR #39 transfer review](docs/research/community-final-audit.md). The original +#109 framework and retained all-size interfaces remain assumptions. This is not +full formal verification, independent human peer review, a worldwide priority +claim, or a practical multiplication benchmark. + +Fresh checks cover complete emitted words and dirty basis vectors, physical +frame transitions, exact fixed-basis profiles, all 4,073,300 data pairs for the +retained geometry, and independent rational recurrence/assembly arithmetic. +The formal packages verify their stated finite/arithmetic contracts. PR #61's +integrated axiom audit contains 169 distinct declarations, including 11 concrete +frontier theorems; its input rows are bound to the replayed finite profile. +They do not formalize the whole multiplication algorithm. + +The [review receipt](docs/research/community-round2-validation.json) distinguishes +fresh maintainer checks from contributor-supplied evidence. Earlier witnesses, +patches and attribution remain available. Submissions after #62 are outside this checkpoint's review; exact reviewed heads +are recorded in the ledger. + +## Reproduce + +```sh +make verify-pair +make verify-joint +make verify-positive +make formal-matrix-verify +# Complete arithmetic, producer, historical and unit-test suite: +make verify +``` + +Python 3.11+, a C++17 compiler and Boost headers are required for the full +arithmetic suite. The formal targets use their pinned Lean versions. See +[reproduction details](docs/reproducibility.md) and [CI layout](docs/ci-verification.md). + +## Historical witnesses and independent patches + + +Each patch applies independently to the **unmodified** pinned source; they are +alternatives, not a sequence to apply together. The +[result history](docs/research/result-history.md) records the earlier mechanisms +and scoped ceilings. The [preserved research index](docs/research/preserved-research.md) +collects the intermediate compression, routing, Fano, and core searches, including +scoped negative results and reproducible certificates. + +| Patch | Conditional saving | Scope | +| --- | --- | --- | +| [frozen-154](patches/frozen-154.patch) | `2^-154` | Original network and recurrence exponents | +| [balanced-153](patches/balanced-153.patch) | `2^-153` | Balanced assembly parameters | +| [same-network-129](patches/same-network-129.patch) | `2^-129` | Original network, sharper recurrence comparison | +| [h46-111](patches/h46-111.patch) | `2^-111` | Smaller network, dyadic parameters | +| [h46-109](patches/h46-109.patch) | `2^-109` | Rational recurrence saving, strict final margin | +| [h46-108](patches/h46-108.patch) | `2^-108` | Variable stopping exponent | +| [h46-rational](patches/h46-rational.patch) | `5.8e-33` | Strongest supplied parameter-only witness | +| [nonadjacent-layout](patches/nonadjacent-layout.patch) | Original parameters retained | Routing proof and revised layout cost only | +| [frozen-nonadjacent-107](patches/frozen-nonadjacent-107.patch) | `2^-107` | Direct routing, original network and recurrence exponents | +| [h46-nonadjacent-78](patches/h46-nonadjacent-78.patch) | `2^-78` | Direct routing with the h = 46 network | +| [h46-nonadjacent-76](patches/h46-nonadjacent-76.patch) | `2^-76` | Direct routing with tuned dimension and stopping parameters | +| [h46-shared-side-75](patches/h46-shared-side-75.patch) | `2^-75` | Stage-1/stage-3 side-role sharing, routing, and parameter tuning | +| [h46-incidence-67](patches/h46-incidence-67.patch) | `2^-67` | Rectangle incidence circuits, full auxiliary sharing, routing, and parameter tuning | +| [h46-dag-63](patches/h46-dag-63.patch) | `2^-63` | Shared intermediate sums and reversible role allocation | +| [h46-shared-point](patches/h46-shared-point.patch) | `13*2^-66` | Cross-group sharing | +| [h50-paired-59](patches/h50-paired-59.patch) | `2^-59` | Paired sums, stopped guard and tighter Gaussian setup | +| **[compact-control-34](patches/compact-control-34.patch)** | **`83/10^12 > 2^-34`** | **Compact controls, complete reservations, local repair and separate complex arity** | +| [complex-compression-31](patches/complex-compression-31.patch) | `2^-31` | Weighted complex circuits, binary phase frames and complete auxiliary sharing | +| **[ternary-30](patches/ternary-30.patch)** | **`2^-30`** | **Ternary five-subset circuit, rational frames and fixed-alphabet interchange** | + +## Citation and license + +Use [CITATION.cff](CITATION.cff), cite the individual contributions used and +include the repository version or commit. [CONTRIBUTORS.md](CONTRIBUTORS.md), +[NOTICE](NOTICE) and source-specific manifests preserve the dependency credits. + +The project is [Apache-2.0](LICENSE). Bundled RaD sources retain their separate +CC0 license and notices. The pinned original OpenAI manuscript remains unchanged +under `upstream/`; its source hashes are in [upstream/manifest.json](upstream/manifest.json). +This project is not an official OpenAI release or endorsement. diff --git a/references/frame-compiler/pr71/SOURCE.json b/references/frame-compiler/pr71/SOURCE.json new file mode 100644 index 0000000000..c8cc31f3d0 --- /dev/null +++ b/references/frame-compiler/pr71/SOURCE.json @@ -0,0 +1,120 @@ +{ + "commit": "1bef94fd40a746452548c84a4a8f8834670a3113", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "Makefile": "6e9e48a677b2f66643226840f574a6535e3564ffb0c72284b60302684a5dfbe4", + "NOTICE": "1e0702aa665673508fa91169163c5785d680637fff636fda01f36e3b127c3ee0", + "README.md": "24817241fcad7f0a294ec6ad9666ee552ed9057e8d89e3c1d27e8fa2c7fe4229", + "certificates/split-pair-compiler.json": "6561fab8609e8aa3a291a8197cd8b834b0881ee0b9a5b991926c2c93c4d5f884", + "certificates/split-pair-kappa.json": 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Actual imported source closure is PR65 plus shared PR48." + } + }, + "status": "Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed" +} diff --git a/references/frame-compiler/pr71/certificates/split-pair-profiles-23.json b/references/frame-compiler/pr71/certificates/split-pair-profiles-23.json new file mode 100644 index 0000000000..bf40dc76b4 --- /dev/null +++ b/references/frame-compiler/pr71/certificates/split-pair-profiles-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":27455,"loss":506,"rank_sum":631971,"field_prime":2305843009213693951,"frames":59803,"distinct_matrices":38745,"crt_matrices":5750,"crt_disagreements":0,"blocks":[0,357148,21253,8022,5466,4156,3835,3250,2612,2109,1750,1529,1008,863,555,461,234,149,40,9,0,23,0,0]} diff --git a/references/frame-compiler/pr71/certificates/split-pair-profiles-25.json b/references/frame-compiler/pr71/certificates/split-pair-profiles-25.json new file mode 100644 index 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15382, + "5": 6461, + "6": 1593, + "7": 694, + "8": 1229, + "9": 411, + "10": 539, + "11": 98, + "12": 671, + "13": 254, + "14": 1927, + "15": 439, + "16": 440, + "17": 487, + "18": 3417, + "19": 6882, + "21": 171, + "22": 23 + }, + "word_sha256": "b0379d99fd6c10307da0d0fc526ed6171f19105a47bae61730fc3745ef60bd9e", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr71/certificates/split-pair-transitions-25.json b/references/frame-compiler/pr71/certificates/split-pair-transitions-25.json new file mode 100644 index 0000000000..e5864300a1 --- /dev/null +++ b/references/frame-compiler/pr71/certificates/split-pair-transitions-25.json @@ -0,0 +1,37 @@ +{ + "h": 25, + "v": 2300, + "R": 36015, + "frames": 84845, + "distinct_transitions": 212584, + "singles": 20700, + "rank_mass": 900975, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 91026, + "2": 108047, + "3": 13560, + "4": 19874, + "5": 8387, + "6": 2967, + "7": 1127, + "8": 1443, + "9": 664, + "10": 791, + "11": 38, + "12": 758, + "13": 149, + "14": 681, + "15": 167, + "16": 2265, + "17": 680, + "18": 566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "word_sha256": "4c956749f0ec72c61875c51099afdf23e69ccea268a9b43b8d46da2ffdb24903", + "copied_centers": 25, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr71/certificates/split-pair-validation.json b/references/frame-compiler/pr71/certificates/split-pair-validation.json new file mode 100644 index 0000000000..471a5bed88 --- /dev/null +++ b/references/frame-compiler/pr71/certificates/split-pair-validation.json @@ -0,0 +1,237 @@ +{ + "axes": { + "23": { + "profile": { + "R": 27455, + "blocks": [ + 0, + 357148, + 21253, + 8022, + 5466, + 4156, + 3835, + 3250, + 2612, + 2109, + 1750, + 1529, + 1008, + 863, + 555, + 461, + 234, + 149, + 40, + 9, + 0, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 5750, + "distinct_matrices": 38745, + "field_prime": 2305843009213693951, + "frames": 59803, + "h": 23, + "loss": 506, + "rank_sum": 631971, + "v": 1771 + }, + "replay": { + "elementary_xors": 162103, + "full_basis_vectors": 30997, + "h": 23, + "histogram": { + "0": 175253, + "1": 58564, + "2": 78945, + "3": 10224, + "4": 15382, + "5": 6461, + "6": 1593, + "7": 694, + "8": 1229, + "9": 411, + "10": 539, + "11": 98, + "12": 671, + "13": 254, + "14": 1927, + "15": 439, + "16": 440, + "17": 487, + "18": 3417, + "19": 6882, + "21": 171, + "22": 23 + }, + "output_roles": 5336, + "rank_mass": 631971, + "roles": 27455, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 673206 + }, + "transitions": { + "R": 27455, + "copied_centers": 23, + "distinct_transitions": 152272, + "frames": 59803, + "h": 23, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69190, + "2": 73632, + "3": 10224, + "4": 15382, + "5": 6461, + "6": 1593, + "7": 694, + "8": 1229, + "9": 411, + "10": 539, + "11": 98, + "12": 671, + "13": 254, + "14": 1927, + "15": 439, + "16": 440, + "17": 487, + "18": 3417, + "19": 6882, + "21": 171, + "22": 23 + }, + "rank_mass": 631971, + "singles": 15939, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 1771, + "word_sha256": "b0379d99fd6c10307da0d0fc526ed6171f19105a47bae61730fc3745ef60bd9e" + } + }, + "25": { + "profile": { + "R": 36015, + "blocks": [ + 0, + 492698, + 27869, + 10467, + 7897, + 5674, + 5027, + 4110, + 3809, + 3047, + 2490, + 2047, + 1814, + 1443, + 1151, + 898, + 567, + 470, + 271, + 163, + 47, + 13, + 0, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 7444, + "distinct_matrices": 52075, + "field_prime": 2305843009213693951, + "frames": 84845, + "h": 25, + "loss": 600, + "rank_sum": 900975, + "v": 2300 + }, + "replay": { + "elementary_xors": 225757, + "full_basis_vectors": 40615, + "h": 25, + "histogram": { + "0": 242882, + "1": 77226, + "2": 114947, + "3": 13560, + "4": 19874, + "5": 8387, + "6": 2967, + "7": 1127, + "8": 1443, + "9": 664, + "10": 791, + "11": 38, + "12": 758, + "13": 149, + "14": 681, + "15": 167, + "16": 2265, + "17": 680, + "18": 566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "output_roles": 6925, + "rank_mass": 900975, + "roles": 36015, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 935228 + }, + "transitions": { + "R": 36015, + "copied_centers": 25, + "distinct_transitions": 212584, + "frames": 84845, + "h": 25, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 91026, + "2": 108047, + "3": 13560, + "4": 19874, + "5": 8387, + "6": 2967, + "7": 1127, + "8": 1443, + "9": 664, + "10": 791, + "11": 38, + "12": 758, + "13": 149, + "14": 681, + "15": 167, + "16": 2265, + "17": 680, + "18": 566, + "19": 828, + "20": 4481, + "21": 8893, + "23": 280, + "24": 25 + }, + "rank_mass": 900975, + "singles": 20700, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 2300, + "word_sha256": "4c956749f0ec72c61875c51099afdf23e69ccea268a9b43b8d46da2ffdb24903" + } + } + }, + "bit_saving": "12854322426487/250000000000000000", + "certificate_sha256": "0fcb53fa374273efab6370953c966e8fa065dbfdba43691843a4788cb2cda42e", + "kappa": "51414646104039/1000000000000000000", + "margins": 7, + "producer_words_regenerated_and_matched": true, + "scope": "Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.", + "source_binding": "Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.", + "status": "PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly", + "strict_constraints": 47 +} diff --git a/references/frame-compiler/pr71/certificates/split-pair-word-23.json.gz b/references/frame-compiler/pr71/certificates/split-pair-word-23.json.gz new file mode 100644 index 0000000000..38b82cbb3d Binary files /dev/null and b/references/frame-compiler/pr71/certificates/split-pair-word-23.json.gz differ diff --git a/references/frame-compiler/pr71/certificates/split-pair-word-25.json.gz b/references/frame-compiler/pr71/certificates/split-pair-word-25.json.gz new file mode 100644 index 0000000000..da9935d15a Binary files /dev/null and b/references/frame-compiler/pr71/certificates/split-pair-word-25.json.gz differ diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr48/SOURCE.json b/references/frame-compiler/pr71/references/frame-compiler/pr48/SOURCE.json new file mode 100644 index 0000000000..4e38e34dc8 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/SOURCE.json @@ -0,0 +1,16 @@ +{ + "files": { + 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"b7194b8586844956904b33e9fe18f0c75606c11b", + "scope": "Unmodified producer inputs for experimental frame compiler; attribution retained in each file", + "source_pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/48" +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py b/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py new file mode 100644 index 0000000000..c7fd42867d --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py @@ -0,0 +1,196 @@ +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit', 'complex'): + data = finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": 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OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": 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0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<3 and choice: + k={1:0,2:(len(groups)-1)//2,3:len(groups)-1}[choice] + if len(groups[k])==2:groups[k:k+1]=[[x] for x in groups[k]] + assert all(len(g) in (1,2) for g in groups) and len(groups) 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": "41187950749917624099/1000000000000000000000000", + "cell_above_band": "666666666665666652937349833360791967/1333388250600666556832132000000000000", + "compact_leaf": "26927049500082375901/1000000000000000000000000", + "compact_reservations": "1/4000000000000", + "delta_below_one_eighth": "999999999999/8000000000000", + "delta_positive": "1/8000000000000", + "epsilon_below_one": "13729317166639208033/333347062650166639208033", + "epsilon_positive": "333333333333000000000000/333347062650166639208033", + "g1_above_kappa": "3408408254232349301008147/3333470626501666392080330000000000000", + "g2_above_kappa": "4241/2500000000000", + "g3_above_kappa": "74937627730682908927817/3333470626501666392080330000000000000", + "g4_above_kappa": "4241/2500000000000", + "g5_above_kappa": "5299956450675231223831763/13333882506006665568321320000000000000", + "g6_above_kappa": "11966897703678564007992423/13333882506006665568321320000000000000", + "g7_above_kappa": "3333196040161742016173902349301008147/3333470626501666392080330000000000000", + "gamma_sublinear": "1/2000000000000", + "guard_width": "13729317166639208033/333347062650166639208033", + "lambda_above_internal": "82375901/2000000000000000000000000", + "lambda_above_sigma": "61024099000082375901/2000000000000000000000000", + "lambda_above_tau": "82375901/2000000000000000000000000", + "lambda_prime_above_lambda": "82375901/2000000000000000000000000", + "lambda_prime_below_one": "41187950499917624099/1000000000000000000000000", + "literal_scalar_guard": "9693793493753822316795466474748", + "phase_boundary": "21966907133275670202633360791967/533355300240266622732852800000000000", + "phase_leaf_above_bit": "53854099/2000000000000", + "phase_local": "109834536999766601613833360791967/2666776501201333113664264000000000000", + "prime_interval_packing": "13729317166639208033/333347062650166639208033", + "q_below_internal": "82375901/1000000000000000000000000", + "q_below_leaf": "26927049500082375901/1000000000000000000000000", + "q_below_reservations": "1/4000000000000", + "q_positive": "41187950499917624099/1000000000000000000000000", + "record_suffix": "13729317166639208033/333347062650166639208033", + "row_product_gap": "6548/25", + "short_record_fallback": "666639206901368489075295096355187267/666694125300333278416066000000000000", + "small_field_exposure": "1/1000000000000" + }, + "finite_bridge": { + "bit": { + "W": 177530859, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis alternating composition and independent replay checks" + }, + "PR44": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "061414a529f1123668872db44d737e362fbe066f", + "contribution": "weighted matching discovery, pinned carrier links and replay profiler; no optimality claim is required" + }, + "PR46": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "71b6c960c89295e952522dd44111df9cfc51ae90", + "contribution": "prior verified composition and exact rational recovery of all data pairs; this increment changes both scalar graphs and pinned matchings" + }, + "PR47": { + "author": "Rohan Arun with Anthropic Claude assistance", + "commit": "117caf164e3b235ef20188aa2dc1b49617e9255c", + "contribution": "contemporaneous hill-climbed graph benchmark; no construction component reused in this increment" + }, + "files": { + 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b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py new file mode 100644 index 0000000000..24070a7d85 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<2^{-15}.} +\] + +The exact bit saving is 4986382/10^11. The next grid value of the bit saving +fails the exact moment test, and the next κ grid value fails the assembly. + +This is **6.782% above PR #57** (4669442391/10^14), **10.092% above PR #54** +(141532521/3125000000000) and **10.849% above PR #53** (4498144/10^11). It +does not use PR #57's compiler or PR #54's clones. These compare asymptotic +exponent savings, not running times. They are conditional research claims +without independent mathematical review or formal verification. + +Section "Stacking with PR #57's frame compiler" below gives a second, larger +witness, κ = 5101691/10^11, that also uses PR #57's compiler. + +## What changes + +Only the scalar producer DAG changes, in `pair_graph.py`, together with its +pinned carrier matching, `links-{23,25}.uses`. Everything else is PR #53's +`research/skip-strips` pipeline, which is PR #48's `research/copied-fixed` +pipeline, with constants recomputed for the new DAG. + +A role is a physical scratch wire. With c additions, q designated outputs and +μ retained carrier links, the role count is R = c + q − μ. A link lets a +donor addition x = u + w continue its carrier into a later consumer t of u, +when the original envelope of x lies inside the envelope of t: the common core +of t lies inside the core of x, and the cover of x lies inside the cover of t. +So R counts the additions that cannot continue a carrier, plus q. + +### 1. Interval strips + +The paired-exclusion recursion (icekylinx PR #18/#36) needs, for each vertex, +every leave-one-out sum of its k strip values v_1, …, v_k. PR #53 used the +skip-prefix layout s_j = A_(j−2) + (v_(j−1) + B_(j+1)). We build every cyclic +interval of the values instead, each from an interval one item shorter: + + I(a, m) = I(a, m−1) + v_(a+m−1), 2 ≤ m ≤ k−1, + +and output s_j = I(j+1, k−1), with the total I(0, k−1) + v_(k−1). The interval +I(a, m) with m < k−1 has the later consumer I(a−1, m+1) of its last item +v_(a+m−1), and its cover lies inside that consumer's cover, so it can continue +a carrier. Only the k outputs and the total stay unmatched. + +This costs k(k−2)+1 additions instead of about 4k. The role count still falls, +because R counts unmatched additions. In a model of one strip, an exact integer +program over every leave-one-out circuit shows that k−1 unmatched additions is +the minimum for k ≤ 8. Skip-prefix leaves 2k−3 unmatched; intervals leave k−1 +or k. Intervals are used for every strip with k ≥ 3 nonzero values; smaller +strips keep PR #53's layout. Value orders are PR #53's: reversed at the top +level, sorted by (support size, ±support) below it. + +### 2. Core-aware pair assembly + +For groups i < j with members (a, a2) and (b, b2), let F = far[i,j] and let +Sa, Sa2, Sb, Sb2 be the strip outputs that omit the other group. Each of the +four outputs is a sum of four pieces, for example +out[a,b] = F + Sa + Sb + e(a2,b2). PR #53 computes left(a,j) = F + Sa, +then out[a,b] = left(a,j) + (Sb + e(a2,b2)). None of those ten additions can +continue a carrier. We compute + + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb) + Sa, Y2 = (F+Sa) + Sb2, + Y3 = (F+Sa2) + e(a,b2), Y4 = (F+Sb2) + e(a,b), + out[a,b] = e(a2,b2) + Y1, out[a,b2] = e(a2,b) + Y2, + out[a2,b] = Y3 + Sb, out[a2,b2] = Y4 + Sa2. + +Each F+S node then has a later consumer of its strip operand whose envelope +contains its own: the same common core and a larger cover. An exact integer +program over every assembly of these nine pieces, with their actual cores and +covers, shows that 8 unmatched additions per group pair is optimal. The cores +matter: a node such as Sa + e(a2,b2) has the two-point core {c, a2}, so a +one-point-core donor cannot continue into it. Each output needs its own +addition and at least one more addition that serves only that output, and +neither can continue a carrier, so 8 is also a lower bound for this +decomposition. + +### Counts + +| h | v | additions c | outputs q | matched μ | roles R | loss | +|---|---|---|---|---|---|---| +| 23 | 1771 | 62294 | 5336 | 38911 | 28719 | 506 | +| 25 | 2300 | 86595 | 6925 | 55844 | 37676 | 600 | + +PR #53 had R23 = 32946 and R25 = 43409. The physical constants are +m = 575, N = 4,073,300, W = 140,924,496 (PR #53: 160,799,739) and +L = 2,226,400. The complete rank is Wm − N + L = 81,029,738,300. The deficit +N − L is unchanged. + +The weighted matching is pinned in `links-{h}.uses`. `optimize_matching.py` +regenerates it from Rohan Arun's PR #44 optimizer with only the graph import +changed. Its output is not trusted: `profiles.cpp` replays every pinned link, +and `producer.py` recounts every link independently. + +## Why the inherited proofs apply + +The new DAG enters the inherited proofs only through properties and +quantities that `producer.py` recomputes, as for PR #41, #43, #47, #48 and #53: + +- **Scalar outputs.** Every addition joins disjoint supports, every node has a + common point, and every output is the exact leave-two-out sum or retained + total, checked on dense global supports. +- **Carrier links.** Every pinned link lies in the admissible adjacency + (causal order and envelope inclusion), with distinct donors and uses. +- **Physical timeline.** The full physical timeline and every dirty basis + vector are checked in both orientations at h = 23 and 25. +- **Fixed-basis profiles.** These are recomputed from the new DAGs and pinned + matchings: 37,728 and 51,927 distinct transition matrices; 6,026 and 7,981 + of them CRT-checked; zero modular disagreements. Exactly h full center + cleanups appear, so the copied-center replacement applies unchanged. +- **Data corners.** These do not depend on the producer. All 4,073,300 pairs + are replayed, and the ten primary-prime failures are recovered by exact + rational elimination. + +The integer programs explain why the links exist; correctness does not depend +on them. + +## Exact arithmetic + +`verify.py` uses PR #43/#48's exact logarithm and exponential enclosures: + +- The moment at a_b = 4986382/10^11 is below 1; at 4986383/10^11 its exact + lower bound exceeds 1. +- Each of the following is excluded at the new bit saving by an exact lower + bound: the complete child lists of PR #57, #54, #53, #48, #47, #46, #44, + #43, #42, #41 and #40, and the PR #36 baseline. +- The inherited balanced assembly passes all 47 strict conditions and seven + margins at κ = 4986133/10^11 and fails at the next grid value. Its + parameters are β = 1/20, h = 10^-12, a_c = 717/10^7, C1 = 1 and row stock + p^2000. + +## Stacking with PR #57's frame compiler + +PR #57 (eumemic, with OpenAI Codex assistance) compiles each set of nodes that +share one original envelope as a single invertible binary map, matches +retained signals to later uses, and reclaims retired roles with paid XOR +clearing. Its compiler, `scripts/experiments/binary_frame_compiler.py`, is +included unchanged through PR #57's own commit on this branch. +`frame/frame_compile.py` feeds it the hash-pinned `pair_graph.py` instead of +PR #53's graph, exactly as PR #57's driver feeds it PR #53's graph. + +The compiled words give the following role counts: + +| h | roles R, this graph | roles R, compiled | shared-frame regions | retained signals | reclaimed roles | +|---|---|---|---|---|---| +| 23 | 28719 | 27918 | 52473 | 37025 | 801 | +| 25 | 37676 | 36586 | 73695 | 53194 | 1090 | + +With W = 137,151,806 the stacked witness gives + +\[ +\kappa=\frac{5101691}{10^{11}}=5.101691\times10^{-5}, +\] + +with exact bit saving 5101952/10^11. This is **9.257% above PR #57** and +2.318% above the plain witness above. PR #57's own result on PR #53's graph +is 4669442391/10^14. + +`frame/frame_verify.py` checks, as PR #57's verifier does: + +- both serialized XOR words, replayed independently on every input and dirty + basis vector in both orientations; +- every frame transition, reconstructed from the actual XOR word; +- all fixed-basis profiles, with bounded-minor and CRT checks; +- the exact moment, the rejection of the next bit-saving grid value, the + exclusion of PR #53's and PR #57's networks at the new saving, all 47 + strict assembly inequalities, seven margins, and the rejection of the next + κ grid value. + +This stacked witness also depends on PR #57's compiler argument, which has +the same review status as PR #57. + +## Reproduce + +```sh +python3 research/pair-assembly/producer.py --work-dir /tmp/pair-assembly +python3 research/pair-assembly/verify.py +python3 research/pair-assembly/frame/frame_verify.py +python3 research/pair-assembly/optimize_matching.py --work-dir /tmp/pair-opt # optional, needs scipy +python3 research/pair-assembly/frame/frame_compile.py # optional, rewrites the words +``` + +`producer.py --record` rewrites the JSON records. Without `--record` it checks +them against fresh regeneration. `make pair-assembly-verify` runs the first +three commands and the tests. + +## Scope and attribution + +This is a conditional finite certificate. It covers the same written proof +obligations as PR #43–#53: the base theorem, the residual compiler, fixed-tape +recursion, the physical meaning of carrier continuations and copied centers, +the analytic/semantic/routing/recovery interfaces and eventual thresholds. +None of these are re-proved here. There is no formal verification or claim of +global optimality. The stacked witness additionally depends on PR #57's +compiler mechanism and its written argument. + +The interval strips and core-aware pair assembly are new here, by Avi +Eisenberg with assistance from Claude (Anthropic). Everything else is +inherited, with all original notices: + +- Avi Eisenberg PR #53: skip-prefix strips and this pipeline's adaptation. +- eumemic PR #57: the joint frame compiler, used unchanged for the stacked + witness. +- Chafik Boukhalfa PR #43/#46/#48: pipeline, recovery, the sorting idea and + verification code. +- Rohan Arun PR #44: weighted matching; also PR #37/#39/#40/#42/#47. +- RaD / hipotures PR #41: alternating order and changed DAGs. +- Dominik Scholz PR #35/#38. +- James Chang PR #34. +- icekylinx PR #18/#24/#32/#36. +- Zhihao Chen PR #21/#23/#29. +- Paureel / Aurel Prosz, Swapnil Jain, Douglas Colkitt, OpenAI, and + Harvey–van der Hoeven. + +Apache-2.0. diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json new file mode 100644 index 0000000000..439c763887 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/SOURCE.json @@ -0,0 +1,147 @@ +{ + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": "70ae24129649f6d6d4ec6360962a80c3c42a38f1", + "contribution": "fixed-middle modular nonvanishing method adapted to exhaustive two-fixed pair check" + }, + "PR40": { + "author": "Rohan Arun", + "commit": "43f59ff533598762cbc43a5e14af2bbbc76fabbd", + "contribution": "contemporaneous both-fixed baseline; matching order improvement is new here" + }, + "PR41": { + "PR": 41, + "author": "RaD / hipotures", + "commit": "d9c96297d455053b795ee58ba108d5cf892e1c04", + "point_order_blob": "a47df953d275f86bf3fcb100cc425ca8854875ca", + "rad_checkpoint": "7e488e6b25dc1713c1f41baaf1cefbf677507cf3", + "subsequent_inspected_head": "03bde70c0c2a453f1ceae20c619b602841405467" + }, + "PR42": { + "author": "Rohan Arun", + "commit": "c6fc08951c1776a9685802b1810a2f15dbbd4f64", + "contribution": "contemporaneous fixed/alternating composition and exact comparison; different carrier matching" + }, + "PR43": { + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "commit": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6", + "contribution": "prior fully checked original-envelope/fixed-basis 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Its functions and binary format are unchanged. Retain the current main header and pin its actual bytes; regenerate inherited certificates on integration." +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json new file mode 100644 index 0000000000..ab8cde595c --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame-compiler.json @@ -0,0 +1,176 @@ +{ + "status": "Joint frame compilation of the pair-assembly graph; complete dirty basis both orientations", + "axes": { + "23": { + "compiled": { + "h": 23, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 27918, + "baseline_pr48_roles": 36432, + "histogram": { + "1": 42694, + "0": 301874, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + }, + "rank_mass": 642620, + "elementary_xors": 148958, + "stats": { + "augmentations": 220, + "regions": 52473, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "clearing_xors": 1398 + }, + "dirty_basis_vectors": 31460, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 26.58313250541687 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 23, + "roles": 27918, + "output_roles": 5336, + "elementary_xors": 148958, + "word_length": 620626, + "full_basis_vectors": 31460, + "rank_mass": 642620, + "histogram": { + "1": 42694, + "0": 162731, + "2": 82328, + "3": 11086, + "4": 10646, + "6": 2005, + "5": 7548, + "8": 1361, + "9": 562, + "10": 597, + "12": 558, + "14": 2005, + "16": 547, + "18": 4220, + "19": 7820, + "22": 23, + "17": 274, + "7": 688, + "15": 396, + "21": 165, + "13": 23 + } + }, + "gzip_sha256": "4629d45d5074f87706db46be3aa3cd369071cd215bc6560d641115aadcce54a0", + "word_sha256": "bd0cbf73756f2e4f8d3879ec6c7a194990eb9ec40aaf3580bdded6994798d920" + }, + "25": { + "compiled": { + "h": 25, + "mode": { + "matching": true, + "reclaim": true + }, + "roles": 36586, + "baseline_pr48_roles": 48329, + "histogram": { + "1": 55478, + "0": 416276, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + }, + "rank_mass": 915250, + "elementary_xors": 205650, + "stats": { + "augmentations": 286, + "regions": 73695, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "clearing_xors": 1827 + }, + "dirty_basis_vectors": 41186, + "complete_dirty_basis_both_orientations": true, + "all_physical_frame_inclusions": true, + "seconds": 51.009533166885376 + }, + "replay": { + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "h": 25, + "roles": 36586, + "output_roles": 6925, + "elementary_xors": 205650, + "word_length": 854800, + "full_basis_vectors": 41186, + "rank_mass": 915250, + "histogram": { + "1": 55478, + "0": 224000, + "2": 115441, + "3": 14362, + "4": 16687, + "5": 10074, + "6": 1767, + "8": 2140, + "9": 790, + "10": 529, + "12": 781, + "14": 625, + "16": 3200, + "18": 519, + "20": 5436, + "21": 10094, + "24": 25, + "17": 687, + "19": 300, + "7": 881, + "23": 220 + } + }, + "gzip_sha256": "1094276c9ee901e4e5c23062775aad2f50bb5a85a67e64e685d79babcf5b8ecb", + "word_sha256": "634d3cc0fa8e4f592b1924c141bc953524ea08bf683059e18d8ad0c2f26785ec" + } + }, + "source": { + "graph": "research/pair-assembly/pair_graph.py", + "graph_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "compiler": "scripts/experiments/binary_frame_compiler.py (PR #57, unchanged)" + } +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py new file mode 100644 index 0000000000..d47c1cb3df --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/frame/frame_verify.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Replay the pair-assembly frame words, actual fixed profiles and assembly. + +Adapted from PR #57's verify_skip_frame.py and skip_frame_compose.py (eumemic, +with OpenAI Codex assistance), with the PR #57 compiler words replaced by the +pair-assembly words. Every XOR word, dirty basis column, frame incidence and +fixed-basis profile is checked; the unchanged data geometry and general +transfer proofs remain inherited dependencies, exactly as in PR #57. +Adapted with assistance from Claude (Anthropic). +Usage: python frame_verify.py [--record] +""" +import sys +sys.dont_write_bytecode = True +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import os +import shlex +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +EXP = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXP)) +import binary_frame_math as arithmetic +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay + +AB_S = 5101952 +KAPPA_S = 5101691 +WIRES_S = 137151806 +MASS_S = 78860441550 +INHERITED = ROOT/'references/frame-compiler/pr48' +OLD = INHERITED/'research/copied-fixed' +AB = Q(AB_S, 10**11) +KAPPA = Q(KAPPA_S, 10**11) +EXCLUDED_ABOVE = Q(AB_S+1, 10**11) +PLAIN_KAPPA = Q(4986133, 10**11) +PR57_KAPPA = Q(4669442391, 10**14) +PR53_KAPPA = Q(4498144, 10**11) + +spec = importlib.util.spec_from_file_location('pair_frame_balanced_assembly', OLD/'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + document = json.loads((INHERITED/'SOURCE.json').read_text()) + for name, digest in document['files'].items(): + assert sha256((INHERITED/name).read_bytes()).hexdigest() == digest, name + record = json.loads((HERE/'frame-compiler.json').read_text()) + graph = ROOT/record['source']['graph'] + assert sha256(graph.read_bytes()).hexdigest() == record['source']['graph_sha256'], 'pair_graph.py changed' + return document, record + + +def profile(profiles, words): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + replayed = words['axes'][str(h)]['replay'] + assert f['R'] == replayed['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == replayed['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (WIRES_S, MASS_S, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=profiles) + + +def compose(p, sources): + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + controls = {} + for name in ('pr53', 'pr57'): + row = json.loads((HERE.parent/f'comparison-{name}.json').read_text()) + rows = {int(t): n for t, n in row['child_multiplicities'].items()} + controls[name] = arithmetic.moment(row['m'], row['W'], rows, AB)['lower'] + assert controls[name] > 1, name+' network not excluded at stacked saving' + prior = json.loads((OLD/'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + try: + balanced.assembly(bridge, AB, KAPPA+Q(1, 10**11), a_complex=Q(717, 10**7)) + next_grid_fails = False + except AssertionError: + next_grid_fails = True + assert next_grid_fails + assert KAPPA > PLAIN_KAPPA > PR57_KAPPA > PR53_KAPPA > Q(1, 2**15) and KAPPA < Q(1, 2**14) + local = [HERE/name for name in ('frame_compile.py', 'frame_verify.py')]+[ + EXP/name for name in ('binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + return dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + controls=dict(PR53_bit_at_stacked_lower=controls['pr53'], PR57_bit_at_stacked_lower=controls['pr57']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(plain_pair_assembly_kappa=PLAIN_KAPPA, ratio_plain=KAPPA/PLAIN_KAPPA, + pr57_kappa=PR57_KAPPA, ratio_pr57=KAPPA/PR57_KAPPA, + pr53_kappa=PR53_KAPPA, ratio_pr53=KAPPA/PR53_KAPPA, next_kappa_grid_fails=next_grid_fails), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(x.relative_to(ROOT)): sha256(x.read_bytes()).hexdigest() for x in local}, + scope='Pair-assembly graph compiled by PR #57\'s unchanged joint frame compiler. Ordered affine residual ' + 'compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery ' + 'interfaces and PR #57\'s compiler argument remain inherited.') + + +def verify(record_mode=False): + inherited, words = check_sources() + profiles = [] + with tempfile.TemporaryDirectory(prefix='pair-frame-verify-') as directory: + work = Path(directory) + profiler = work/'profiles' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(INHERITED/'scripts/partial_swap'), + str(EXP/'binary_frame_profiles.cpp'), '-o', str(profiler)], check=True) + for h in (23, 25): + word = HERE/f'frame-word-{h}.json.gz' + axis = words['axes'][str(h)] + packed = word.read_bytes() + assert sha256(packed).hexdigest() == axis['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == axis['word_sha256'] + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == axis['replay'] + transitions = work/f'word{h}.bin' + prepared = json.loads(json.dumps(prepare(word, transitions))) + path = HERE/f'frame-transitions-{h}.json' + if record_mode: + path.write_text(json.dumps(prepared, indent=2)+'\n') + assert prepared == json.loads(path.read_text()) + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + path = HERE/f'frame-profiles-{h}.json' + if record_mode: + path.write_text(json.dumps(prof, indent=2)+'\n') + assert prof == json.loads(path.read_text()) + profiles.append(prof) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + p = profile(profiles, words) + result = compose(p, dict(inherited=inherited, compiler_record=words['source'])) + (HERE/'frame-certificate.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional stacked kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + print('47 strict inequalities, seven margins, next grid values rejected, PR #53 and #57 excluded', flush=True) + return result + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--record', action='store_true') + verify(parser.parse_args().record) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py new file mode 100644 index 0000000000..eef8e1eba0 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/pair-assembly/pair_graph.py @@ -0,0 +1,248 @@ +"""Interval strips and core-aware pair assembly, stacked on PR #53. + +Only the scalar addition DAG changes. Everything else is inherited from +Avi Eisenberg's PR #53 research/skip-strips pipeline, which builds on Chafik +Boukhalfa's PR #48 research/copied-fixed pipeline, Rohan Arun's PR #44 +weighted carrier matching, exact data-corner recovery (PR #46), RaD / +hipotures PR #41 alternating pair order and PR #43's original-envelope / +fixed I+J framework. Those build in turn on icekylinx PR #18/#32/#36 and +earlier credited work. + +New here, two changes to how the paired-exclusion recursion places its sums: + +1. Interval strips. A strip of k values needs every leave-one-out sum. We + build every cyclic interval of the values, each one item longer than an + interval already built: + I(a, m) = I(a, m-1) + v_(a+m-1), + and output s_j = I(j+1, k-1). Each interval I(a, m) with m < k-1 has the + later consumer I(a-1, m+1) of its last item, with a containing cover, so + it can continue a retained carrier. Only the k outputs and the total stay + unmatched. This costs k(k-2)+1 additions instead of about 4k, but the role + count R = additions + outputs - links falls. In a model of one strip, an + exact integer program shows k-1 unmatched additions is the minimum for + k <= 8; intervals reach k-1 or k. They are used for every strip with + k >= 3 nonzero values; smaller strips keep PR #53's layout. + +2. Core-aware pair assembly. For groups i < j with members (a, a2) and + (b, b2), let F = far[i,j] and let Sa, Sa2, Sb, Sb2 be the strip outputs. + Each of the four outputs is F + Sa + Sb + e(a2, b2) and its analogues. We + compute + F+Sa, F+Sa2, F+Sb, F+Sb2, + Y1 = (F+Sb)+Sa, Y2 = (F+Sa)+Sb2, + Y3 = (F+Sa2)+e(a,b2), Y4 = (F+Sb2)+e(a,b), + out[a,b] = e(a2,b2)+Y1, out[a,b2] = e(a2,b)+Y2, + out[a2,b] = Y3+Sb, out[a2,b2] = Y4+Sa2. + Each F+S node then has a later consumer of its strip operand with a + containing envelope (equal common core, larger cover). An exact integer + program over all assemblies of these nine pieces, with the actual cores + and covers, shows 8 unmatched additions per group pair is optimal; the + inherited assembly has 10. + +All supports, envelopes, links and profiles are checked by the inherited +pipeline; nothing here is trusted. + +Apache-2.0, like the inherited files. Prepared with assistance from Claude +(Anthropic). +""" +from itertools import combinations +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h, common): + """RaD PR #41 alternating global pair order (as specialized in PR #43/#48).""" + pairs = [(a, a+1) for a in range(0, h-1, 2) if common not in (a, a+1)] + if common % 2: + pairs.reverse() + head = [x for pair in pairs for x in pair] + return head + [x for x in range(h) if x != common and x not in head] + + +def prefix_suffix(c, vals): + """Ordinary leave-one-out: total and s_j = A_{j-1} + B_{j+1}.""" + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0]*(n+1) + for i in range(n-1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i+1]) + return prefix[-1], [c.add(prefix[i], suffix[i+1]) for i in range(n)] + + +def skip_prefix(c, vals): + """PR #53: s_j = A_{j-2} + (v_{j-1} + B_{j+1}) (1-indexed).""" + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0]*(k+1) + for i in range(1, k): + A[i] = c.add(A[i-1], v[i]) + B = [0]*(k+2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i+1]) + out = [0]*(k+1) + out[1] = B[2] + for j in range(2, k+1): + out[j] = c.add(A[j-2], c.add(v[j-1], B[j+1])) + return c.add(A[k-1], v[k]), out[1:] + + +def interval_splits(k): + """Every cyclic interval I(a, m), 2 <= m <= k-1, as I(a, m-1) + v_(a+m-1); total last.""" + full = (1 << k)-1 + interval = lambda a, m: sum(1 << ((a+t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m-1), 1 << ((a+m-1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k-1), 1 << (k-1))] + + +def interval_layout(fallback): + """Interval strips for k >= 3 values; the fallback handles k <= 2.""" + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + splits = interval_splits(k) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in splits: + node[S] = c.add(node[L], node[R]) + full = (1 << k)-1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + """Apply a layout to values sorted by (support size, sign*support); restore order.""" + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign*c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0]*len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + """Zero entries are omitted; their leave-one-out value is the total.""" + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0]*len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total]*len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def circuit_class(h): + deep_sign = 1 if h == 23 else -1 + top = reversed_layout(interval_layout(skip_prefix)) + deep = sorted_layout(interval_layout(skip_prefix), deep_sign) + + class PairAssemblyCircuit(PairedExclusionCircuit): + base_threshold = 2 + + def total(self, values): + values = [x for x in values if x] + if h == 23: + values.reverse() + else: + values.sort(key=lambda node: (self.support[node].bit_count(), self.support[node]), reverse=True) + result = 0 + for node in values: + result = self.add(result, node) + return result + + def block(self, points, edges, weights): + level = getattr(self, '_level', -1) + 1 + self._level = level + try: + return self._block(points, edges, weights, level) + finally: + self._level = level - 1 + + def _block(self, points, edges, weights, level): + if len(points) <= self.base_threshold: + return PairedExclusionCircuit.block(self, points, edges, weights) + layout = top if level == 0 else deep + groups = self.grouping(points) + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + wt = {i: self.total([weights[a] for a in g] + [e(a, b) for a, b in combinations(g, 2)]) + for i, g in enumerate(groups)} + total, outside, far = self.block(list(range(ng)), coarse, wt) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + carry = self.total([weights[u] for u in g if u != a]) + vals = [self.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + st, one = leave_one_out(self, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + single = {a: self.add(outside[i], sums[a]) for i, g in enumerate(groups) for a in g} + for i, g in enumerate(groups): + for a, b in combinations(g, 2): + out[a, b] = outside[i] + for i, j in combinations(range(ng), 2): + if len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + FSa, FSa2 = self.add(F, Sa), self.add(F, Sa2) + FSb, FSb2 = self.add(F, Sb), self.add(F, Sb2) + Y1 = self.add(FSb, Sa) + Y2 = self.add(FSa, Sb2) + Y3 = self.add(FSa2, e(a, b2)) + Y4 = self.add(FSb2, e(a, b)) + out[a, b] = self.add(e(a2, b2), Y1) + out[a, b2] = self.add(e(a2, b), Y2) + out[a2, b] = self.add(Y3, Sb) + out[a2, b2] = self.add(Y4, Sa2) + continue + for a in groups[i]: + left = self.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = self.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = self.add(left, self.add(strips[b][i], cross)) + return total, single, out + return PairAssemblyCircuit + + +def graph(h): + assert h in (23, 25) + local = circuit_class(h)(h-1) + total = local.pair(list(range(h-1)))[0] + local.outputs[()] = total + stack = [total] + while stack: + node = stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions = sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h, local, point_order=alternating_points) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md new file mode 100644 index 0000000000..7248e4e2b7 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/README.md @@ -0,0 +1,74 @@ +# Reordering the rank-pair physical compilation + +This experiment changes the schedule of equal-rank regions in PR #63's +composition of the PR #62 scalar graph and PR #60 rank-first compiler. The +23-axis uses increasing `(rank, cover, core)`; the 25-axis uses increasing rank +and decreasing minimum node number. The scalar identities, matched carrier +candidates, synthesis, and descending-rank retirement policy are unchanged. + +Reordering changes which retired physical roles are available when a region +is compiled. The resulting words have the same 27,918 and 36,586 physical +roles, but different paid fixed-I+J profiles. The selected schedules came +from a bounded comparison of reverse-node, core-cover, cover-core, and +reverse-core-cover orders. Core-cover was screened only; the other three +23-axis words and the reverse-node 25-axis word were independently replayed +and physically profiled before selection. Reversing both axes was weaker +than the selected mixed schedule. These finite tests do not prove optimality. + +## Why the schedule remains valid + +Every region retains its exact original envelope and its original linear +map. The wrapper checks every incoming inter-region dependency and every +selected-candidate direction against the new order. Thus all required inputs +are available, and retained carriers still travel forward. The admissibility argument uses these explicit dependency inequalities; +rank ties alone do not certify topological order, especially for source +frames. The complete serialized physical word is replayed on every input +and dirty basis vector in both orientations, and all frame inclusions and +actual fixed-basis profiles are independently regenerated. + +The literal rank identity and all paid endpoint/data/exterior terms use the +unchanged inherited profile constructor. No histogram estimate substitutes +for the physical word. The general transfer, routing, analytic, recovery, +and fixed-tape hypotheses remain inherited conditions; this is a finite +conditional certificate rather than a new formal proof of those hypotheses. + +## Reproduce + +From the repository root, with assertions enabled: + +```sh +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/verify.py --rebuild +PYTHONDONTWRITEBYTECODE=1 python3 research/reordered-rank-pair/test_negative.py +``` + +The first command checks source/artifact hashes, independently replays both +committed words, rebuilds their fixed-I+J profiles, and recomposes the paid +global profile. `--rebuild` also recompiles both words and requires exact +byte equality with the committed decompressed witnesses. Disposable output +goes under `build/reordered-rank-pair` (or `--work-dir`). The tests reject a +missing physical XOR, understated physical role count, changed word/profile +digests, a backward region dependency, and execution with Python assertions +disabled. Arithmetic witnesses and their +independent controls are in `arithmetic/`. + +## Attribution + +The graph is Avi Eisenberg's PR #62 interval-strip/core-aware pair assembly, +prepared with Claude assistance, with its retained credits to PR #53, #48, +#44, #46, #41, #43, and earlier icekylinx work. Chafik Boukhalfa's PR #60 +rank-first compiler derives from eumemic's PR #57 joint frame compiler, +both with OpenAI Codex assistance. Dominik Scholz's PR #63 combines those +sources, with OpenAI GPT-6 Astra assistance. Alejandro Zarzuelo Urdiales's +PR #61 supplies precedent for rational parameter refinement. This bounded +region-order experiment and its packaging are by Rohan Arun with OpenAI +Codex assistance. Original Apache-2.0 notices remain applicable. + +## Live comparison at publication + +PR #64 (`790a14e28e935398072b9a9a68694ce7fba8940f`, @rfu08) reports +`20411033624901463/400000000000000000000` for the unchanged #63 profiles, +with additional independent verification and scoped Lean formalization. +The present changed-schedule bound exceeds that reported value; exact +arithmetic and the source pin are in `current-comparison.json`. This is only +a bound comparison, not a comparison of formal proof coverage. diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md new file mode 100644 index 0000000000..fed8b1bc5d --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/README.md @@ -0,0 +1,174 @@ +# Exact arithmetic for the reordered rank-pair witness + +The selected complete paid profile admits + +- bit saving `a = 5103158916233/100000000000000000`; +- backoff `h = 1/1000000000000`, unchanged from PR63; +- `kappa = 2041159402879/40000000000000000 = 0.000051028985071975`. + +All 47 strict assembly inequalities and all seven margins pass. The next bit +saving on the 1e-18 grid has moment strictly above one; the next kappa on that +grid fails the unchanged balanced assembly. The finite sufficient arithmetic +cutoff remains `log2(input) >= 14000000000000`. This is an eventual arithmetic +threshold, not a practical runtime claim or the complete all-size threshold. + +The exact gain above PR63's `5102757/10^11` is +`56602879/40000000000000000`, approximately 0.0027731518 percent relative. +The construction gain is separated from parameter precision: + +| Check | Bit saving | Kappa | Gain versus PR63 | +|---|---:|---:|---:| +| Same 1e-11 grid and same h as PR63 | 0.00005103158 | 0.00005102897 | 0.0000000014 | +| Refined 1e-18 grid; same h | 0.000051031589162330 | 0.000051028985071975 | 0.000000001415071975 | + +The first row passes even with PR63's original low-order exponential bounds, +and its next bit grid point fails with those bounds. Thus its 1.4e-9 gain does +not depend on tightening the numerical enclosure. Precision adds a further +`602879/40000000000000000 = 1.5071975e-11`. + +## Reproduction and source linkage + +Run from any checkout location using Python 3.11 or later: + +```sh +python3 -B research/reordered-rank-pair/arithmetic/refine.py +python3 -B research/reordered-rank-pair/arithmetic/audit.py +python3 -B -m unittest discover -s research/reordered-rank-pair/arithmetic -p test_arithmetic.py -v +``` + +The default commands recompute and compare without writing outputs. An +intentional certificate update uses `--record` on the first two commands. +`refine.py` accepts `--profile PATH` and `--certificate PATH`; `audit.py` +accepts `--certificate PATH` and `--receipt PATH`. + +`certificate.json` pins `../paired-candidate.json`, both arithmetic scripts, +the inherited logarithm implementation and the inherited balanced assembly +by SHA256. All paths are repository relative. It includes the complete exact +per-child logarithm and exponential intervals, weighted moment bounds, +assembly slacks, all seven margins, next-grid failures, comparisons and +sufficient arithmetic cutoffs. `audit-receipt.json` records an independently +computed enclosure and ten deliberate assembly failures. + +This package checks the supplied complete paid profile. The parent +`../verify.py` checks the words, physical replay, actual profile/CRT results, +paid profile assembly and its correspondence to `../paired-candidate.json`. +An arithmetic pass alone does not prove that physical linkage. + +## Rational logarithm enclosure + +For `y >= 1`, put `z = (y-1)/(y+1)`. With `0 <= z < 1`, + +`log(y) = 2 * sum(j>=0, z^(2j+1)/(2j+1))`. + +Every term is nonnegative. Truncation after indices `0,...,J-1` is therefore a +lower bound. For the tail, `2j+1 >= 2J+1` and the powers form a geometric series, +so the upper remainder is + +`2*z^(2J+1)/((2J+1)*(1-z^2))`. + +The inherited helper reduces by powers of 2 to `1 <= y <= 2`, uses `J=32`, +adds the corresponding multiple of `log(2)`, then rounds downward/upward to +the 1e-30 rational grid. These operations preserve the enclosure. + +The independent audit instead reduces by powers of 3/2 to +`1 <= y <= 3/2`, uses `J=60`, and adds the corresponding multiple of +`log(3/2)`. Its exact logarithm enclosure is checked to lie inside the recorded +inherited interval for every child. The two implementations share the +mathematical atanh-series identity but use different range reduction, term +counts and evaluation code; neither relies on machine floating-point logs. + +## Rational exponential and complete moment enclosure + +For a child of dimension `t`, multiplicity `n`, arity `m` and width `W`, the +weight is `w=t*n/(m*W) > 0`. With bit saving `a>0`, its contribution to the +characteristic moment is `w*exp(a*log(m/t))`. The complete histogram includes +all paid parts; neither rare children nor physical transitions are omitted. + +Write `u=a*log_lower` and `v=a*log_upper`. The checker verifies +`0 <= u <= v < 1`. For `S_d(x)=sum(j=0..d, x^j/j!)`, positivity gives + +`S_d(u) <= exp(a*log(m/t))`. + +At `v`, the first omitted term is `v^(d+1)/(d+1)!`; each later term divided by +its predecessor is at most `v/(d+2) < 1`. A geometric majorant therefore gives + +`exp(a*log(m/t)) <= S_d(v) + v^(d+1)/((d+1)!*(1-v/(d+2)))`. + +The primary checker uses `d=8`. It rounds the lower expression downward and +the upper expression upward to the 1e-40 rational grid, multiplies by each +positive exact weight, and sums. Directed rounding can only widen the +interval. Every arithmetic operation uses integers and exact Fractions. + +The independent audit evaluates the exponential by a recurrence through +degree 12. It checks `v<1/1000`, rounds input bounds outward, and bounds the +remaining tail by twice the first omitted term. This is valid because all +successive tail ratios are below 1/2. It independently confirms that the +accepted upper moment is below one and the successor lower moment is above +one. No empirical epsilon, decimal-log assumption or float tolerance enters +the acceptance decision. + +All weights and `log(m/t)` are strictly positive, since `0= 1 + k = 0 + while x > Q(3, 2): + x /= Q(3, 2) + k += 1 + def small(y): + z = (y-1)/(y+1) + power, total = z, Q() + for j in range(60): + total += power/Q(2*j+1) + power *= z*z + return 2*total, 2*total+2*power/(121*(1-z*z)) + lo, hi = small(x) + blo, bhi = small(Q(3, 2)) + return lo+k*blo, hi+k*bhi + + +def independent_moment(profile, saving, recorded_terms): + low, high = Q(), Q() + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + for t, n in sorted(rows.items()): + lo, hi = log_interval(Q(profile['m'], t)) + recorded = recorded_terms[str(t)] + assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper']) + u, v = lo*saving, hi*saving + assert 0 < u <= v < Q(1, 1000) + # Directed rounding of input logs bounds rational denominator sizes. + u = Q(refine.floor_scaled(u, 10**40), 10**40) + v = Q(refine.ceiling_scaled(v, 10**40), 10**40) + tlo, thi = Q(1), Q(1) + elo, ehi = Q(1), Q(1) + for j in range(1, 13): + tlo, thi = tlo*u/j, thi*v/j + elo, ehi = elo+tlo, ehi+thi + # First omitted term is degree13; subsequent ratios <1/2. + ehi += 2*thi*v/13 + weight = Q(t*n, profile['m']*profile['W']) + low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40) + high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40) + return low, high + + +def audit(certificate): + profile_path = ROOT/certificate['profile_path'] + assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256'] + for name, digest in certificate['source_sha256'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + source = json.loads(profile_path.read_text()) + p = source['bit'] + assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank'] + accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms']) + rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms']) + assert accepted[1] < 1 < rejected[0] + controls = {} + for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]: + params = variant['assembly']['parameters'] + result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h'])) + assert refine.arithmetic.js(result) == variant['assembly'] + assert len(result['constraints']) == 47 and len(result['margins']) == 7 + assert all(v > 0 for v in result['constraints'].values()) + for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))), + ('zero_backoff', dict(h=Q())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))]: + call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h'])) + call.update(kwargs) + try: + refine.balanced.assembly(source['finite_bridge'], **call) + except refine.balanced.InvalidAssembly as error: + controls[name+'/'+label] = str(error) + else: + raise AssertionError('Negative control accepted: '+name+'/'+label) + next_a = Q(certificate['next_bit_saving']) + best = Q(certificate['preferred']['kappa']) + cap = next_a/(1+next_a) + assert cap > best + return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60, + independent_exp_degree=12, independent_tail='twice first omitted term', + independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1, + variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls, + fixed_profile_balanced_family_kappa_strict_upper=cap, + remaining_possible_parameter_gain_upper=cap-best) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json') + parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json') + parser.add_argument('--record', action='store_true') + args = parser.parse_args() + result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text()))) + if args.record: + args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed' + print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls') + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/certificate.json new file mode 100644 index 0000000000..346cf87ea3 --- /dev/null +++ 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mode 100644 index 0000000000..399299089e --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python3 +"""Exact arithmetic screen of the reordered rank-pair complete physical profile. + +Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced +assembly (PR34 and successors). New directed Taylor bounds are documented in +this file. Prepared with OpenAI assistance. Inherited licenses apply. +Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from math import factorial +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[3] +sys.path.insert(0, str(ROOT/'scripts/experiments')) +import binary_frame_math as arithmetic +spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def floor_scaled(x, denominator): + return (x * denominator).numerator // (x * denominator).denominator + + +def ceiling_scaled(x, denominator): + return -floor_scaled(-x, denominator) + + +def exact_moment(m, width, rows, saving, degree=8, rounding=10**40): + """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q. + + At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u). + The tail at v has first term v^(d+1)/(d+1)!; successive ratios + are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper. + Directed rounding per exp bound preserves both inequalities. + The inherited logarithm helper encloses log(m/t) rationally. + """ + assert type(saving) is Q and 0 < saving < 1 and degree >= 1 + lo, hi = Q(), Q() + terms = {} + for t, count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 0 < t < m and count > 0 + loglo, loghi = arithmetic.logs(Q(m, t)) + u, v = saving*loglo, saving*loghi + assert 0 <= u <= v < 1 + lower = sum((u**j / factorial(j) for j in range(degree+1)), Q()) + upper = sum((v**j / factorial(j) for j in range(degree+1)), Q()) + upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2)) + lower = Q(floor_scaled(lower, rounding), rounding) + upper = Q(ceiling_scaled(upper, rounding), rounding) + weight = Q(t*count, m*width) + lo += weight*lower + hi += weight*upper + terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi, + exp_lower=lower, exp_upper=upper) + return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi, + degree=degree, rounding_denominator=rounding, terms=terms) + + +def assemble(bridge, saving, h, denominator): + preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h) + kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator) + accepted = balanced.assembly(bridge, saving, kappa, h=h) + assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7 + assert all(v > 0 for v in accepted['constraints'].values()) + assert all(v > kappa for v in accepted['margins'].values()) + try: + balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h) + except balanced.InvalidAssembly as error: + rejected = str(error) + else: + raise AssertionError('Next kappa grid unexpectedly passes') + return dict(kappa=kappa, assembly=accepted, + next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected, + eventual_bounds=balanced.cutoffs(bridge, accepted)) + + +def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)): + profile_path = profile_path.resolve() + source = json.loads(profile_path.read_text()) + profile = source['bit'] + bridge = source['finite_bridge'] + m, width = profile['m'], profile['W'] + rows = {int(t): n for t, n in profile['child_multiplicities'].items()} + assert sum(t*n for t, n in rows.items()) == profile['total_rank'] + assert bridge['bit']['W'] == width + low, high = 1, floor_scaled(Q(717, 10**7), denominator) + assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1 + assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1 + steps = 0 + while low+1 < high: + mid = (low+high)//2 + test = exact_moment(m, width, rows, Q(mid, denominator)) + if test['upper'] < 1: + low = mid + elif test['lower'] > 1: + high = mid + else: + raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision') + steps += 1 + saving = Q(low, denominator) + accepted = exact_moment(m, width, rows, saving) + rejected = exact_moment(m, width, rows, Q(high, denominator)) + assert accepted['upper'] < 1 < rejected['lower'] + preferred = assemble(bridge, saving, h, denominator) + coarse_denom = 10**11 + coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom) + assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1 + coarse = assemble(bridge, coarse_bit, h, coarse_denom) + inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit) + inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom)) + assert inherited_coarse['upper'] < 1 < inherited_next['lower'] + coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'], + next_bit_lower=inherited_next['lower']) + # Same coarse grid/backoff as PR63 separates the structural gain from + # the additional precision refinement suggested by the PR61 precedent. + prior = Q(source['kappa']) + paths = (Path(__file__), Path(__file__).with_name('audit.py'), + ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__)) + return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier', + profile_path=str(profile_path.relative_to(ROOT)), + profile_sha256=sha256(profile_path.read_bytes()).hexdigest(), + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths}, + grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving, + next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected, + preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'], + difference=preferred['kappa']-prior, + structural_gain_on_original_grid=coarse['kappa']-prior, + additional_precision_gain=preferred['kappa']-coarse['kappa']), + proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.', + 'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.', + 'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.', + 'Neither global optimality nor measured practical speedup is claimed.']) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json') + parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json')) + parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result') + args = parser.parse_args() + result = arithmetic.js(build_certificate(args.profile)) + if args.record: + args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed' + print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'], + kappa=result['preferred']['kappa'], constraints=47, margins=7, + next_grid_controls='PASS', comparison=result['comparison']), indent=2)) + + +if __name__ == '__main__': + main() diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py new file mode 100644 index 0000000000..e23cba24ec --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/test_arithmetic.py @@ -0,0 +1,68 @@ +"""Meaningful certificate verification and deliberate-failure controls.""" +import sys +sys.dont_write_bytecode = True +from copy import deepcopy +from fractions import Fraction as Q +import json +from pathlib import Path +import subprocess +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import refine +import audit + + +class ExactArithmeticTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.certificate = json.loads((HERE/'certificate.json').read_text()) + cls.profile = json.loads((refine.ROOT/cls.certificate['profile_path']).read_text())['bit'] + + def test_complete_reproduction(self): + actual = refine.arithmetic.js(refine.build_certificate(refine.ROOT/self.certificate['profile_path'])) + self.assertEqual(actual, self.certificate) + + def test_independent_enclosures_and_controls(self): + actual = refine.arithmetic.js(audit.audit(self.certificate)) + self.assertEqual(actual, json.loads((HERE/'audit-receipt.json').read_text())) + self.assertEqual(len(actual['controls']), 10) + + def test_next_bit_grid_is_rejected(self): + p = self.profile + result = refine.exact_moment(p['m'], p['W'], {int(t):n for t,n in p['child_multiplicities'].items()}, Q(self.certificate['next_bit_saving'])) + self.assertGreater(result['lower'], 1) + + def test_forged_accepted_bit_is_rejected(self): + forged = deepcopy(self.certificate) + forged['bit_saving'] = forged['next_bit_saving'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_forged_source_digest_is_rejected(self): + forged = deepcopy(self.certificate) + forged['profile_sha256'] = '0'*64 + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_omitted_constraint_is_rejected(self): + forged = deepcopy(self.certificate) + del forged['preferred']['assembly']['constraints']['K_geometry'] + with self.assertRaises(AssertionError): + audit.audit(forged) + + def test_float_saving_refused(self): + with self.assertRaises(AssertionError): + refine.exact_moment(2, 1, {1:1}, 0.01) + + def test_python_optimization_is_rejected(self): + for script in ('refine.py', 'audit.py'): + result = subprocess.run([sys.executable, '-B', '-O', str(HERE/script)], + cwd=refine.ROOT, capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json new file mode 100644 index 0000000000..1d539de130 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/current-comparison.json @@ -0,0 +1,9 @@ +{ + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", + "head": "790a14e28e935398072b9a9a68694ce7fba8940f", + "source": "PR body reported bound, checked 2026-10-08; not an independent audit of PR64", + "kappa": "2041159402879/40000000000000000", + "pr64_kappa": "20411033624901463/400000000000000000000", + "difference": "560403888537/400000000000000000000", + "relative_gain": "560403888537/20411033624901463" +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json new file mode 100644 index 0000000000..42958fc74b --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-compiler.json @@ -0,0 +1,195 @@ +{ + "artifact_sha256": { + "frame-profiles-23.json": "fec377bcf1512a427674983256b900229d4133026445b6e680c6e1e6dde5af7d", + "frame-profiles-25.json": "28b4b911e26fbc02dde0d2e1458ed16227f756126ab8144d6d45e164d1165262", + "frame-transitions-23.json": "86646f1110595294cccc15603c552f0a153574a690b69c3b144d84a449891103", + "frame-transitions-25.json": "c333c348665d12b95e168ca4fac48bfdca335104edd0f29c81fe94bec292e774", + "frame-word-23.json.gz": "a44e038e1c548ea8ac31dd04acc2bba7951b22e17df7b7ad3464ea2b504a8da4", + "frame-word-25.json.gz": "ad8b299697f90b185b6b791313b505586be97965519052100d097df6199e00c5", + "paired-candidate.json": "34a500d739537235dfc5d24325c22856ca4567b9eac998a3bce9b13db5501940" + }, + "axes": { + "23": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 36432, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 31460, + "elementary_xors": 149137, + "h": 23, + "histogram": { + "0": 302057, + "1": 42694, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "2": 82722, + "21": 165, + "22": 23, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 642620, + "roles": 27918, + "stats": { + "augmentations": 220, + "clearing_xors": 1577, + "matched": 37025, + "multi_node_regions": 10350, + "reclaimed": 801, + "regions": 52473 + } + }, + "gzip_sha256": "a44e038e1c548ea8ac31dd04acc2bba7951b22e17df7b7ad3464ea2b504a8da4", + "replay": { + "elementary_xors": 149137, + "full_basis_vectors": 31460, + "h": 23, + "histogram": { + "0": 162914, + "1": 42694, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "2": 82722, + "21": 165, + "22": 23, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525 + }, + "output_roles": 5336, + "rank_mass": 642620, + "roles": 27918, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 621342 + }, + "schedule": "cover-core", + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4" + }, + "25": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 48329, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 41186, + "elementary_xors": 205977, + "h": 25, + "histogram": { + "0": 416741, + "1": 55478, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "2": 115781, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 915250, + "roles": 36586, + "stats": { + "augmentations": 286, + "clearing_xors": 2154, + "matched": 53194, + "multi_node_regions": 13975, + "reclaimed": 1090, + "regions": 73695 + } + }, + "gzip_sha256": "ad8b299697f90b185b6b791313b505586be97965519052100d097df6199e00c5", + "replay": { + "elementary_xors": 205977, + "full_basis_vectors": 41186, + "h": 25, + "histogram": { + "0": 224465, + "1": 55478, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "2": 115781, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569 + }, + "output_roles": 6925, + "rank_mass": 915250, + "roles": 36586, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 856108 + }, + "schedule": "reverse-node", + "word_sha256": "a54443429f47c486016771ce0436effda098e142afc52861c20957e9ff8e086b" + } + }, + "source_sha256": { + "research/pair-assembly/frame/frame_verify.py": "fafe25d57166a747eeb847444a2e02dd7eed19038b93a2c495014d147d04a8fb", + "research/pair-assembly/pair_graph.py": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420", + "research/reordered-rank-pair/test_negative.py": "88832242e6f74e3fe08d109d4f21ff188a9ca0ae50c3e8f31da0243fe9501510", + "research/reordered-rank-pair/verify.py": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352", + "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3", + "scripts/experiments/binary_frame_profiles.cpp": "8e2e391d3ee57cbb1372c68e4aa031e1b861321536eabd642ada54e12e678669", + "scripts/experiments/binary_frame_replay.py": "392e78e62d7685c99a5888a7da743ea6c3dcad631af4a743c91e0c09348442bc", + "scripts/experiments/rank_pair_compiler.py": "9984aaccf880e4840402322d76678bfddb33ce7e494af78430a43429f51b85fd" + }, + "status": "Exact topological scheduling of unchanged PR63 graph/compiler; both physical orientations and fixed profiles checked" +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json new file mode 100644 index 0000000000..3b648dbe21 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-23.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "loss": 506, + "rank_sum": 642620, + "field_prime": 2305843009213693951, + "frames": 52475, + "distinct_matrices": 36399, + "crt_matrices": 6049, + "crt_disagreements": 0, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json new file mode 100644 index 0000000000..19cc34b4ca --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-profiles-25.json @@ -0,0 +1,40 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "loss": 600, + "rank_sum": 915250, + "field_prime": 2305843009213693951, + "frames": 73697, + "distinct_matrices": 50394, + "crt_matrices": 8127, + "crt_disagreements": 0, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ] +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json new file mode 100644 index 0000000000..2883a5f7c9 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 27918, + "frames": 52475, + "distinct_transitions": 138016, + "singles": 15939, + "rank_mass": 642620, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 53320, + "2": 77409, + "3": 11086, + "4": 10683, + "5": 7723, + "6": 1994, + "7": 294, + "8": 1362, + "9": 525, + "10": 442, + "11": 11, + "12": 467, + "13": 22, + "14": 2005, + "15": 551, + "16": 547, + "17": 365, + "18": 4220, + "19": 7820, + "21": 165, + "22": 23 + }, + "word_sha256": "09c20f4e46207b7c91092cefb2b851c88694b6c12d3bf5091333cd8a78a197a4", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json new file mode 100644 index 0000000000..3b4bc33ff6 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-transitions-25.json @@ -0,0 +1,35 @@ +{ + "h": 25, + "v": 2300, + "R": 36586, + "frames": 73697, + "distinct_transitions": 190838, + "singles": 20700, + "rank_mass": 915250, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 69278, + "2": 108881, + "3": 14362, + "4": 16908, + "5": 10263, + "6": 1767, + "7": 541, + "8": 2115, + "9": 569, + "10": 529, + "12": 599, + "13": 25, + "14": 530, + "16": 3130, + "17": 869, + "18": 519, + "19": 395, + "20": 5436, + "21": 10164, + "23": 220, + "24": 25 + }, + "word_sha256": "a54443429f47c486016771ce0436effda098e142afc52861c20957e9ff8e086b", + "copied_centers": 25, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz new file mode 100644 index 0000000000..3a7c7c41c1 Binary files /dev/null and b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-23.json.gz differ diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz new file mode 100644 index 0000000000..6a239a3e9f Binary files /dev/null and b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/frame-word-25.json.gz differ diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json new file mode 100644 index 0000000000..dbfad24526 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/paired-candidate.json @@ -0,0 +1,252 @@ +{ + "bit": { + "L": 2226400, + "N": 4073300, + "W": 137151806, + "axes": [ + { + "R": 27918, + "blocks": [ + 0, + 343849, + 16857, + 10540, + 5782, + 4156, + 3911, + 3635, + 2858, + 2284, + 1804, + 1716, + 1262, + 1077, + 711, + 589, + 352, + 193, + 114, + 0, + 45, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6049, + "distinct_matrices": 36399, + "field_prime": 2305843009213693951, + "frames": 52475, + "h": 23, + "loss": 506, + "rank_sum": 642620, + "v": 1771 + }, + { + "R": 36586, + "blocks": [ + 0, + 474640, + 25158, + 12097, + 6776, + 5735, + 5500, + 4875, + 3784, + 3209, + 2695, + 2649, + 1906, + 1663, + 1344, + 1127, + 711, + 585, + 380, + 181, + 113, + 0, + 55, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8127, + "distinct_matrices": 50394, + "field_prime": 2305843009213693951, + "frames": 73697, + "h": 25, + "loss": 600, + "rank_sum": 915250, + "v": 2300 + } + ], + "child_multiplicities": { + "1": 1725126040, + "10": 8922045, + "11": 8638179, + "12": 6278126, + "13": 5422273, + "14": 4015524, + "15": 3350617, + "16": 2068781, + "17": 9626535, + "18": 935180, + "19": 320551, + "2": 83325918, + "20": 303623, + "21": 16346100, + "22": 97405, + "23": 72402275, + "25": 64793806, + "3": 45665787, + "4": 25298896, + "481": 8146600, + "5": 19715485, + "525": 64793806, + "529": 64211400, + "6": 18735800, + "7": 16994125, + "8": 13274864, + "9": 10936339 + }, + "deficit": 1846900, + "m": 575, + "maxchild": 529, + "parts": { + "data": { + "1": 73319400, + "17": 8146600, + "21": 8146600, + "481": 8146600 + }, + "data_growth_23": { + "1": 8146600, + "21": 8146600 + }, + "data_growth_25": { + "1": 8146600, + "23": 8146600 + }, + "exterior_23": { + "23": 64211400, + "529": 64211400 + }, + "exterior_25": { + "25": 64793806, + "525": 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}, + "complex": { + "W": 537696432, + "halving_degree": 20, + "m": 784, + "maxchild": 756, + "s": 421548223824, + "scalar_group_upper": 4793351472, + "scalar_terms": [ + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + }, + { + "c": 78437, + "copied_center_extra_groups": 56, + "h": 28, + "invocations": 3276, + "local_group_upper": 729892, + "v": 3276 + } + ], + "wire_bits": 30 + }, + "rows": { + "coefficient": 852, + "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential", + "degree": 2000, + "degree_gap": "6548/25", + "suffix_slope": 8000 + }, + "semantic": { + "B": 9696565176891520488614054257040, + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "E": 9696565176891520488192506033216, + "induction_gap": 533311084729033626873772984137200, + "literal_charge": 2771683137698171397039558468, + "strict_literal_gap": 9693793493753822316795466474748 + } + }, + "kappa": "5102757/100000000000", + "source": { + "axis23": "research/reordered-rank-pair/frame-profiles-23.json", + "axis25": "research/reordered-rank-pair/frame-profiles-25.json", + "profile_constructor": "research/pair-assembly/frame/frame_verify.py" + } +} diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py new file mode 100644 index 0000000000..a219a87719 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/test_negative.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +"""Adversarial controls for the reordered serialized words and scheduling.""" +import sys +sys.dont_write_bytecode=True +import gzip,json,tempfile,subprocess +from pathlib import Path +import verify + +def rejected(label,call): + try:call() + except (AssertionError,IndexError,ValueError): + print('PASS rejected '+label,flush=True) + else:raise AssertionError('Invalid control accepted: '+label) + +def main(): + optimized=subprocess.run([sys.executable,'-B','-O',str(verify.HERE/'verify.py')],capture_output=True,text=True) + assert optimized.returncode!=0 and 'Assertions must remain enabled' in optimized.stderr + print('PASS rejected optimized Python invocation',flush=True) + work=verify.ROOT/'build/reordered-rank-pair';work.mkdir(parents=True,exist_ok=True) + original=json.loads(gzip.decompress((verify.HERE/'frame-word-23.json.gz').read_bytes())) + with tempfile.TemporaryDirectory(prefix='negative-',dir=work) as temporary: + path=Path(temporary)/'mutated.json' + bad=dict(original);bad['ops']=original['ops'][1:] + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('omitted physical XOR',lambda:verify.replay(path)) + bad=dict(original);bad['R']=original['R']-1 + path.write_text(json.dumps(bad,separators=(',',':'))) + rejected('understated physical role count',lambda:verify.replay(path)) + records=json.loads((verify.HERE/'frame-compiler.json').read_text()) + for name in ('frame-word-23.json.gz','frame-profiles-23.json'): + path.write_bytes((verify.HERE/name).read_bytes()+b' ') + rejected('changed digest '+name,lambda name=name:require_digest(path,records['artifact_sha256'][name])) + # Two equal-rank regions with an actual dependency must not be reversed. + blocks=[{'rank':1,'nodes':[1],'inputs':[],'candidates':[]}, + {'rank':1,'nodes':[2],'inputs':[1],'candidates':[]}] + invalid=lambda h:(None,blocks,[],{}, {1:0,2:1},{},[0,1],None) + rejected('backward region dependency',lambda:verify.reordered_build(invalid,'reverse-node')(23)) + print('PASS all six reordered-word negative controls',flush=True) + +def require_digest(path,expected):assert verify.sha(path)==expected + +if __name__=='__main__':main() diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py new file mode 100644 index 0000000000..5ac300ecd0 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/research/reordered-rank-pair/verify.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Replay, profile, or deterministically rebuild a reordered PR63 circuit. + +PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik +Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance. +Region scheduling experiment: Rohan Arun with OpenAI Codex assistance. +Apache-2.0; inherited notices and mathematical dependencies remain applicable. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile +from hashlib import sha256 +from pathlib import Path + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +EXP=ROOT/'scripts/experiments' +sys.path[:0]=[str(EXP),str(ROOT/'scripts')] +from binary_frame_replay import replay +from binary_frame_profile_prepare import prepare +import binary_frame_math as arithmetic + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module + +def sha(path):return sha256(path.read_bytes()).hexdigest() + +def reordered_build(original,mode): + def build(h): + parts=list(original(h)) + c,blocks,uses,value_uses,owner,signal,order,contains=parts + if mode=='reverse-node': + key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes'])) + elif mode=='cover-core': + key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0]) + else:raise ValueError(mode) + parts[6]=sorted(range(len(blocks)),key=key) + position={g:i for i,g in enumerate(parts[6])} + for g,b in enumerate(blocks): + for x in b['inputs']: + assert position[owner[x]]=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr65/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<= j+1 proves persistence.", + "common_cutoff": 14000000000000, + "cutoff_log2_input": { + "alpha": 6143424401, + "compact": 24573697601, + "geometry": 3999931956149, + "guard": 4350062, + "log_p": 25, + "normalization": 14000000000000, + "period": 49147395201, + "phase_cell": 19, + "reservoir": 14, + "stopped_leaf": 252 + }, + "power_checkpoints": [ + { + "log2_input": 14000000000000, + "powers": { + "alpha": { + "exponent": 714467976, + "rhs": 112000000156824, + "rhs_bits": 47 + }, + "compact": { + "exponent": 714467976, + "rhs": 448000000627232, + "rhs_bits": 49 + }, + "leaf": { + "exponent": 666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 714467976, + "rhs": 224000000313576, + "rhs_bits": 48 + }, + "rows": { + "exponent": 714467976, + "rhs": 112000000156824000, + "rhs_bits": 57 + } + } + }, + { + "log2_input": 28000000000000, + "powers": { + "alpha": { + "exponent": 1428935953, + "rhs": 224000000156824, + "rhs_bits": 48 + }, + "compact": { + "exponent": 1428935953, + "rhs": 896000000627232, + "rhs_bits": 50 + }, + "leaf": { + "exponent": 1333333333333, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 1428935953, + "rhs": 448000000313576, + "rhs_bits": 49 + }, + "rows": { + "exponent": 1428935953, + "rhs": 224000000156824000, + "rhs_bits": 58 + } + } + }, + { + "log2_input": 56000000000000, + "powers": { + "alpha": { + "exponent": 2857871906, + "rhs": 448000000156824, + "rhs_bits": 49 + }, + "compact": { + "exponent": 2857871906, + "rhs": 1792000000627232, + "rhs_bits": 51 + }, + "leaf": { + "exponent": 2666666666666, + "rhs": 3136, + "rhs_bits": 12 + }, + "period": { + "exponent": 2857871906, + "rhs": 896000000313576, + "rhs_bits": 50 + }, + "rows": { + "exponent": 2857871906, + "rhs": 448000000156824000, + "rhs_bits": 59 + } + } + }, + { + "log2_input": 112000000000000, + "powers": { + "alpha": { + "exponent": 5715743812, + "rhs": 896000000156824, + "rhs_bits": 50 + }, + "compact": { + "exponent": 5715743812, + "rhs": 3584000000627232, + "rhs_bits": 52 + }, + "leaf": { + 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a/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py b/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py new file mode 100644 index 0000000000..fe70b5cf01 --- /dev/null +++ b/references/frame-compiler/pr71/references/frame-compiler/pr67/research/slot-cost-rank-pair/compiler.py @@ -0,0 +1,266 @@ +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +U aa,bb; +while(std::cin>>aa>>bb){ + assert(aa=frames[aa].rank); + if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i E +on the live control. The carrier is only an XOR control and its clean signal +is unchanged. Its later use can still raise it from E to G. Repeated use is +subject to the same inclusion test with its then-current frame, so the entire +physical frame path remains nested. + +This introduces no free copies, source-dependent runtime choice, or uncharged +frame jump. Candidate selection happens once while constructing a fixed finite +word. Every operation in that word is still a literal two-slot XOR. + +## Dirty state and frames + +The compiler's block transformations remain invertible on all incoming dirty +coordinates. Each additional clearing operation is invertible too. Therefore +the complete mixer M is invertible. The inherited word has the form + + M, J, inverse(M), V, M, J, inverse(M), V. + +Its dirty-scratch cancellation argument only requires the mixer to be a fixed +invertible word and its clean signal map to give the required injection. The +new controls preserve those properties. This argument is supplemented by +independent serialized replay on **every** input and dirty basis vector for +both h=23 and h=25 and both orientations; see `selected-replay-*.json`. + +Frame preparation independently reconstructs every transition from the actual +XOR list, checks it against the auxiliary event log, and checks every inclusion. +All frames remain the inherited original-envelope projectors. Consequently +the same fixed-I+J formulas and bounded-minor/CRT argument apply without a new +projector formula or denominator bound. The ranked/global profiles use 6,049 +and 7,997 CRT-checked matrices and report zero modular disagreements. + +Neither W nor total rank changes. The actual fixed-basis child profiles change +because different clearing expressions promote different slots at different +points. This is the source of the finite moment improvement; counting roles +alone misses it. + +## The selected finite profile improves every concave power + +There is also an exact comparison independent of the selected parameter grid. +Let d_t be the selected child multiplicity minus PR #63's pinned multiplicity. +The integer certificate `concavity-screen.json` checks + + sum(t*d_t) = 0, + C_k = sum(min(t,k)*d_t) <= 0 for every integer 1 <= k <= 529, + +with a strict inequality for some k. Its smallest C_k is -619850. The source +profile is pinned to PR #63 commit `aa7701b68540b7863d3b66a414e4319915d6282d` +in `comparison-pr63.json`. For any f with f(0)=0 and decreasing discrete +increments, the identity + + sum(d_t*f(t)) = sum_(k=1..528) (2*f(k)-f(k-1)-f(k+1))*C_k + +holds because the linear mass term vanishes. For f(t)=t^(1-a), 01 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) ++ slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();pending={};stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): +@@ -149,7 +151,8 @@ + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 +- return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) ++ endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 ++ return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} +@@ -161,6 +164,9 @@ + old,e=bb[p];row^=old;expr^=e + return expr + for s in anchors:ins(s) ++ for s,target in pending.items(): ++ if contains(blocks[frames[s]]['frame'],blocks[g]['frame']) and contains(blocks[g]['frame'],blocks[target]['frame']): ++ ins(s);stats['live_anchor_candidates']+=1 + best=None + # Inspect every eligible dependent candidate across all retired ranks. + # Rank the actual fixed-basis growth/cleanup profiles by an integer entropy score. +@@ -176,7 +182,9 @@ + if best is None or key= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py b/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/references/frame-compiler/pr71/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp b/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/references/frame-compiler/pr71/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 1 and kappa > previous_kappa + bridge = json.loads((OLD/'certificate.json').read_text())['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/split-pair/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr67_commit='b3745601e947a94316bf25c2c6263d93c06e3364', + pr67_kappa=previous_kappa, ratio_pr67=kappa/previous_kappa, + absolute_gain_pr67=kappa-previous_kappa, + pr67_complete_profile_exclusion_lower=prior65_lower, + full_pr67_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected split-pair partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'split-pair-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py b/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py new file mode 100644 index 0000000000..1290ef2eb8 --- /dev/null +++ b/references/frame-compiler/pr71/scripts/experiments/split_pair_engine.py @@ -0,0 +1,275 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py b/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py new file mode 100644 index 0000000000..7908c963a4 --- /dev/null +++ b/references/frame-compiler/pr71/scripts/experiments/verify_split_pair.py @@ -0,0 +1,78 @@ +#!/usr/bin/env python3 +"""Replay the aligned split-pair/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from split_pair_compose import compose, check_sources +from split_pair_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'split-pair-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='split-pair-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + 'c++', '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'split-pair-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'split-pair-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'split-pair-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'split-pair-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'split-pair-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/references/frame-compiler/pr71/tests/test_split_pair.py b/references/frame-compiler/pr71/tests/test_split_pair.py new file mode 100644 index 0000000000..5088cff133 --- /dev/null +++ b/references/frame-compiler/pr71/tests/test_split_pair.py @@ -0,0 +1,238 @@ +"""Physical and exact-arithmetic controls for the aligned split/pair witness.""" +from copy import deepcopy +from fractions import Fraction +from itertools import combinations +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile +import unittest +from unittest.mock import patch + +ROOT = Path(__file__).resolve().parents[1] +EXPERIMENTS = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXPERIMENTS)) +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from binary_frame_math import moment + + +class SplitPairControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.words = {h: json.loads(gzip.decompress((ROOT/f'certificates/split-pair-word-{h}.json.gz').read_bytes())) + for h in (23,25)} + + def reject_mutation(self, mutate, checker='both'): + for h, original in self.words.items(): + with self.subTest(h=h), tempfile.TemporaryDirectory() as directory: + changed = deepcopy(original) + mutate(changed) + path = Path(directory)/'word.json' + path.write_text(json.dumps(changed, separators=(',', ':'))+'\n') + with self.assertRaises((AssertionError, ValueError, IndexError, KeyError)): + if checker != 'transitions': + replay(path) + if checker != 'replay': + prepare(path, Path(directory)/'transitions.bin') + + def test_selected_words_pass_independent_replay(self): + recorded = json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + actual = replay(ROOT/f'certificates/split-pair-word-{h}.json.gz') + self.assertEqual(json.loads(json.dumps(actual)), recorded['axes'][str(h)]['replay']) + + def test_omitted_literal_xor_is_rejected(self): + self.reject_mutation(lambda word: word['ops'].pop(0)) + + def test_self_xor_is_rejected(self): + def mutate(word): + word['ops'][0][1] = word['ops'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_non_nested_operation_frame_is_rejected(self): + def mutate(word): + narrow = next(i for i,(core,cover) in enumerate(word['frames']) if core == cover) + operation = next(op for op in word['ops'] if word['frames'][op[2]][0] != word['frames'][op[2]][1]) + operation[2] = narrow + self.reject_mutation(mutate) + + def test_aliased_terminal_role_is_rejected(self): + def mutate(word): + word['outputs'][1][0] = word['outputs'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_missing_copied_center_is_rejected(self): + def mutate(word): + index = next(i for i,(_,_,_,target) in enumerate(word['outputs']) if len(target) == 1) + word['outputs'].pop(index) + self.reject_mutation(mutate) + + def test_omitted_transition_cannot_reduce_paid_profile(self): + self.reject_mutation(lambda word: word['events'].pop(0), 'transitions') + + def test_understated_physical_width_is_rejected(self): + def mutate(word): + word['R'] -= 1 + self.reject_mutation(mutate) + + def test_complete_pr67_profile_fails_new_bit_saving(self): + from split_pair_arithmetic import refine + previous = json.loads((ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/paired-candidate.json').read_text())['bit'] + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + result = refine.exact_moment(previous['m'], previous['W'], {int(t): n for t,n in previous['child_multiplicities'].items()}, Fraction(current['bit_saving'])) + self.assertGreater(result['lower'], 1) + self.assertGreater(Fraction(current['kappa']), Fraction(current['comparison']['pr67_kappa'])) + + def test_private_import_preserves_path_and_arithmetic_module(self): + import split_pair_graph as provider + import split_pair_arithmetic as arithmetic + sentinel = object() + existing = sys.modules.get('refine', sentinel) + previous_path = sys.path[:] + graph, schedule = provider._private_modules() + refine, audit = arithmetic.private_arithmetic() + self.assertIs(audit.refine, refine) + self.assertIs(sys.modules.get('refine', sentinel), existing) + self.assertEqual(sys.path, previous_path) + + def test_failed_graph_build_restores_original_providers(self): + import split_pair_graph as provider + previous_class, previous_points = provider._graph.circuit_class, provider._graph.alternating_points + with patch.object(provider._graph, 'graph', side_effect=RuntimeError('deliberate graph failure')): + with self.assertRaises(RuntimeError): + provider.graph(23) + self.assertIs(provider._graph.circuit_class, previous_class) + self.assertIs(provider._graph.alternating_points, previous_points) + + def test_failed_compilation_restores_engine_graph_and_schedule(self): + import split_pair_compiler as producer + previous_graph, previous_build = producer.compiler.graph, producer.compiler.build + missing = object() + runtime = {name:getattr(producer.compiler,name,missing) for name in ('PENDING_COST','ORACLE_EXE','ORACLE_INPUT','oracles')} + with patch.object(producer.compiler, 'compile_', side_effect=RuntimeError('deliberate compiler failure')): + with self.assertRaises(RuntimeError): + producer.compile_axis(23) + self.assertIs(producer.compiler.graph, previous_graph) + self.assertIs(producer.compiler.build, previous_build) + for name,value in runtime.items(): + self.assertIs(getattr(producer.compiler,name,missing),value) + + def test_uncertified_configurations_are_rejected(self): + import split_pair_graph as provider + wrong_anchor = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_anchor['anchor'] = False + boolean_group = deepcopy(provider.EXPECTED_CONFIGS[23]); boolean_group['groups'][0] = True + changed_schedule = deepcopy(provider.EXPECTED_CONFIGS[23]); changed_schedule['schedule'] = 'reverse-node' + for changed in (wrong_anchor, boolean_group, changed_schedule): + with self.subTest(configuration=changed), patch.object(provider.json, 'loads', return_value=changed): + with self.assertRaises(ValueError): + provider.configuration(23) + for dimension in (True, 22, 24, '23'): + with self.subTest(dimension=dimension), self.assertRaises(ValueError): + provider.configuration(dimension) + + def test_recursive_weighted_exclusions_and_contraction(self): + import split_pair_graph as provider + for h in (23,25): + block_sizes = [] + parent = provider._graph.circuit_class(h) + selected = provider.split_class(parent, provider.configuration(h)['groups']) + case = self + class Audited(selected): + def grouping(self, points): + groups = super().grouping(points) + case.assertEqual([x for group in groups for x in group], list(points)) + case.assertLess(len(groups), len(points)) + return groups + + def _block(self, points, edges, weights, level): + def expected(omitted): + values = [value for pair,value in edges.items() if not set(pair) & omitted] + values += [value for point,value in weights.items() if point not in omitted] + support = 0 + for value in values: + case.assertEqual(support & self.support[value], 0) + support |= self.support[value] + return support + total, single, pairs = super()._block(points, edges, weights, level) + case.assertEqual(self.support[total], expected(set())) + case.assertEqual(set(single), set(points)) + for a in points: + case.assertEqual(self.support[single[a]], expected({a})) + case.assertEqual(set(pairs), set(combinations(points,2))) + for a,b in combinations(points,2): + case.assertEqual(self.support[pairs[a,b]], expected({a,b})) + block_sizes.append(len(points)) + return total, single, pairs + local = Audited(h-1) + block_sizes.clear() + local.pair(list(range(h-1))) + self.assertEqual(sorted(block_sizes, reverse=True), [h-1, 12 if h==23 else 13, 7 if h==23 else 8, 5, 3, 2]) + + def test_next_fine_grid_points_and_old_assembly_controls_reject(self): + from split_pair_arithmetic import refine + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + bit = current['bit']; saving = Fraction(current['bit_saving']); kappa = Fraction(current['kappa']) + grid = Fraction(1,10**18) + rows = {int(t): n for t,n in bit['child_multiplicities'].items()} + self.assertLess(refine.exact_moment(bit['m'],bit['W'],rows,saving)['upper'], 1) + self.assertGreater(refine.exact_moment(bit['m'],bit['W'],rows,saving+grid)['lower'], 1) + for label, variant in ( + ('next_kappa', dict(kappa=kappa+grid)), + ('zero_backoff', dict(h=Fraction())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))): + call = dict(a_bit=saving, kappa=kappa, h=Fraction(1,10**12));call.update(variant) + with self.subTest(control=label), self.assertRaises(refine.balanced.InvalidAssembly): + refine.balanced.assembly(current['finite_bridge'], **call) + + def test_mass_preserving_profile_mutation_is_rejected(self): + from split_pair_compose import check_sources + profile_path = ROOT/'certificates/split-pair-profiles-23.json' + changed = json.loads(profile_path.read_text()) + before = sum(t*n for t,n in enumerate(changed['blocks'])) + changed['blocks'][2] += 3; changed['blocks'][3] -= 2 + self.assertTrue(all(n >= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'split-pair-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from split_pair_compose import check_sources + manifest_path = ROOT/'research/split-pair/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/split-pair-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import split_pair_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('split_pair_graph.py', 'split_pair_engine.py', 'split_pair_compiler.py', 'split_pair_arithmetic.py', 'split_pair_compose.py', 'verify_split_pair.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/references/frame-compiler/pr71/tests/test_split_pair_pending.py b/references/frame-compiler/pr71/tests/test_split_pair_pending.py new file mode 100644 index 0000000000..e6d63f72a4 --- /dev/null +++ b/references/frame-compiler/pr71/tests/test_split_pair_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/split_pair_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main() diff --git a/research/balanced-split/PROOF.md b/research/balanced-split/PROOF.md new file mode 100644 index 0000000000..c34f8542cc --- /dev/null +++ b/research/balanced-split/PROOF.md @@ -0,0 +1,251 @@ +# Finite certificate and inherited scope + +## 1. Exact change and provenance + +This construction preserves PR71's anchored `[1,1,2]` split recursion, +PR65 region schedules, PR67 profile-cost reclamation and PR68 pending live +controls with next-use scoring. It composes three finite choices: PR69's +balanced coarse parenthesization, future-compatible unit completion, and a +bounded adaptation of PR70 carry exchanges. The contributor originals, +licenses and notices are retained in hash-checked archives. The published +PR71 source, words and complete arithmetic certificate are preserved at +`1bef94fd40a746452548c84a4a8f8834670a3113` for the full-profile comparison. +The new namespace is `balanced-split`. Two portable engines differ from the +independently audited discovery engines only in the repository-relative ROOT +constant; their relocation patches and SHA256s are recorded. + +The h23 coarse cell uses columns when `i+ji}, & j\le i+1,\\ +\operatorname{rank}\,U_{\le i}W_{\ge j}^{T}, & j\ge i+1. +\end{cases} +$$ + +*Proof.* Let G_j be the span of e_j,…,e_{m−1}. For j > i, the identity +vanishes on the corner, so M's corner equals −U_{≤i}W_{≥j}^T. For j ≤ i+1, +take the following steps. + +1. M is the projector onto ker Y = ker W^T along im Y = im U. Therefore + M(G) = (G + im Y) ∩ ker Y for every subspace G. +2. Hence dim M(G_j) = dim(G_j + im U) − r = (m−j) + rank U_{i}. +4. ρ(i,j) is the dimension of M(G_j) after deleting coordinates > i, which + is the difference of the two dimensions. ∎ + +The NE pivots of the top-row-first, rightmost-pivot elimination are exactly +the positions where the second difference + +$$ +\rho(i,j)-\rho(i-1,j)-\rho(i,j+1)+\rho(i-1,j+1) +$$ + +equals one. Maximal diagonal runs of pivots are the recursive children, as +in the inherited profiler. + +## 4. The fixed PR34 basis + +The PR34 reversed (23,25) basis gives the physical image of X⊗B the entries + +$$ +Y_{kl}=X_{\lambda(k),\lambda(l)}\,v_{o(k)}\nu_{o(l)}. +$$ + +Here λ(k) and o(k) are the local and other-axis coordinates of physical index +k = 25α + β. For axis 23, λ(k) = M_β(α) and o(k) = β; for axis 25 the roles +are swapped. For each local coordinate a, o maps {k : λ(k) = a} bijectively +onto the other axis. + +Factor X = U_X W_X^T with W_X^T U_X = I and set U = D_v Û, W = D_ν Ŵ, where +Û_k = (U_X)_{λ(k)}. Then + +$$ +W^T U = \sum_a (\nu\cdot v)\,W_{X,a}^T U_{X,a} = I. +$$ + +Every line has v = t + 3·1 > 0 and +ν = t/2 − 5/(3(n+1))·1 with all entries nonzero and ν·v = 1. Lemma 1 +therefore gives, with S = λ[0,j) and T = λ(i,m): + +- rank U_{i} = rank X[:, T]; +- rank U_{≤i} W_{≥j}^T = rank X[λ[0,i], λ[j,m)]. + +The profile is the same for every one of the N/v_h lines, so one profile per +merged edge suffices. + +Below the band j ∈ {i, i+1}, ρ is a sum of a function of i and a function of +j, so its second differences vanish. Above the band, ρ depends only on the +sets λ[0,i] and λ[j,m). Pivots there can occur only where a new local row and +a new local column first appear. The certifier evaluates the band and these +at most h² positions. It asserts that every second difference is 0 or 1 and +that there are exactly m − r pivots. + +The tests check two things against direct exact elimination of the full +physical matrix I − Y: + +- Lemma 1 on random layouts with this bijection property; +- that the identity X = I_h reproduces the inherited exterior profile + [m−2h, h]. + +## 5. Exact local ranks (Lemma 2) + +The profiler's envelope projector is A = diag(o) + UV^T/d, with U and V +integer matrices of rank at most two. Their rows depend only on whether a +coordinate is in the core, in the cover minus the core, or outside the cover. +Both choices of X therefore have the form + +$$ +X = \Delta + \sigma UV^T/d, +$$ + +with Δ a 0/1 diagonal and σ = ±1. Write k for the number of columns of U. + +For row and column sets S and T: + +- Let P = S ∩ T ∩ supp Δ, S_0 = S∖P and T_0 = T∖P. +- Let C = dI_k + σ Σ_{p∈P} V_p^T U_p. +- Let Z be a basis of ker U_{S_0} and Y a basis of ker V_{T_0}. + +Then + +$$ +\operatorname{rank}X[S,T]=|P|+\operatorname{rank}U_{S_0}+\operatorname{rank}V_{T_0}+\operatorname{rank}(Y^TCZ)-k. +$$ + +*Proof.* The bordered matrix [[Δ_{ST}, σU_S], [−V_T^T, dI]] has rank +k + rank X[S,T]; this is the Schur complement on dI. Eliminating the |P| unit +pivots of Δ leaves [[0, σU_{S_0}], [−V_{T_0}^T, C]]. + +A matrix [[0, A], [B, C]] has rank rank A + rank B + rank(Y^T C Z): reduce A +and B to full-rank blocks with invertible column and row operations, then +clear C outside the kernel directions. ∎ + +All quantities are integer vectors and at most 2×2 determinants, so every +rank is exact over Q. No modular reduction is used. + +## 6. Composition + +Each axis's selection lists the entrance roles and the exit roles. For each +selected role: + +- The unchanged inherited profiler profiles the removed local transitions, + (0 → first) or (last → I_h). The composer subtracts them from PR79's local + blocks and asserts the result is nonnegative. +- The role's exterior is removed from the bank N/v_h · R. +- Its merged edge contributes its certified runs, multiplied by N/v_h. + +The composer asserts: + +- merged rank mass = removed rank mass + (m−h) × number of merged roles; +- total rank = mW − N + L = 77,120,639,900. + +Roles, W and the deficit are unchanged. + +## 7. Finite bridge + +The largest bit child becomes 552 (it was 529). The least D with +575^D > 2·552^D is 17, so: + +- the bit halving degree becomes 17 and the product-row coefficient + 17·27 + 20·30 = 1059; +- the row stock p^2000 is replaced by p^2200, with gap + 2200 − (51/25)·1059 = 991/25 > 0; +- the suffix condition becomes b_in^{1−ε} > 8800(log_2 b_in + 8), which still + holds eventually. + +The row degree is a free stock parameter: PR29 used p^47000 and the +structured-bulk assembly p^108000. It enters only the row-product slack and +the eventual cutoffs, not κ. The inherited `validate_bridge` recomputes these +fields from maxchild and W and rejects stale values. + +## 8. Scope + +The per-role choice uses first-order profile cost and is a discovery +heuristic; only the composed exact profile is claimed. Every other +assumption is inherited unchanged, including: + +- the ordered affine residual compiler and all-size recursion; +- routing, prime selection and exact recovery; +- the fixed-tape and analytic transfer; +- the complex layer. + +There is no claim of global optimality, a full formalization or a practical +speedup. diff --git a/research/merged-exterior/README.md b/research/merged-exterior/README.md new file mode 100644 index 0000000000..5000b6cc59 --- /dev/null +++ b/research/merged-exterior/README.md @@ -0,0 +1,84 @@ +# Merged auxiliary exteriors + +This finite conditional witness gives +**κ = 55354656014473/10^18 = 5.5354656014473×10^-5**, with bit saving +**27678860161103/(5·10^17)**. It is **6.9746%** above PR79's witness, which +is its base. + +**Idea.** In the inherited accounting every auxiliary role pays a separate +exterior edge I − I_h⊗B with profile [h, m−2h]. Auxiliary source frames are +free, so this residual can be merged into the role's creation edge +I − (I_h − A_first)⊗B. For a role that is not an output, it can instead be +merged into its retirement edge I − A_last⊗B. Each role takes whichever of +the three options has the lowest profile cost. Words, gates, XORs, W and the +deficit are unchanged. + +| Quantity | h23 | h25 | +|---|---:|---:| +| Auxiliary roles R | 27,297 | 35,684 | +| Merged at creation | 15,410 | 20,111 | +| Merged at retirement | 4,216 | 5,149 | +| Unchanged | 7,671 | 10,424 | +| Distinct merged edges certified | 8,537 | 10,601 | + +The first-order profile cost Σ t·n_t·ln(m/t) drops from 3.5686×10^10 to +3.3359×10^10. + +**Corner-rank lemma** ([PROOF.md](PROOF.md) §3–5). Let M = I − Y with +Y = UW^T and W^T U = I. Then the NE corner rank of M is + +- (i−j+1) − r + rank U_{i} for j ≤ i+1; +- rank U_{≤i}W_{≥j}^T for j ≥ i+1. + +In the PR34 fixed basis these reduce to ranks of local submatrices X[S,T], so +the profile is the same for every other-axis line. Each X[S,T] is a 0/1 +diagonal plus a rank ≤2 correction. Its rank is computed exactly over Q from +2×2 integer determinants, with no modular step. + +**Bridge change.** Merged edges create bit children up to **552**, above the +inherited 529. As a result: + +- the bit halving degree becomes **17** (it was 9); +- the row coefficient becomes 1059; +- the product row stock is raised from p^2000 to **p^2200**, with gap 991/25. + +This affects only the row-product slack and the eventual cutoffs, not κ +(§7). + +```sh +make merged-exterior-verify +make verify +``` + +The focused target does the following: + +1. Checks the controlled permutations against the pinned PR34 module. +2. Recomputes every candidate edge profile exactly and replays the per-role + selection. There are 24,586 candidate edges for h23 and 31,717 for h25. +3. Profiles the removed transitions with the unchanged inherited profiler. +4. Rebuilds the complete child list on top of PR79's verified profile. +5. Checks the exact and independent moment enclosures, and that the next grid + point is rejected. +6. Verifies the 47 assembly constraints and the seven margins with the + recomputed bridge. + +It takes about 4 minutes on 4 cores. + +As an additional discovery-time check, all 19,138 selected edges were compared +with direct NE elimination of the full 575×575 physical matrix for one line +modulo 2^31−1, with no mismatch. Unit tests check Lemma 1 against exact +elimination on random layouts. + +Builds on @chafreaky [#79](https://github.com/CrocSwap/integer-mult-bounds/pull/79) +and the work it composes: + +- @eumemic [#57](https://github.com/CrocSwap/integer-mult-bounds/pull/57), [#69](https://github.com/CrocSwap/integer-mult-bounds/pull/69) +- @rohangar1 [#59](https://github.com/CrocSwap/integer-mult-bounds/pull/59) +- @ikeboy [#62](https://github.com/CrocSwap/integer-mult-bounds/pull/62) +- @DominikScholz [#63](https://github.com/CrocSwap/integer-mult-bounds/pull/63), [#68](https://github.com/CrocSwap/integer-mult-bounds/pull/68) +- @rohanarun [#65](https://github.com/CrocSwap/integer-mult-bounds/pull/65), [#67](https://github.com/CrocSwap/integer-mult-bounds/pull/67) +- @alejandrozu [#70](https://github.com/CrocSwap/integer-mult-bounds/pull/70) +- @chafreaky [#60](https://github.com/CrocSwap/integer-mult-bounds/pull/60), [#71](https://github.com/CrocSwap/integer-mult-bounds/pull/71) + +It also uses the PR34 fixed basis (jamesyc) and the PR29 two-stage endpoint +note. The merged exteriors are by eumemic with Anthropic Claude assistance. diff --git a/research/split-pair/PROOF.md b/research/split-pair/PROOF.md new file mode 100644 index 0000000000..7c61cff2ac --- /dev/null +++ b/research/split-pair/PROOF.md @@ -0,0 +1,200 @@ +# Finite certificate and inherited scope + +## 1. Exact change and provenance + +The scalar provider starts with the preserved PR62 interval-strip/core-aware +pair graph as carried by PR65 at +`49e84f939d15b618b50714eb039cabf97c74256a`. It changes only the group partition +and point permutation. The compiled region orders are PR65's `cover-core` +for h=23 and `reverse-node` for h=25. The reclamation engine composes PR67's +all-rank profile-cost selection with PR68's pending live-carrier lifecycle and +both frame-containment tests, then scores pending controls against their +known next-use frame. Its exact diff from the original PR67 engine is +preserved in `engine-changes.patch`. The inherited PR60 engine, independent +word/profile tools and refined arithmetic remain byte-identical archived +dependencies. The configuration, compiler records, literal words, transition +records and profiles belong to this package's separate `split-pair` namespace. + +PR59's split operation, PR62/63's pair graph, PR65's scheduling and arithmetic, +PR67's cost selection, PR68's pending controls, PR60's ranked reclamation and +PR57's reversible compiler have different +authors. The source archive and NOTICE retain that provenance. No optimality +assertion in an inherited discovery discussion is used in this certificate. + +## 2. Ordered partition, contraction, and weighted scalar identities + +At recursive level d, begin with the ordinary ordered groups of size one or +two. The vector `[1,1,2]` requests the first group for d=0,1 and the middle +group for d=2. A selected two-point group is replaced by its two singleton +groups, and no point is lost, repeated, or reordered. A singleton is left +alone. At later levels no split is requested. Splitting is permitted only +when the number n of points is greater than three. + +For n≥4, the resulting number of groups is at most ceil(n/2)+1≤n−1. For n=3 +the unchanged grouping has two groups. Blocks of size at most two use the +inherited direct base case. Thus every recursive call has fewer points and +the recursion terminates. This is a general contraction argument, not an +inference from the two finite compilation runs. + +The recursion accepts disjoint weighted vertices and edges. Between two +coarse groups, its coarse edge is the sum of all original edges between them. +A coarse vertex weight contains every old vertex weight in its group and +every internal edge of that group. These terms partition the original +weighted total. By induction, recursive totals and all single/pair exclusions +therefore have exactly the intended supports. + +When both groups contain two points, the preserved four-output assembly +combines their common distant total, the appropriate two strips, and the +remaining cross edge. Each sum uses disjoint supports. With a singleton +group, the inherited generic decomposition supplies the corresponding sum. +The specialized four-output identity is never called on an invalid group +shape. Interval strips provide the sum omitting each designated strip value; +their supports follow from the cyclic-interval recurrence. The provider's +scalar verification checks all final exclusions, disjoint additions, and the +common-point condition. The focused tests additionally check the weighted +identity at every recursive block and verify strict partition contraction. + +## 3. Aligned common-point permutations + +For common point c, take the inherited alternating permutation of all points +other than c. Among fixed global pairs (0,1), (2,3), … disjoint from c, choose +the lexicographically first pair. Move those two points to the front, in their +pair order, leaving the other points in their previous relative order. There +is always an intact pair for h=23,25. The resulting list is a permutation of +exactly the points other than c. + +Relabeling a scalar exclusion circuit by a permutation preserves its total +and exclusion identities. Applying that relabeling separately at each common +point preserves the intended full triple-input map. The first split pair is +now aligned across copies whenever the selected intact pair agrees. This can +change the shared addition DAG and physical cost without changing the linear +map. Dense scalar outputs and exact supports are checked in both dimensions. + +## 4. Actual schedules and physical reversibility + +The PR65 wrapper sorts regions by `(rank, cover, core)` for h=23 and +`(rank, -minimum_node)` for h=25. It changes only their execution order. +Before compilation, every incoming dependency is required to precede its +consumer and every carrier candidate is required to go to a later region. +No backward candidate or dependency is admitted. + +Within each region, the inherited reversible synthesis completes the desired outputs +and retained carriers to a full independent physical basis, synthesizes an +invertible XOR transformation, and reclaims retired roles only when frame +containment and signal-span checks permit it. All clearing XORs are literal +operations in the word. + +The pending map records the already assigned next-use region of each live +physical role. Incoming roles are removed from this map on entering their +assigned region. A retained carrier or outgoing copy receives its next-use +entry when assigned. A live role in frame F with next-use frame G is eligible +as a clearing control in frame E only when F⊆E⊆G. Its inclusion in a +compile-time elimination basis does not itself perform an operation. If a +selected literal clearing expression uses it, the role is an XOR control, +so its value is unchanged. Its charged frame raise F→E remains compatible +with its later raise E→G. Repeated uses recheck the then-current frames. + +PR67 enumerates eligible dependent retired roles and records their literal +clearing expressions without mutating any physical role while comparing +candidates. A stored expression therefore remains valid. Its integer score +uses the fixed-basis transition profile with weights +floor(t·midpoint(log(t))·10^30), with exact rational log enclosures. For a role +currently in frame F, promoted to E, and cleaned up at G, the score is + + H(F→G) − H(F→E) − H(E→G). + +The new rule uses a pending role's already known next-use frame as G; for +other roles G remains the full-space cleanup endpoint. This changes only the +heuristic ordering of valid expressions. Eligibility, the full invertible +basis construction, containment checks and literal charging remain required. +There is no use of runtime data to choose a word and no claim that the score +optimizes the final moment. + +Full-basis replay checks both orientations on every +ordinary input and every dirty scratch basis column; scratch is arbitrary, +not an uncharged supply of zeros. Final outputs, copied centers and distinct +terminal roles are checked. The frame checker reconstructs every raise from +the literal word and requires equality to the recorded transitions. + +The fixed-I+J profiler consumes those actual transitions. It uses the pinned +bounded-minor bound and CRT moduli, checks their sufficient product, and +requires agreement. Every resulting profile is recomputed and compared. +Mutation tests reject missing operations, invalid frames, aliased terminals, +missing centers, missing transitions and understated physical width. + +## 5. Complete paid recursive profile + +Put a=23, b=25, m=ab=575, and +N=binom(23,3)binom(25,3)=4,073,300. The verified auxiliary role counts are +R23=27,455 and R25=36,015. With vh=binom(h,3), + + W = 2N + (N/v23) R23 + (N/v25) R25 = 135,075,665. + +Every part of the recursive child multiset is included: + +| Source | Multiplicities | +|---|---| +| Two data orientations | 18N children of rank 1; 2N each of ranks 21,17,481 | +| Endpoint copy | N children of rank 1 | +| Axis h internal profiles | (N/vh) times every nonzero entry of its actual profile | +| Axis h exterior | (N/vh)Rh children at each rank h and m−2h | +| Axis h data growth | 2N children at each rank 1 and h−2 | + +Each axis profile satisfies sum(t·blocks[t])=hRh+h(h−1), has no omitted +positive multiplicity, and contains no rank-zero child. Consequently + + L = Σh (N/vh) h(h−1) = 2,226,400, + Σt t nt = mW − N + L = 77,666,660,475, + mW − Σt t nt = 1,846,900. + +Every child has 01 for b in blocks) ++ slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();pending={};stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): +@@ -149,7 +151,8 @@ + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 +- return profile_entropy(old,1)-profile_entropy(old,target)-profile_entropy(target,1) ++ endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 ++ return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} +@@ -161,6 +164,9 @@ + old,e=bb[p];row^=old;expr^=e + return expr + for s in anchors:ins(s) ++ for s,target in pending.items(): ++ if contains(blocks[frames[s]]['frame'],blocks[g]['frame']) and contains(blocks[g]['frame'],blocks[target]['frame']): ++ ins(s);stats['live_anchor_candidates']+=1 + best=None + # Inspect every eligible dependent candidate across all retired ranks. + # Rank the actual fixed-basis growth/cleanup profiles by an integer entropy score. +@@ -176,7 +182,9 @@ + if best is None or keystep and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority):''' +check(s.count(completion)==1 and s.count(changed_start)==1,'Changed source not uniquely recognized') +check(s.replace(changed_start,old_start).replace(completion,' for i in range(len(ins)):')==old,'Compiler changed beyond the claimed unit-completion priority') +tree=ast.parse(s) +helpers=[n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name in ('basis','independent')] +namespace={};exec(compile(ast.Module(body=helpers,type_ignores=[]),str(SOURCE),'exec'),namespace) +basis=namespace['basis'];independent=namespace['independent'] +future=next(n for n in ast.walk(tree) if isinstance(n,ast.FunctionDef) and n.name=='future_priority') +contains=lambda a,b:not(b[0]&~a[0]) and not(a[1]&~b[1]) +# Actual-use fixtures distinguish future compatible uses from backward or nonnested uses. +ns=dict(position={0:0,1:1,2:2,3:3},step=1,b={'frame':(1,3),'inputs':[10,11,12,13]},blocks=[{'frame':(1,3)},{'frame':(1,3)},{'frame':(1,7)},{'frame':(1,5)}],uses=[(10,2,None),(10,2,('terminal',)),(11,2,None),(11,0,None),(12,3,None),(13,3,None)],value_uses={10:[0,1],11:[2,3],12:[4],13:[5]},contains=contains,slots=[7,1,3,3],ins=[0,1,2,3]) +exec(compile(ast.Module(body=[future],type_ignores=[]),str(SOURCE),'exec'),ns) +check([ns['future_priority'](i) for i in range(4)]==[(-2,3,0),(-1,1,1),(0,2,2),(0,2,3)],'Priority does not use compatible actual future uses, symbolic support, index') +check(sorted(range(4),key=ns['future_priority'])==[0,1,2,3],'Priority is not deterministic') +# General span argument is below; these adversarial numerical fixtures check the actual helpers and literal synthesis. +rng=Random(20261008);cases=0;operations=0 +for n in range(1,10): + for trial in range(250): + rows=[] + for _ in range(rng.randrange(n+1)*3): + candidate=rng.randrange(1,1<>i&1) + if j!=i: + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];ops.append((a,z)) + for j in range(n): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];ops.append((j,i)) + check(rr==[1< 1 and kappa > previous_kappa + bridge = finite_bridge(p['W']) + validate_bridge(bridge, p['W']) + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/balanced-split/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113', + pr71_kappa=previous_kappa, ratio_pr71=kappa/previous_kappa, + absolute_gain_pr71=kappa-previous_kappa, + pr71_complete_profile_exclusion_lower=prior71_lower, + full_pr71_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected balanced-split partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring, PR69 balanced coarse sums, future unit completion and bounded PR70 carry exchanges; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'balanced-split-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/scripts/experiments/balanced_split_engine.py b/scripts/experiments/balanced_split_engine.py new file mode 100644 index 0000000000..e1a9883726 --- /dev/null +++ b/scripts/experiments/balanced_split_engine.py @@ -0,0 +1,278 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + # Three deterministic improving exchanges, preserving both matroid constraints. + def carry_price(edge): + g,u,i=edge;producer=owner[blocks[g]['inputs'][i]];target=uses[u][1] + return (-profile_entropy(g+2,target+2)+profile_entropy(g+2,1) + +profile_entropy(0,producer+2)+profile_entropy(producer+2,target+2)) + prices=[carry_price(edge) for edge in edges] + priority=sorted(range(len(edges)),key=lambda e:(prices[e],edges[e])) + initial_count=len(chosen);initial_price=sum(prices[e] for e in chosen) + def carry_can(e,drop=None): + g,u,i=edges[e] + rows=blocks[g]['outbasis']+[1<=prices[f]:continue + if not carry_can(e,f if edges[f][0]==g else None):continue + else: + f=next((z for z in sorted(blocks[g]['selected'],key=lambda z:(-prices[z],z)) if prices[e]>s&1;e^=1<step and contains(b['frame'],blocks[uses[u][1]]['frame']) for u in value_uses[b['inputs'][i]]) + return (-compatible,slots[ins[i]].bit_count(),i) + for i in sorted(range(len(ins)),key=future_priority): + if independent(echelon,1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + _graph = _graphs[h] + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/scripts/experiments/merged_exterior.py b/scripts/experiments/merged_exterior.py new file mode 100644 index 0000000000..f168f6f705 --- /dev/null +++ b/scripts/experiments/merged_exterior.py @@ -0,0 +1,284 @@ +#!/usr/bin/env python3 +"""Merged auxiliary exteriors: exact physical profiles and per-role selection. + +Each auxiliary role pays one exterior residual E = I - I_h (x) B (profile +[h, m-2h]). Because auxiliary source frames are free, E may instead be added +to the role's first residual (entrance edge I - (I_h - A_first) (x) B) or, for +a role that is not an output, to its final cleanup (exit edge I - A_last (x) B). +research/merged-exterior/PROOF.md proves that the fixed-basis profile of such +an edge depends only on ranks of local submatrices X[S, T] (Lemma 1). Every +rank here is computed exactly over Q in integer arithmetic (Lemma 2). + +Usage: merged_exterior.py OUTDIR [WORKERS] (writes merged-exterior-selection.json) +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode = True + +from collections import Counter +from hashlib import sha256 +from math import log +from multiprocessing import Pool +from pathlib import Path +import gzip, json, os + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +OUT = ROOT / 'certificates' +BASE = 'balanced-split' +A_, B_ = 23, 25 +M_ = A_ * B_ + + +def corner_labels(h): + """PR34 reversed (23,25) corner labels (research/copied-fixed/reversed/pr34/independent_controls.py).""" + d = 2 * h + 1; b = h + 2 + r = list(range(h)) + [h - 1] + list(range(h)) + c = list(range(h)) + [0] + list(range(h)) + return [(r[i], i % b) for i in range(d)], [(c[j], (h * b - d + j) % b) for j in range(d)] + + +def completion(h, rows, cols): + """PR34 controlled permutations M_beta: prescribed corner labels, then increasing completion.""" + b = h + 2; m = h * b; d = len(rows) + partial = [{} for _ in range(b)] + for seq, offset in [(rows, 0), (cols, m - d)]: + for k, (label, residue) in enumerate(seq): + alpha, physical = divmod(offset + k, b) + assert residue == physical + partial[residue][alpha] = label + result = [] + for prescribed in partial: + remaining = iter(sorted(set(range(h)) - set(prescribed.values()))) + result.append([prescribed[i] if i in prescribed else next(remaining) for i in range(h)]) + return result + + +PERMS = completion(A_, *corner_labels(A_)) + + +def local_index(h): + """Local coordinate of physical index i = 25*alpha + beta for the axis of dimension h.""" + if h == A_: + return [PERMS[i % B_][i // B_] for i in range(M_)] + assert h == B_ + return [i % B_ for i in range(M_)] + + +def flags(lam): + """prefix[i] = local coordinates of physical rows < i; suffix[j] = of physical columns >= j.""" + prefix = [0] + for x in lam: + prefix.append(prefix[-1] | 1 << x) + suffix = [0] * (len(lam) + 1) + for j in range(len(lam) - 1, -1, -1): + suffix[j] = suffix[j + 1] | 1 << lam[j] + return prefix, suffix + + +def projector(core, cover, h): + """Fixed-I+J envelope projector A = diag(o) + U V^T / d in exact integers. + + Same entries as binary_frame_profiles.cpp. Coordinates fall in three classes + (core, cover minus core, outside cover); U and V rows depend only on the class. + """ + full = (1 << h) - 1 + c = core.bit_count(); out = cover & ~core; nn = out.bit_count() + classes = (core, out, full & ~cover) + w = (4, 3, 3); z = (3 * (h + 1) - 10, -10, -10); o = (0, 1, 0) + if c == 3: + assert core == cover, 'three-point cores are source lines' + return classes, [(w[k],) for k in range(3)], [(z[k],) for k in range(3)], 6 * (h + 1), out + assert c in (1, 2) and core & ~cover == 0 + s = 3 - c + d = 3 * (h + 1) * (s * s + (c - 1) * nn) + U = [(o[k], w[k]) for k in range(3)] + V = [(s * z[k] - 3 * (h + 1) * (c - 1) * o[k], 3 * (h + 1) * s * o[k] + nn * z[k]) for k in range(3)] + return classes, U, V, d, out + + +def operator(core, cover, h, complement): + """X = A (mask o, +UV^T/d) or X = I - A (mask 1-o, -UV^T/d).""" + classes, U, V, d, out = projector(core, cover, h) + full = (1 << h) - 1 + return (classes, U, V, d, full & ~out, -1) if complement else (classes, U, V, d, out, 1) + + +def kernel(rows, k): + """Integer basis of {x in Q^k : r.x = 0 for every row r}, k <= 2.""" + rows = [r for r in rows if any(r)] + if not rows: + return [(1,)] if k == 1 else [(1, 0), (0, 1)] + if k == 1: + return [] + a, b = rows[0] + if any(a * y - b * x for x, y in rows[1:]): + return [] + return [(-b, a)] + + +def small_rank(M): + """Rank of an at most 2x2 integer matrix.""" + if not M or not M[0] or not any(any(r) for r in M): + return 0 + if len(M) == 2 and len(M[0]) == 2 and M[0][0] * M[1][1] - M[0][1] * M[1][0]: + return 2 + return 1 + + +def rank(X, S, T): + """Exact rank over Q of X[S, T] for X = diag(mask) + sigma U V^T / d (PROOF.md, Lemma 2).""" + classes, U, V, d, mask, sigma = X + if not S or not T: + return 0 + P = S & T & mask + S0, T0 = S & ~P, T & ~P + k = len(U[0]) + counts = [(P & cls).bit_count() for cls in classes] + C = [[d * (a == b) + sigma * sum(n * V[c][a] * U[c][b] for c, n in enumerate(counts)) + for b in range(k)] for a in range(k)] + Z = kernel([U[c] for c, cls in enumerate(classes) if S0 & cls], k) + Y = kernel([V[c] for c, cls in enumerate(classes) if T0 & cls], k) + C22 = [[sum(y[a] * C[a][b] * z[b] for a in range(k) for b in range(k)) for z in Z] for y in Y] + return P.bit_count() + (k - len(Z)) + (k - len(Y)) + small_rank(C22) - k + + +def runs(pivots): + """Maximal runs of consecutive pivots (i,j),(i+1,j+1) in row order.""" + out, run = [], 0 + for k, (i, j) in enumerate(pivots): + if k and i == pivots[k - 1][0] + 1 and j == pivots[k - 1][1] + 1: + run += 1 + else: + if run: + out.append(run) + run = 1 + if run: + out.append(run) + return sorted(out, reverse=True) + + +def merged_profile(X, h, fl): + """NE profile of I - Y, Y the physical image of the local idempotent X (x) any line (Lemma 1).""" + prefix, suffix = fl + m = len(prefix) - 1 + full = (1 << h) - 1 + cache = {} + + def R(S, T): + key = (S, T) + if key not in cache: + cache[key] = rank(X, S, T) + return cache[key] + + r = R(full, full) + + def rho(i, j): + if i < 0 or j >= m: + return 0 + if j <= i + 1: + return (i - j + 1) - r + R(prefix[j], full) + R(full, suffix[i + 1]) + return R(prefix[i + 1], suffix[j]) + + def piv(i, j): + z = rho(i, j) - rho(i - 1, j) - rho(i, j + 1) + rho(i - 1, j + 1) + assert z in (0, 1) + return z + + # Second differences vanish below the band j in {i, i+1}; above it they are + # nonzero only where a new local row and a new local column first appear. + pivots = {(i, j) for i in range(m) for j in (i, i + 1) if j < m and piv(i, j)} + rows = [i for i in range(m) if prefix[i + 1] != prefix[i]] + cols = [j for j in range(m) if suffix[j] != suffix[j + 1]] + pivots |= {(i, j) for i in rows for j in cols if j >= i + 2 and piv(i, j)} + assert len(pivots) == m - r, (len(pivots), m, r) + return m - r, runs(sorted(pivots)) + + +def local_profile(X, h): + """Inherited local NE profile of an h x h residual, with rank <= 2 charged as singletons.""" + rows = [(1 << (i + 1)) - 1 for i in range(h)] + cols = [((1 << h) - 1) & ~((1 << j) - 1) for j in range(h)] + [0] + rho = [[rank(X, rows[i], cols[j]) for j in range(h + 1)] for i in range(h)] + pivots = [(i, j) for i in range(h) for j in range(h) + if rho[i][j] - (rho[i - 1][j] if i else 0) - rho[i][j + 1] + (rho[i - 1][j + 1] if i else 0)] + rr = rank(X, (1 << h) - 1, (1 << h) - 1) + assert len(pivots) == rr + return rr, ([1] * rr if rr <= 2 else runs(pivots)) + + +def cost(blocks): + return sum(t * log(M_ / t) for t in blocks) + + +def load_word(h): + path = OUT / f'{BASE}-word-{h}.json.gz' + raw = path.read_bytes() + d = json.loads(gzip.decompress(raw)) + assert d['h'] == h + first, last = {}, {} + for s, a, b in d['events']: + first.setdefault(s, b) + last[s] = b + outputs = {s for s, g, c, t in d['outputs']} + assert sorted(first) == list(range(d['R'])) + return d, first, last, outputs, sha256(raw).hexdigest() + + +def evaluate(job): + """Exact costs for one (kind, frame) key: removed local edge, merged edge.""" + h, kind, frame, core, cover = job + if kind == 'entrance': + removed = local_profile(operator(core, cover, h, False), h) # 0 -> A_first + merged = merged_profile(operator(core, cover, h, True), h, FLAGS[h]) # I - (I - A_first) (x) B + else: + removed = local_profile(operator(core, cover, h, True), h) # A_last -> I_h + merged = merged_profile(operator(core, cover, h, False), h, FLAGS[h]) # I - A_last (x) B + return (kind, frame), removed, merged + + +FLAGS = {h: flags(local_index(h)) for h in (A_, B_)} + + +def select(h, workers): + d, first, last, outputs, digest = load_word(h) + F, R = d['frames'], d['R'] + keys = {('entrance', first[s]) for s in range(R)} | {('exit', last[s]) for s in range(R) if s not in outputs} + jobs = [(h, k, g, *F[g]) for k, g in sorted(keys)] + with Pool(workers) as pool: + result = {key: (removed, merged) for key, removed, merged in pool.map(evaluate, jobs, chunksize=8)} + exterior = cost([h, M_ - 2 * h]) + choice = {} + for s in range(R): + options = [(0.0, 'standard')] + for kind, g in (('entrance', first[s]), ('exit', last[s])): + if kind == 'exit' and s in outputs: + continue + (rr, removed), (mr, merged) = result[kind, g] + assert mr == rr + M_ - h + options.append((cost(removed) + exterior - cost(merged), kind)) + gain, kind = max(options) + if kind != 'standard' and gain > 1e-9: + choice[s] = kind + used = sorted({(choice[s], first[s] if choice[s] == 'entrance' else last[s]) for s in choice}) + return dict(h=h, R=R, word_sha256=digest, + entrance=sorted(s for s in choice if choice[s] == 'entrance'), + exit=sorted(s for s in choice if choice[s] == 'exit'), + merged_edges={f'{k}:{g}': dict(rank=result[k, g][1][0], runs=result[k, g][1][1]) for k, g in used}, + candidate_edges=len(keys)) + + +def selection(workers=None): + workers = workers or (len(os.sched_getaffinity(0)) if hasattr(os, 'sched_getaffinity') else os.cpu_count()) + return {str(h): select(h, workers) for h in (A_, B_)} + + +if __name__ == '__main__': + outdir = Path(sys.argv[1]) + record = selection(int(sys.argv[2]) if len(sys.argv) > 2 else None) + outdir.mkdir(parents=True, exist_ok=True) + (outdir / 'merged-exterior-selection.json').write_text(json.dumps(record, sort_keys=True, separators=(',', ':')) + '\n') + for h, r in record.items(): + print(f'h={h}: roles {r["R"]}, entrance {len(r["entrance"])}, exit {len(r["exit"])}, ' + f'merged edges {len(r["merged_edges"])} of {r["candidate_edges"]} candidates', flush=True) diff --git a/scripts/experiments/merged_exterior_compose.py b/scripts/experiments/merged_exterior_compose.py new file mode 100644 index 0000000000..b309f3006d --- /dev/null +++ b/scripts/experiments/merged_exterior_compose.py @@ -0,0 +1,170 @@ +#!/usr/bin/env python3 +"""Compose the PR79 balanced-split witness with merged auxiliary exteriors. + +Each selected role loses its entrance (0 -> first frame) or final cleanup +(last frame -> I_h) local transition and its exterior [h, m-2h], and gains one +exactly profiled merged edge. The removed transitions are profiled by the +unchanged inherited profiler. Words, data, endpoint copies and the complex +layer are PR79's. The finite bridge is recomputed for the new largest child. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode = True + +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import json, struct, subprocess, tempfile + +import binary_frame_math as arithmetic +import balanced_split_compose as base +from split_pair_arithmetic import refine, audit +from merged_exterior import A_, B_, M_, OUT, ROOT, HERE, load_word + +ROW_DEGREE = 2200 # product row stock p^2200 (PROOF.md, section 4) + + +def removed_transitions(h, chosen): + d, first, last, outputs, digest = load_word(h) + assert digest == chosen['word_sha256'] and d['R'] == chosen['R'] + assert not set(chosen['entrance']) & set(chosen['exit']) and not set(chosen['exit']) & outputs + frames = [(0, 0, 0), (0, 0, h)] + [(c, u, 1 if c == u else u.bit_count() - c.bit_count()) for c, u in d['frames']] + removed = Counter() + for s in chosen['entrance']: + removed[0, first[s] + 2] += 1 + for s in chosen['exit']: + removed[last[s] + 2, 1] += 1 + mass = sum((frames[b][2] - frames[a][2]) * n for (a, b), n in removed.items()) + edges = Counter([f'entrance:{first[s]}' for s in chosen['entrance']] + [f'exit:{last[s]}' for s in chosen['exit']]) + return frames, removed, mass, d['v'], edges + + +def profile_removed(h, frames, removed, mass, v): + """Unchanged inherited profiler on the removed transitions only.""" + with tempfile.TemporaryDirectory(prefix='merged-exterior-') as tmp: + tmp = Path(tmp) + binary = tmp / 'profiles' + subprocess.run(['c++', '-O2', '-std=c++17', '-I', str(ROOT / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(HERE / 'binary_frame_profiles.cpp'), '-o', str(binary)], check=True) + path = tmp / f'removed{h}.bin' + with path.open('wb') as f: + # R=0 and loss=mass satisfy the inherited header check sum == h*R + loss. + f.write(struct.pack('<6I2Q', h, v, 0, len(frames), len(removed), 0, mass, mass)) + for c, u, r in frames: + f.write(struct.pack('<2QI', c, u, r)) + for (a, b), n in sorted(removed.items()): + f.write(struct.pack('<2Iq', a, b, n)) + subprocess.run([str(binary), str(path)], check=True, capture_output=True, text=True) + prof = json.loads(Path(str(path) + '.profiles.json').read_text()) + assert prof['crt_disagreements'] == 0 and prof['rank_sum'] == mass + return prof['blocks'] + + +def profile(selection): + p = base.profile() # PR79 complete profile and all of its checks + m, N, W, L = p['m'], p['N'], p['W'], p['L'] + parts = {name: Counter(rows) for name, rows in p['parts'].items()} + axes = {} + for f in p['axes']: + h = f['h'] + chosen = selection[str(h)] + frames, removed, mass, v, edges = removed_transitions(h, chosen) + assert v == f['v'] + blocks = profile_removed(h, frames, removed, mass, v) + rep = N // v + internal = Counter({t: n for t, n in enumerate(f['blocks']) if n}) + internal.subtract(Counter({t: n for t, n in enumerate(blocks) if n})) + assert min(internal.values()) >= 0, 'removed more than present' + merged = Counter() + for key, count in edges.items(): + e = chosen['merged_edges'][key] + assert sum(e['runs']) == e['rank'] and len(e['runs']) and max(e['runs']) < m + for t in e['runs']: + merged[t] += count + assert set(chosen['merged_edges']) == set(edges) + roles = len(chosen['entrance']) + len(chosen['exit']) + # Each merged role trades its removed local edge and one exterior (rank m-h) for one edge. + assert sum(t * n for t, n in merged.items()) == mass + roles * (m - h) + bank = rep * (f['R'] - roles) + parts[f'internal_{h}'] = Counter({t: n * rep for t, n in internal.items() if n}) + parts[f'merged_{h}'] = Counter({t: n * rep for t, n in merged.items()}) + parts[f'exterior_{h}'] = Counter({h: bank, m - 2 * h: bank}) + axes[str(h)] = dict(R=f['R'], entrance_roles=len(chosen['entrance']), exit_roles=len(chosen['exit']), + merged_edges=len(edges), removed_rank_mass=mass, removed_blocks=blocks, + word_sha256=chosen['word_sha256']) + rows = sum(parts.values(), Counter()) + total = sum(t * n for t, n in rows.items()) + assert total == m * W - N + L == p['total_rank'] and all(0 < t < m for t in rows) + return dict(m=m, N=N, W=W, L=L, total_rank=total, deficit=m * W - total, maxchild=max(rows), + child_multiplicities=dict(sorted(rows.items())), parts=parts, axes=axes) + + +def finite_bridge(width, maxchild): + """PR79 bridge with the bit layer's largest child, halving degree and row stock updated.""" + bridge = base.finite_bridge(width) + bridge['bit']['maxchild'] = maxchild + bridge['bit']['halving_degree'] = refine.balanced.halving_degree(bridge['bit']['m'], maxchild) + coefficient = sum(bridge[k]['halving_degree'] * bridge[k]['wire_bits'] for k in ('bit', 'complex')) + bridge['rows'].update(coefficient=coefficient, degree=ROW_DEGREE, + degree_gap=ROW_DEGREE - Q(51, 25) * coefficient, suffix_slope=4 * ROW_DEGREE) + refine.balanced.validate_bridge(bridge) + return bridge + + +def best_saving(p, denominator): + """Largest grid saving whose exact upper moment is below one.""" + lo, hi = 1, denominator // 10**4 + assert refine.exact_moment(p['m'], p['W'], p['child_multiplicities'], Q(hi, denominator))['lower'] > 1 + while hi - lo > 1: + mid = (lo + hi) // 2 + if refine.exact_moment(p['m'], p['W'], p['child_multiplicities'], Q(mid, denominator))['upper'] < 1: + lo = mid + else: + hi = mid + return Q(lo, denominator) + + +def compose(selection): + denominator = 10**18 + grid = Q(1, denominator) + p = profile(selection) + bit = best_saving(p, denominator) + exact = refine.exact_moment(p['m'], p['W'], p['child_multiplicities'], bit) + excluded = refine.exact_moment(p['m'], p['W'], p['child_multiplicities'], bit + grid) + assert exact['upper'] < 1 < excluded['lower'] + js = arithmetic.js(dict(p, parts={})) + independent = audit.independent_moment(js, bit, arithmetic.js(exact['terms'])) + rejected = audit.independent_moment(js, bit + grid, arithmetic.js(exact['terms'])) + assert independent[1] < 1 < rejected[0] + bridge = finite_bridge(p['W'], p['maxchild']) + assembled = refine.assemble(bridge, bit, Q(1, 10**12), denominator) + kappa = assembled['kappa'] + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + pr79 = json.loads((OUT / 'balanced-split-kappa.json').read_text()) + previous = Q(pr79['kappa']) + old = {int(t): n for t, n in pr79['bit']['child_multiplicities'].items()} + pr79_lower = refine.exact_moment(pr79['bit']['m'], pr79['bit']['W'], old, bit)['lower'] + assert pr79_lower > 1 and kappa > previous + return dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + kappa=kappa, bit_saving=bit, bit_saving_excluded_above=bit + grid, grid_denominator=denominator, + bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=rejected[0], rejected_upper=rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + comparison=dict(pr79_commit='9a58e62cf9e8954a4dde3c9b1372d733c276a6d1', pr79_kappa=previous, + ratio_pr79=kappa / previous, pr79_complete_profile_exclusion_lower=pr79_lower), + selection_sha256=sha256(json.dumps(selection, sort_keys=True, separators=(',', ':')).encode()).hexdigest()) + + +if __name__ == '__main__': + outdir = Path(sys.argv[1]) + selection = json.loads((outdir / 'merged-exterior-selection.json').read_text()) + result = compose(selection) + (outdir / 'merged-exterior-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=1, sort_keys=True) + '\n') + print(f'kappa {result["kappa"]} = {float(result["kappa"]):.12e}; bit saving {float(result["bit_saving"]):.12e}; ' + f'maxchild {result["bit"]["maxchild"]}; ratio to PR79 {float(result["comparison"]["ratio_pr79"]):.5f}', flush=True) diff --git a/scripts/experiments/pin_balanced_split_sources.py b/scripts/experiments/pin_balanced_split_sources.py new file mode 100644 index 0000000000..a4bc483ecc --- /dev/null +++ b/scripts/experiments/pin_balanced_split_sources.py @@ -0,0 +1,53 @@ +#!/usr/bin/env python3 +"""Explicit source and finite-input freeze for the selected split/pair witness.""" +from hashlib import sha256 +import json +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +NAMES = ('balanced_split_graph.py', 'balanced_split_compiler.py', 'split_pair_arithmetic.py', + 'balanced_split_engine.py', 'balanced_split_exchange_engine.py', + 'balanced_split_compose.py', 'audit_balanced_split_completion.py', 'audit_balanced_split_exchange.py', + 'split_pair_engine.py', 'verify_balanced_split.py', 'pin_balanced_split_sources.py', + 'joint_dual_reclaim_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp') + + +def required_paths(): + names = {'scripts/experiments/'+name for name in NAMES} + names.update(('.gitattributes', 'Makefile', 'README.md', 'NOTICE', '.github/workflows/verify.yml', 'research/balanced-split/README.md', + 'research/balanced-split/PROOF.md', 'research/balanced-split/parameters.json', + 'research/balanced-split/engine-provenance.json', 'research/balanced-split/engine-relocation-23.patch', + 'research/balanced-split/engine-relocation-25.patch', + 'tests/test_balanced_split.py', 'tests/test_balanced_split_pending.py', + 'certificates/balanced-split-compiler.json')) + for h in (23,25): + names.add(f'research/balanced-split/config-{h}.json') + names.update(f'certificates/balanced-split-{kind}-{h}.{extension}' + for kind,extension in (('word','json.gz'),('profiles','json'),('transitions','json'))) + for prior in ('48', '59-split-operation', '65', '67', '68', '69', '70', '71'): + relative = Path('references/frame-compiler/pr'+prior) + manifest = json.loads((ROOT/relative/'SOURCE.json').read_text()) + names.add(str(relative/'SOURCE.json')) + names.update(str(relative/name) for name in manifest['files']) + return names + + +def run(): + result = dict( + baseline_pr71_commit='1bef94fd40a746452548c84a4a8f8834670a3113', + coarse_pr69_commit='91aa1f17e6e3fc063241686a41a34ddd0dc24c50', + exchange_pr70_commit='98147912b80a2656da0416487be53f1f5e8dfdcc', + baseline_pr65_commit='49e84f939d15b618b50714eb039cabf97c74256a', + profile_cost_pr67_commit='b3745601e947a94316bf25c2c6263d93c06e3364', + pending_live_pr68_commit='734c58e225e9d2254570c3b50296ed96943f62ea', + split_operation_pr59_commit='641f22e52913db784f3b6ff1176b0c2945aae45b', + author='Chafik Boukhalfa with OpenAI Codex assistance', + scope='Explicit source and finite-input freeze. Credited contributor originals and complete published PR71 physical/arithmetic baseline are preserved. Exact composition and validation receipts are derived.', + files={name:sha256((ROOT/name).read_bytes()).hexdigest() for name in sorted(required_paths())}) + (ROOT/'research/balanced-split/SOURCE.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + return len(result['files']) + + +if __name__ == '__main__': + print('Pinned',run(),'sources and finite inputs') diff --git a/scripts/experiments/pin_split_pair_sources.py b/scripts/experiments/pin_split_pair_sources.py new file mode 100644 index 0000000000..879d6699dc --- /dev/null +++ b/scripts/experiments/pin_split_pair_sources.py @@ -0,0 +1,48 @@ +#!/usr/bin/env python3 +"""Explicit source and finite-input freeze for the selected split/pair witness.""" +from hashlib import sha256 +import json +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +NAMES = ('split_pair_graph.py', 'split_pair_compiler.py', 'split_pair_arithmetic.py', + 'split_pair_engine.py', + 'split_pair_compose.py', 'verify_split_pair.py', 'pin_split_pair_sources.py', + 'joint_dual_reclaim_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp') + + +def required_paths(): + names = {'scripts/experiments/'+name for name in NAMES} + names.update(('Makefile', 'README.md', 'NOTICE', 'research/split-pair/README.md', + 'research/split-pair/PROOF.md', 'research/split-pair/parameters.json', + 'research/split-pair/engine-provenance.json', 'research/split-pair/engine-changes.patch', + 'tests/test_split_pair.py', 'tests/test_split_pair_pending.py', + 'certificates/split-pair-compiler.json')) + for h in (23,25): + names.add(f'research/split-pair/config-{h}.json') + names.update(f'certificates/split-pair-{kind}-{h}.{extension}' + for kind,extension in (('word','json.gz'),('profiles','json'),('transitions','json'))) + for prior in ('48', '59-split-operation', '65', '67', '68'): + relative = Path('references/frame-compiler/pr'+prior) + manifest = json.loads((ROOT/relative/'SOURCE.json').read_text()) + names.add(str(relative/'SOURCE.json')) + names.update(str(relative/name) for name in manifest['files']) + return names + + +def run(): + result = dict( + baseline_pr65_commit='49e84f939d15b618b50714eb039cabf97c74256a', + profile_cost_pr67_commit='b3745601e947a94316bf25c2c6263d93c06e3364', + pending_live_pr68_commit='734c58e225e9d2254570c3b50296ed96943f62ea', + split_operation_pr59_commit='641f22e52913db784f3b6ff1176b0c2945aae45b', + author='Chafik Boukhalfa with OpenAI Codex assistance', + scope='Explicit source and finite-input freeze. Credited contributor originals and complete published PR65 physical/arithmetic baseline are preserved. Exact composition and validation receipts are derived.', + files={name:sha256((ROOT/name).read_bytes()).hexdigest() for name in sorted(required_paths())}) + (ROOT/'research/split-pair/SOURCE.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + return len(result['files']) + + +if __name__ == '__main__': + print('Pinned',run(),'sources and finite inputs') diff --git a/scripts/experiments/split_pair_arithmetic.py b/scripts/experiments/split_pair_arithmetic.py new file mode 100644 index 0000000000..a34aeb543b --- /dev/null +++ b/scripts/experiments/split_pair_arithmetic.py @@ -0,0 +1,39 @@ +"""Private adapters for the unchanged PR65 directed arithmetic and audit.""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode = True + +import importlib.util +from pathlib import Path + +BASELINE = Path(__file__).resolve().parents[2] / 'references/frame-compiler/pr65' + + +def _load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + module = importlib.util.module_from_spec(spec) + spec.loader.exec_module(module) + return module + + +def private_arithmetic(): + here = BASELINE / 'research/reordered-rank-pair/arithmetic' + previous_path = sys.path[:] + absent = object() + previous_refine = sys.modules.get('refine', absent) + try: + refine = _load('split_pair_private_refine', here / 'refine.py') + sys.modules['refine'] = refine + audit = _load('split_pair_private_arithmetic_audit', here / 'audit.py') + assert audit.refine is refine + return refine, audit + finally: + sys.path[:] = previous_path + if previous_refine is absent: + sys.modules.pop('refine', None) + else: + sys.modules['refine'] = previous_refine + + +refine, audit = private_arithmetic() diff --git a/scripts/experiments/split_pair_compiler.py b/scripts/experiments/split_pair_compiler.py new file mode 100644 index 0000000000..1ebfc5c752 --- /dev/null +++ b/scripts/experiments/split_pair_compiler.py @@ -0,0 +1,90 @@ +#!/usr/bin/env python3 +"""Compile aligned split frames with profile-cost pending live reclamation.""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode = True + +import argparse +import gzip +from hashlib import sha256 +import json +from pathlib import Path +import os +import shlex +import subprocess +import tempfile + +import split_pair_engine as compiler +import split_pair_graph as producer + +ROOT = Path(__file__).resolve().parents[2] + + +def source_record(): + return dict(pr65=producer.checked_manifest(producer.BASELINE), + pr67=producer.checked_manifest(ROOT / 'references/frame-compiler/pr67'), + pr68=producer.checked_manifest(ROOT / 'references/frame-compiler/pr68'), + inherited=producer.checked_manifest(ROOT / 'references/frame-compiler/pr48')) + + +def compile_axis(h): + config = producer.configuration(h) + provenance = json.loads((ROOT/'research/split-pair/engine-provenance.json').read_text()) + assert sha256(Path(compiler.__file__).read_bytes()).hexdigest() == provenance['portable_engine_sha256'], 'Selected engine changed' + previous_graph, previous_build = compiler.graph, compiler.build + absent = object() + runtime_names = ('oracles', 'ORACLE_EXE', 'ORACLE_INPUT', 'PENDING_COST') + previous_runtime = {name:getattr(compiler, name, absent) for name in runtime_names} + try: + compiler.graph = producer.graph + compiler.build = producer.ordered_build(previous_build, h) + compiler.PENDING_COST = True + with tempfile.TemporaryDirectory(prefix='split-pair-compile-') as directory: + work = Path(directory) + oracle = work/'profile-oracle' + subprocess.run([*shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'), + str(ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/profile_oracle.cpp'), + '-o', str(oracle)], check=True) + compiler.oracles = [] + compiler.ORACLE_EXE, compiler.ORACLE_INPUT = str(oracle), str(work/'oracle-input.bin') + try: + result, word = compiler.compile_(h, matching=True, reclaim=True, dirty=True) + finally: + for process in compiler.oracles: + process.stdin.close() + assert process.wait(timeout=10) == 0, 'Discovery profile oracle failed' + finally: + compiler.graph, compiler.build = previous_graph, previous_build + for name, value in previous_runtime.items(): + if value is absent: + if hasattr(compiler, name): + delattr(compiler, name) + else: + setattr(compiler, name, value) + result.pop('seconds', None) + result['scalar'] = producer.graph(h).verify() + result['graph_configuration'] = config + result['source_pr65_head'] = source_record()['pr65']['commit'] + result['baseline_pr65_roles'] = {23: 27918, 25: 36586}[h] + result['source_pr67_head'] = source_record()['pr67']['commit'] + result['source_pr68_head'] = source_record()['pr68']['commit'] + result['reclamation_order'] = 'all eligible retired ranks, exact integer profile cost, XOR count, slot ID' + result['pending_live_controls'] = True + result['pending_cost_uses_next_use_frame'] = True + result['paid_clones'] = 0 + return result, word + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--h', type=int, choices=(23, 25), required=True) + parser.add_argument('--output', type=Path, required=True) + parser.add_argument('--word', type=Path, required=True) + args = parser.parse_args() + result, word = compile_axis(args.h) + raw = (json.dumps(word, separators=(',', ':')) + '\n').encode() + args.word.write_bytes(gzip.compress(raw, mtime=0) if args.word.suffix == '.gz' else raw) + args.output.write_text(json.dumps(result, indent=2) + '\n') + print(json.dumps(result), flush=True) diff --git a/scripts/experiments/split_pair_compose.py b/scripts/experiments/split_pair_compose.py new file mode 100644 index 0000000000..e08ce74f33 --- /dev/null +++ b/scripts/experiments/split_pair_compose.py @@ -0,0 +1,161 @@ +"""Complete paid split/pair profile and PR65's exact refined balanced assembly. + +The unchanged full physical words determine every auxiliary multiplicity. +Only fixed-basis finite claims are certified; all-size transfer remains inherited. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode = True + +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import gzip +import json + +import binary_frame_math as arithmetic +from split_pair_arithmetic import refine, audit +from split_pair_graph import checked_manifest +from split_pair_compiler import source_record +from pin_split_pair_sources import required_paths + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +OUT = ROOT / 'certificates' +INHERITED = ROOT / 'references/frame-compiler/pr48' +OLD = INHERITED / 'research/copied-fixed' +BASELINE = ROOT / 'references/frame-compiler/pr65' +BASELINE_CASE = BASELINE / 'research/reordered-rank-pair' +PROFILE_BASELINE = ROOT / 'references/frame-compiler/pr67/research/slot-cost-rank-pair' + + +def check_sources(): + sources = source_record() + operation = ROOT / 'references/frame-compiler/pr59-split-operation' + checked_manifest(operation) + local = json.loads((ROOT/'research/split-pair/SOURCE.json').read_text()) + assert required_paths() <= set(local['files']), 'Incomplete source/finite-input closure' + for name, digest in local['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name + engine = ROOT / 'scripts/experiments/joint_dual_reclaim_compiler.py' + assert engine.read_bytes() == (BASELINE/'scripts/experiments/rank_pair_compiler.py').read_bytes() + provenance = json.loads((ROOT/'research/split-pair/engine-provenance.json').read_text()) + assert sha256((HERE/'split_pair_engine.py').read_bytes()).hexdigest() == provenance['portable_engine_sha256'] + for name in ('binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp'): + assert (HERE/name).read_bytes() == (BASELINE/'scripts/experiments'/name).read_bytes() + return dict(sources, split_operation=checked_manifest(operation)) + + +def profile(): + parameters = json.loads((ROOT/'research/split-pair/parameters.json').read_text()) + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + profiles = [json.loads((OUT / f'split-pair-profiles-{h}.json').read_text()) for h in (a, b)] + words = json.loads((OUT / 'split-pair-compiler.json').read_text()) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + receipts = [] + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + recorded = words['axes'][str(h)] + replay = recorded['replay'] + receipt = json.loads((OUT / f'split-pair-transitions-{h}.json').read_text()) + for key in ('h', 'v', 'R'): + assert f[key] == receipt[key] + assert f['R'] == replay['roles'] == recorded['compiled']['roles'] == parameters['roles'][str(h)] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == receipt['rank_mass'] == replay['rank_mass'] + assert f['blocks'][0] == 0 and f['blocks'][h] == 0 # Positive children; copied centers already included. + assert receipt['transition_events_equal_independent_xor_word_reconstruction'] + packed = (OUT / f'split-pair-word-{h}.json.gz').read_bytes() + assert sha256(packed).hexdigest() == recorded['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == recorded['word_sha256'] == receipt['word_sha256'] + histogram = {str(k): v for k, v in replay['histogram'].items() if int(k)} + side = replay['output_roles']-h + histogram['2'] -= side + histogram['1'] += 2*side + assert histogram == receipt['rank_histogram_with_side_growth_split_into_singletons'] + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + receipts.append(receipt) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (parameters['W'], parameters['total_rank'], 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, + maxchild=max(rows), child_multiplicities=dict(sorted(rows.items())), + parts=parts, axes=profiles, words=receipts) + + +def compose(): + sources = check_sources() + parameters = json.loads((ROOT/'research/split-pair/parameters.json').read_text()) + bit_saving, kappa = Q(parameters['bit_saving']), Q(parameters['kappa']) + denominator = parameters['grid_denominator'] + assert type(denominator) is int and denominator == 10**18 + grid = Q(1, denominator) + assert json.loads((OUT/'split-pair-compiler.json').read_text())['source'] == source_record() + p = profile() + exact = refine.exact_moment(p['m'], p['W'], p['child_multiplicities'], bit_saving) + excluded = refine.exact_moment(p['m'], p['W'], p['child_multiplicities'], bit_saving+grid) + assert exact['upper'] < 1 < excluded['lower'] + independent = audit.independent_moment(arithmetic.js(p), bit_saving, arithmetic.js(exact['terms'])) + independent_rejected = audit.independent_moment(arithmetic.js(p), bit_saving+grid, arithmetic.js(exact['terms'])) + assert independent[1] < 1 < independent_rejected[0] + prior65 = json.loads((PROFILE_BASELINE/'arithmetic/certificate.json').read_text()) + oldprofile = json.loads((PROFILE_BASELINE/'paired-candidate.json').read_text()) + oldbit = oldprofile['bit'] + previous_kappa = Q(prior65['preferred']['kappa']) + previous_rows = {int(t): n for t,n in oldbit['child_multiplicities'].items()} + prior65_lower = refine.exact_moment(oldbit['m'], oldbit['W'], previous_rows, bit_saving)['lower'] + assert prior65_lower > 1 and kappa > previous_kappa + bridge = json.loads((OLD/'certificate.json').read_text())['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = refine.assemble(bridge, bit_saving, Q(1, 10**12), denominator) + assert assembled['kappa'] == kappa + assert all(value > 0 for value in assembled['assembly']['constraints'].values()) + assert all(value > kappa for value in assembled['assembly']['margins'].values()) + coarse_denominator = 10**11 + coarse_bit = Q(refine.floor_scaled(bit_saving, coarse_denominator), coarse_denominator) + coarse = refine.assemble(bridge, coarse_bit, Q(1, 10**12), coarse_denominator) + assert arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], coarse_bit)['upper'] < 1 + result = dict( + status='Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed', + source_manifest_sha256=sha256((ROOT/'research/split-pair/SOURCE.json').read_bytes()).hexdigest(), + kappa=kappa, bit_saving=bit_saving, bit_saving_excluded_above=bit_saving+grid, + grid_denominator=denominator, bit=dict(p, moment=exact, excluded_moment=excluded), + independent_enclosures=dict(accepted_lower=independent[0], accepted_upper=independent[1], + rejected_lower=independent_rejected[0], rejected_upper=independent_rejected[1]), + assembly=assembled['assembly'], eventual_bounds=assembled['eventual_bounds'], finite_bridge=bridge, + next_kappa=assembled['next_kappa'], next_kappa_rejection=assembled['next_kappa_rejection'], + coarse_grid_control=dict(bit_saving=coarse_bit, **coarse), + comparison=dict(pr67_commit='b3745601e947a94316bf25c2c6263d93c06e3364', + pr67_kappa=previous_kappa, ratio_pr67=kappa/previous_kappa, + absolute_gain_pr67=kappa-previous_kappa, + pr67_complete_profile_exclusion_lower=prior65_lower, + full_pr67_child_list_excluded_at_new_bit_saving=True), + exactness=[arithmetic.exactness(h) for h in (23,25)], sources=sources, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR62/63 interval pair assembly, selected split-pair partition and point permutation, PR65 schedules, PR67 profile-cost reclamation, PR68 pending live controls and selected next-use scoring; complete literal words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, all-size recursion, finite scalar overhead, routing, prime selection, exact recovery and fixed-tape/analytic transfer remain inherited. Arithmetic cutoffs are not full operational thresholds.')) + (OUT/'split-pair-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS finite conditional kappa='+str(kappa)+'; bit saving='+str(bit_saving), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/scripts/experiments/split_pair_engine.py b/scripts/experiments/split_pair_engine.py new file mode 100644 index 0000000000..1290ef2eb8 --- /dev/null +++ b/scripts/experiments/split_pair_engine.py @@ -0,0 +1,275 @@ +# Composition of PR67 profile-cost reclamation and PR68 pending live controls. +# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance. +# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance. +# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62 +# and eumemic PR57. Apache-2.0; all inherited notices remain applicable. +"""Exact-envelope block synthesis on the pinned PR48 scalar graph. +Experimental finite compiler; no fixed-I+J profile or multiplication claim. +""" +# Derived from eumemic's PR57 compiler; original notices remain applicable. +# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance. +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +from pathlib import Path +ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48' +from hashlib import sha256 +import json +manifest=json.loads((ROOT/'SOURCE.json').read_text()) +for name,digest in manifest['files'].items(): + assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name +sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')] +from changed_graph import graph +from collections import defaultdict,Counter,deque +import argparse,json,time,struct + +def independent(rows,vec): + for row in rows: + vec=min(vec,vec^row) + return bool(vec) +def basis(rows): + out=[] + for vec in rows: + for row in out:vec=min(vec,vec^row) + if vec:out.append(vec) + return out + +def build(h): + c=graph(h);groups={};owner={};signal={};blocks=[] + for x in sorted(c.active): + key=(c.core[x],c.union[x]) + if key not in groups: + groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[])) + g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x) + signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1) + for x in sorted(c.active): + for y in c.args[x]or(): + if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y) + uses=[];value_uses=defaultdict(list) + for g,b in enumerate(blocks): + b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]] + for y in b['inputs']: + k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k) + for target,x in c.outputs.items(): + k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k) + for g,b in enumerate(blocks): + b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count() + order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes']))) + place={g:i for i,g in enumerate(order)} + def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1]) + for g,b in enumerate(blocks): + coeff={y:1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + import subprocess,struct + from binary_frame_math import logs + # Integer midpoint enclosures give a reproducible discovery score. + # Every candidate is independently checked by the complete exact screen. + weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)] + oracle_input=Path(ORACLE_INPUT) + with oracle_input.open('wb') as stream: + stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1))) + stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h)) + for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank'])) + oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1) + oracles.append(oracle) + cache={} + def profile_entropy(a,b): + if (a,b) not in cache: + oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush() + answer=oracle.stdout.readline() + assert answer, 'profile oracle failed' + parts=list(map(int,answer.split()));assert len(parts)==h+1 + cache[a,b]=sum(n*w for n,w in zip(parts,weights)) + return cache[a,b] + def profile_cost(a,g): + old=frames[a]+2;target=g+2 + endpoint=pending[a]+2 if PENDING_COST and a in pending else 1 + return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1] + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1< 3 and choice: + index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice] + if len(groups[index]) == 2: + groups[index:index+1] = [[point] for point in groups[index]] + assert all(len(group) in (1, 2) for group in groups) + assert len(groups) < len(points) + assert sorted(point for group in groups for point in group) == sorted(points) + return groups + return SplitPair + + +def graph(h): + config = configuration(h) + original = _graph.circuit_class + previous_points = _graph.alternating_points + try: + _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups']) + if config['anchor']: + def anchored_points(dimension, common): + points = previous_points(dimension, common) + pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)] + chosen = min(pairs) + result = list(chosen) + [x for x in points if x not in chosen] + assert sorted(result) == [x for x in range(dimension) if x != common] + return result + _graph.alternating_points = anchored_points + return _graph.graph(h) + finally: + _graph.circuit_class = original + _graph.alternating_points = previous_points + + +def ordered_build(original, h): + mode = configuration(h)['schedule'] + if mode == 'original': + return original + return _schedule.reordered_build(original, mode) diff --git a/scripts/experiments/verify_balanced_split.py b/scripts/experiments/verify_balanced_split.py new file mode 100644 index 0000000000..67e084e583 --- /dev/null +++ b/scripts/experiments/verify_balanced_split.py @@ -0,0 +1,80 @@ +#!/usr/bin/env python3 +"""Replay the aligned balanced-split/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import os +import shlex +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from balanced_split_compose import compose, check_sources +from balanced_split_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'balanced-split-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='balanced-split-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + *shlex.split(os.environ.get('CXX', 'c++')), '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'balanced-split-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'balanced-split-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'balanced-split-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'balanced-split-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'balanced-split-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/scripts/experiments/verify_merged_exterior.py b/scripts/experiments/verify_merged_exterior.py new file mode 100644 index 0000000000..ba11bc6b5f --- /dev/null +++ b/scripts/experiments/verify_merged_exterior.py @@ -0,0 +1,49 @@ +#!/usr/bin/env python3 +"""Replay the merged-exterior selection, exact profiles and composition. + +Checks the controlled permutations against the pinned PR34 module, recomputes +every candidate merged and removed edge profile in exact integer arithmetic, +replays the per-role selection, recomposes the complete recursive profile on +the PR79 witness and compares both certificates. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode = True + +from hashlib import sha256 +from pathlib import Path +import importlib.util, json + +import binary_frame_math as arithmetic +from merged_exterior import OUT, PERMS, ROOT, selection +from merged_exterior_compose import compose + +GEOMETRY = ROOT / 'research/copied-fixed/reversed' + + +def check_permutations(): + """Compare with the pinned PR34 module, loaded by the inherited loader (host resource caps omitted).""" + pinned = json.loads((GEOMETRY / 'geometry-source.json').read_text())['sha256']['pr34/independent_controls.py'] + source = GEOMETRY / 'pr34/independent_controls.py' + assert sha256(source.read_bytes()).hexdigest() == pinned, 'pinned PR34 source changed' + spec = importlib.util.spec_from_file_location('merged_exterior_geometry', GEOMETRY / 'geometry.py') + geometry = importlib.util.module_from_spec(spec) + spec.loader.exec_module(geometry) + controls = geometry.load('pr34_independent_merged_exterior', source) + assert controls.completion(23, *controls.corner_labels(23)) == PERMS, 'controlled permutations differ from pinned PR34' + + +def verify(): + check_permutations() + replayed = selection() + stored = json.loads((OUT / 'merged-exterior-selection.json').read_text()) + assert replayed == stored, 'selection or exact merged profiles differ' + result = json.loads(json.dumps(arithmetic.js(compose(stored)))) + assert result == json.loads((OUT / 'merged-exterior-kappa.json').read_text()), 'composition differs' + print(f'PASS merged exteriors: kappa={result["kappa"]}; bit saving={result["bit_saving"]}; ' + f'largest child {result["bit"]["maxchild"]}', flush=True) + + +if __name__ == '__main__': + verify() diff --git a/scripts/experiments/verify_split_pair.py b/scripts/experiments/verify_split_pair.py new file mode 100644 index 0000000000..7908c963a4 --- /dev/null +++ b/scripts/experiments/verify_split_pair.py @@ -0,0 +1,78 @@ +#!/usr/bin/env python3 +"""Replay the aligned split-pair/interval words with profile-cost pending live compilation and exact profiles. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +import sys +if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + +from hashlib import sha256 +from pathlib import Path +import json +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from split_pair_compose import compose, check_sources +from split_pair_compiler import compile_axis + + +def verify(): + import sys + if sys.flags.optimize: + raise ValueError('Assertions must remain enabled') + check_sources() + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'split-pair-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='split-pair-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + 'c++', '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'split-pair-word-{h}.json.gz' + import gzip + compiled, regenerated = compile_axis(h) + assert json.loads(json.dumps(compiled)) == stored['axes'][str(h)]['compiled'], 'Regenerated compiler receipt differs' + regenerated_raw = (json.dumps(regenerated, separators=(',', ':'))+'\n').encode() + assert regenerated_raw == gzip.decompress(word.read_bytes()), 'Regenerated physical word differs' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'split-pair-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'split-pair-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'split-pair-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + producer_words_regenerated_and_matched=True, + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'split-pair-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify() diff --git a/tests/test_balanced_split.py b/tests/test_balanced_split.py new file mode 100644 index 0000000000..175e7af890 --- /dev/null +++ b/tests/test_balanced_split.py @@ -0,0 +1,251 @@ +"""Physical and exact-arithmetic controls for the aligned split/pair witness.""" +from copy import deepcopy +from fractions import Fraction +from itertools import combinations +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile +import unittest +from unittest.mock import patch + +ROOT = Path(__file__).resolve().parents[1] +EXPERIMENTS = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXPERIMENTS)) +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from binary_frame_math import moment + + +class SplitPairControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.words = {h: json.loads(gzip.decompress((ROOT/f'certificates/balanced-split-word-{h}.json.gz').read_bytes())) + for h in (23,25)} + + def reject_mutation(self, mutate, checker='both'): + for h, original in self.words.items(): + with self.subTest(h=h), tempfile.TemporaryDirectory() as directory: + changed = deepcopy(original) + mutate(changed) + path = Path(directory)/'word.json' + path.write_text(json.dumps(changed, separators=(',', ':'))+'\n') + with self.assertRaises((AssertionError, ValueError, IndexError, KeyError)): + if checker != 'transitions': + replay(path) + if checker != 'replay': + prepare(path, Path(directory)/'transitions.bin') + + def test_selected_words_pass_independent_replay(self): + recorded = json.loads((ROOT/'certificates/balanced-split-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + actual = replay(ROOT/f'certificates/balanced-split-word-{h}.json.gz') + self.assertEqual(json.loads(json.dumps(actual)), recorded['axes'][str(h)]['replay']) + + def test_omitted_literal_xor_is_rejected(self): + self.reject_mutation(lambda word: word['ops'].pop(0)) + + def test_self_xor_is_rejected(self): + def mutate(word): + word['ops'][0][1] = word['ops'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_non_nested_operation_frame_is_rejected(self): + def mutate(word): + narrow = next(i for i,(core,cover) in enumerate(word['frames']) if core == cover) + operation = next(op for op in word['ops'] if word['frames'][op[2]][0] != word['frames'][op[2]][1]) + operation[2] = narrow + self.reject_mutation(mutate) + + def test_aliased_terminal_role_is_rejected(self): + def mutate(word): + word['outputs'][1][0] = word['outputs'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_missing_copied_center_is_rejected(self): + def mutate(word): + index = next(i for i,(_,_,_,target) in enumerate(word['outputs']) if len(target) == 1) + word['outputs'].pop(index) + self.reject_mutation(mutate) + + def test_omitted_transition_cannot_reduce_paid_profile(self): + self.reject_mutation(lambda word: word['events'].pop(0), 'transitions') + + def test_understated_physical_width_is_rejected(self): + def mutate(word): + word['R'] -= 1 + self.reject_mutation(mutate) + + def test_complete_pr71_profile_fails_new_bit_saving(self): + from split_pair_arithmetic import refine + previous = json.loads((ROOT/'references/frame-compiler/pr71/certificates/split-pair-kappa.json').read_text())['bit'] + current = json.loads((ROOT/'certificates/balanced-split-kappa.json').read_text()) + result = refine.exact_moment(previous['m'], previous['W'], {int(t): n for t,n in previous['child_multiplicities'].items()}, Fraction(current['bit_saving'])) + self.assertGreater(result['lower'], 1) + self.assertGreater(Fraction(current['kappa']), Fraction(current['comparison']['pr71_kappa'])) + + def test_private_import_preserves_path_and_arithmetic_module(self): + import balanced_split_graph as provider + import split_pair_arithmetic as arithmetic + sentinel = object() + existing = sys.modules.get('refine', sentinel) + previous_path = sys.path[:] + graph, schedule = provider._private_modules() + refine, audit = arithmetic.private_arithmetic() + self.assertIs(audit.refine, refine) + self.assertIs(sys.modules.get('refine', sentinel), existing) + self.assertEqual(sys.path, previous_path) + + def test_failed_graph_build_restores_original_providers(self): + import balanced_split_graph as provider + previous_class, previous_points = provider._graph.circuit_class, provider._graph.alternating_points + with patch.object(provider._graph, 'graph', side_effect=RuntimeError('deliberate graph failure')): + with self.assertRaises(RuntimeError): + provider.graph(23) + self.assertIs(provider._graph.circuit_class, previous_class) + self.assertIs(provider._graph.alternating_points, previous_points) + + def test_failed_compilation_restores_engine_graph_and_schedule(self): + import balanced_split_compiler as producer + previous_graph, previous_build = producer.ENGINES[23].graph, producer.ENGINES[23].build + missing = object() + runtime = {name:getattr(producer.ENGINES[23],name,missing) for name in ('PENDING_COST','ORACLE_EXE','ORACLE_INPUT','oracles')} + with patch.object(producer.ENGINES[23], 'compile_', side_effect=RuntimeError('deliberate compiler failure')): + with self.assertRaises(RuntimeError): + producer.compile_axis(23) + self.assertIs(producer.ENGINES[23].graph, previous_graph) + self.assertIs(producer.ENGINES[23].build, previous_build) + for name,value in runtime.items(): + self.assertIs(getattr(producer.ENGINES[23],name,missing),value) + + def test_uncertified_configurations_are_rejected(self): + import balanced_split_graph as provider + wrong_anchor = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_anchor['anchor'] = False + boolean_group = deepcopy(provider.EXPECTED_CONFIGS[23]); boolean_group['groups'][0] = True + changed_schedule = deepcopy(provider.EXPECTED_CONFIGS[23]); changed_schedule['schedule'] = 'reverse-node' + wrong_coarse = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_coarse['coarse'] = 'row' + omitted_completion = deepcopy(provider.EXPECTED_CONFIGS[23]); omitted_completion['future_completion'] = False + extra_exchanges = deepcopy(provider.EXPECTED_CONFIGS[23]); extra_exchanges['carry_exchange_passes'] = 3 + for changed in (wrong_anchor, boolean_group, changed_schedule, wrong_coarse, omitted_completion, extra_exchanges): + with self.subTest(configuration=changed), patch.object(provider.json, 'loads', return_value=changed): + with self.assertRaises(ValueError): + provider.configuration(23) + for dimension in (True, 22, 24, '23'): + with self.subTest(dimension=dimension), self.assertRaises(ValueError): + provider.configuration(dimension) + + def test_recursive_weighted_exclusions_and_contraction(self): + import balanced_split_graph as provider + for h in (23,25): + block_sizes = [] + parent = provider._graphs[h].circuit_class(h) + selected = provider.split_class(parent, provider.configuration(h)['groups']) + case = self + class Audited(selected): + def grouping(self, points): + groups = super().grouping(points) + case.assertEqual([x for group in groups for x in group], list(points)) + case.assertLess(len(groups), len(points)) + return groups + + def _block(self, points, edges, weights, level): + def expected(omitted): + values = [value for pair,value in edges.items() if not set(pair) & omitted] + values += [value for point,value in weights.items() if point not in omitted] + support = 0 + for value in values: + case.assertEqual(support & self.support[value], 0) + support |= self.support[value] + return support + total, single, pairs = super()._block(points, edges, weights, level) + case.assertEqual(self.support[total], expected(set())) + case.assertEqual(set(single), set(points)) + for a in points: + case.assertEqual(self.support[single[a]], expected({a})) + case.assertEqual(set(pairs), set(combinations(points,2))) + for a,b in combinations(points,2): + case.assertEqual(self.support[pairs[a,b]], expected({a,b})) + block_sizes.append(len(points)) + return total, single, pairs + local = Audited(h-1) + block_sizes.clear() + local.pair(list(range(h-1))) + self.assertEqual(sorted(block_sizes, reverse=True), [h-1, 12 if h==23 else 13, 7 if h==23 else 8, 5, 3, 2]) + + def test_next_fine_grid_points_and_old_assembly_controls_reject(self): + from split_pair_arithmetic import refine + current = json.loads((ROOT/'certificates/balanced-split-kappa.json').read_text()) + bit = current['bit']; saving = Fraction(current['bit_saving']); kappa = Fraction(current['kappa']) + grid = Fraction(1,10**18) + rows = {int(t): n for t,n in bit['child_multiplicities'].items()} + self.assertLess(refine.exact_moment(bit['m'],bit['W'],rows,saving)['upper'], 1) + self.assertGreater(refine.exact_moment(bit['m'],bit['W'],rows,saving+grid)['lower'], 1) + for label, variant in ( + ('next_kappa', dict(kappa=kappa+grid)), + ('zero_backoff', dict(h=Fraction())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))): + call = dict(a_bit=saving, kappa=kappa, h=Fraction(1,10**12));call.update(variant) + with self.subTest(control=label), self.assertRaises(refine.balanced.InvalidAssembly): + refine.balanced.assembly(current['finite_bridge'], **call) + + def test_mass_preserving_profile_mutation_is_rejected(self): + from balanced_split_compose import check_sources + profile_path = ROOT/'certificates/balanced-split-profiles-23.json' + changed = json.loads(profile_path.read_text()) + before = sum(t*n for t,n in enumerate(changed['blocks'])) + changed['blocks'][2] += 3; changed['blocks'][3] -= 2 + self.assertTrue(all(n >= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'balanced-split-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from balanced_split_compose import check_sources + manifest_path = ROOT/'research/balanced-split/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/balanced-split-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import balanced_split_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_all_threshold_dependent_bridge_fields_are_checked(self): + from balanced_split_compose import finite_bridge, validate_bridge + expected = finite_bridge(134126064) + self.assertTrue(validate_bridge(expected, 134126064)) + for section,key in (('bit','wire_bits'),('rows','coefficient'),('rows','degree'),('rows','degree_gap'),('rows','suffix_slope')): + changed = deepcopy(expected) + changed[section][key] = Fraction(changed[section][key])+1 + with self.subTest(field=section+'.'+key), self.assertRaisesRegex(AssertionError, 'Stale finite bridge'): + validate_bridge(changed, 134126064) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('balanced_split_graph.py', 'balanced_split_engine.py', 'balanced_split_compiler.py', 'split_pair_arithmetic.py', 'balanced_split_exchange_engine.py', 'balanced_split_compose.py', 'verify_balanced_split.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/tests/test_balanced_split_pending.py b/tests/test_balanced_split_pending.py new file mode 100644 index 0000000000..cce267112e --- /dev/null +++ b/tests/test_balanced_split_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/balanced_split_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/balanced-split-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main() diff --git a/tests/test_merged_exterior.py b/tests/test_merged_exterior.py new file mode 100644 index 0000000000..f50d3f9d84 --- /dev/null +++ b/tests/test_merged_exterior.py @@ -0,0 +1,103 @@ +import random +import sys +import unittest +from fractions import Fraction as Q +from pathlib import Path + +sys.path.insert(0, str(Path(__file__).resolve().parents[1] / 'scripts/experiments')) +import merged_exterior as me + + +def dense(X, h): + classes, U, V, d, mask, sigma = X + cls = [next(c for c, part in enumerate(classes) if part >> i & 1) for i in range(h)] + return [[Q(int(i == j and mask >> i & 1)) + Q(sigma * sum(a * b for a, b in zip(U[cls[i]], V[cls[j]])), d) + for j in range(h)] for i in range(h)] + + +def rational_rank(rows): + rows = [r[:] for r in rows] + rank = 0 + for c in range(len(rows[0]) if rows else 0): + p = next((k for k in range(rank, len(rows)) if rows[k][c]), None) + if p is None: + continue + rows[rank], rows[p] = rows[p], rows[rank] + for k in range(len(rows)): + if k != rank and rows[k][c]: + f = rows[k][c] / rows[rank][c] + rows[k] = [x - f * y for x, y in zip(rows[k], rows[rank])] + rank += 1 + return rank + + +def ne_runs(M): + """Top-row-first, rightmost-pivot elimination over Q.""" + M = [r[:] for r in M] + pivots = [] + for i in range(len(M)): + j = max((j for j, x in enumerate(M[i]) if x), default=None) + if j is None: + continue + pivots.append((i, j)) + for k in range(i + 1, len(M)): + if M[k][j]: + f = M[k][j] / M[i][j] + M[k] = [x - f * y for x, y in zip(M[k], M[i])] + return len(pivots), me.runs(pivots) + + +def random_frame(rng, h): + c = rng.choice((1, 2, 3)) + core = sum(1 << x for x in rng.sample(range(h), c)) + if c == 3: + return core, core + return core, core | sum(1 << x for x in rng.sample(range(h), rng.randrange(1, h - c))) + + +class MergedExteriorTest(unittest.TestCase): + def test_exact_rank_matches_rational_elimination(self): + rng = random.Random(2325) + for h in (23, 25): + for _ in range(40): + X = me.operator(*random_frame(rng, h), h, rng.random() < 0.5) + D = dense(X, h) + S = sum(1 << x for x in range(h) if rng.random() < 0.6) + T = sum(1 << x for x in range(h) if rng.random() < 0.6) + sub = [[D[i][j] for j in range(h) if T >> j & 1] for i in range(h) if S >> i & 1] + self.assertEqual(me.rank(X, S, T), rational_rank(sub) if sub and sub[0] else 0) + + def test_operators_are_idempotent(self): + rng = random.Random(7) + for h in (23, 25): + for _ in range(4): + frame = random_frame(rng, h) + for complement in (False, True): + D = dense(me.operator(*frame, h, complement), h) + self.assertEqual([[sum(D[i][k] * D[k][j] for k in range(h)) for j in range(h)] for i in range(h)], D) + + def test_lemma_profile_matches_direct_elimination(self): + """Random layouts pairing each local coordinate once with each line coordinate.""" + rng = random.Random(46) + h, n = 23, 3 + for _ in range(12): + layout = [(a, c) for a in range(h) for c in range(n)] + rng.shuffle(layout) + lam = [a for a, c in layout] + v = [rng.randrange(1, 9) for _ in range(n)] + nu0 = [rng.randrange(1, 9) for _ in range(n)] + nu = [Q(x, sum(a * b for a, b in zip(nu0, v))) for x in nu0] + X = me.operator(*random_frame(rng, h), h, rng.random() < 0.5) + D = dense(X, h) + M = [[Q(int(k == l)) - D[a][b] * v[c] * nu[e] for l, (b, e) in enumerate(layout)] + for k, (a, c) in enumerate(layout)] + self.assertEqual(me.merged_profile(X, h, me.flags(lam)), ne_runs(M)) + + def test_layout_reproduces_inherited_exterior(self): + for h in (23, 25): + identity = ((((1 << h) - 1), 0, 0), [(0,)] * 3, [(0,)] * 3, 1, (1 << h) - 1, 1) + self.assertEqual(me.merged_profile(identity, h, me.FLAGS[h]), (me.M_ - h, [me.M_ - 2 * h, h])) + + +if __name__ == '__main__': + unittest.main() diff --git a/tests/test_split_pair.py b/tests/test_split_pair.py new file mode 100644 index 0000000000..5088cff133 --- /dev/null +++ b/tests/test_split_pair.py @@ -0,0 +1,238 @@ +"""Physical and exact-arithmetic controls for the aligned split/pair witness.""" +from copy import deepcopy +from fractions import Fraction +from itertools import combinations +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile +import unittest +from unittest.mock import patch + +ROOT = Path(__file__).resolve().parents[1] +EXPERIMENTS = ROOT/'scripts/experiments' +sys.path.insert(0, str(EXPERIMENTS)) +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from binary_frame_math import moment + + +class SplitPairControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.words = {h: json.loads(gzip.decompress((ROOT/f'certificates/split-pair-word-{h}.json.gz').read_bytes())) + for h in (23,25)} + + def reject_mutation(self, mutate, checker='both'): + for h, original in self.words.items(): + with self.subTest(h=h), tempfile.TemporaryDirectory() as directory: + changed = deepcopy(original) + mutate(changed) + path = Path(directory)/'word.json' + path.write_text(json.dumps(changed, separators=(',', ':'))+'\n') + with self.assertRaises((AssertionError, ValueError, IndexError, KeyError)): + if checker != 'transitions': + replay(path) + if checker != 'replay': + prepare(path, Path(directory)/'transitions.bin') + + def test_selected_words_pass_independent_replay(self): + recorded = json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + actual = replay(ROOT/f'certificates/split-pair-word-{h}.json.gz') + self.assertEqual(json.loads(json.dumps(actual)), recorded['axes'][str(h)]['replay']) + + def test_omitted_literal_xor_is_rejected(self): + self.reject_mutation(lambda word: word['ops'].pop(0)) + + def test_self_xor_is_rejected(self): + def mutate(word): + word['ops'][0][1] = word['ops'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_non_nested_operation_frame_is_rejected(self): + def mutate(word): + narrow = next(i for i,(core,cover) in enumerate(word['frames']) if core == cover) + operation = next(op for op in word['ops'] if word['frames'][op[2]][0] != word['frames'][op[2]][1]) + operation[2] = narrow + self.reject_mutation(mutate) + + def test_aliased_terminal_role_is_rejected(self): + def mutate(word): + word['outputs'][1][0] = word['outputs'][0][0] + self.reject_mutation(mutate, 'replay') + + def test_missing_copied_center_is_rejected(self): + def mutate(word): + index = next(i for i,(_,_,_,target) in enumerate(word['outputs']) if len(target) == 1) + word['outputs'].pop(index) + self.reject_mutation(mutate) + + def test_omitted_transition_cannot_reduce_paid_profile(self): + self.reject_mutation(lambda word: word['events'].pop(0), 'transitions') + + def test_understated_physical_width_is_rejected(self): + def mutate(word): + word['R'] -= 1 + self.reject_mutation(mutate) + + def test_complete_pr67_profile_fails_new_bit_saving(self): + from split_pair_arithmetic import refine + previous = json.loads((ROOT/'references/frame-compiler/pr67/research/slot-cost-rank-pair/paired-candidate.json').read_text())['bit'] + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + result = refine.exact_moment(previous['m'], previous['W'], {int(t): n for t,n in previous['child_multiplicities'].items()}, Fraction(current['bit_saving'])) + self.assertGreater(result['lower'], 1) + self.assertGreater(Fraction(current['kappa']), Fraction(current['comparison']['pr67_kappa'])) + + def test_private_import_preserves_path_and_arithmetic_module(self): + import split_pair_graph as provider + import split_pair_arithmetic as arithmetic + sentinel = object() + existing = sys.modules.get('refine', sentinel) + previous_path = sys.path[:] + graph, schedule = provider._private_modules() + refine, audit = arithmetic.private_arithmetic() + self.assertIs(audit.refine, refine) + self.assertIs(sys.modules.get('refine', sentinel), existing) + self.assertEqual(sys.path, previous_path) + + def test_failed_graph_build_restores_original_providers(self): + import split_pair_graph as provider + previous_class, previous_points = provider._graph.circuit_class, provider._graph.alternating_points + with patch.object(provider._graph, 'graph', side_effect=RuntimeError('deliberate graph failure')): + with self.assertRaises(RuntimeError): + provider.graph(23) + self.assertIs(provider._graph.circuit_class, previous_class) + self.assertIs(provider._graph.alternating_points, previous_points) + + def test_failed_compilation_restores_engine_graph_and_schedule(self): + import split_pair_compiler as producer + previous_graph, previous_build = producer.compiler.graph, producer.compiler.build + missing = object() + runtime = {name:getattr(producer.compiler,name,missing) for name in ('PENDING_COST','ORACLE_EXE','ORACLE_INPUT','oracles')} + with patch.object(producer.compiler, 'compile_', side_effect=RuntimeError('deliberate compiler failure')): + with self.assertRaises(RuntimeError): + producer.compile_axis(23) + self.assertIs(producer.compiler.graph, previous_graph) + self.assertIs(producer.compiler.build, previous_build) + for name,value in runtime.items(): + self.assertIs(getattr(producer.compiler,name,missing),value) + + def test_uncertified_configurations_are_rejected(self): + import split_pair_graph as provider + wrong_anchor = deepcopy(provider.EXPECTED_CONFIGS[23]); wrong_anchor['anchor'] = False + boolean_group = deepcopy(provider.EXPECTED_CONFIGS[23]); boolean_group['groups'][0] = True + changed_schedule = deepcopy(provider.EXPECTED_CONFIGS[23]); changed_schedule['schedule'] = 'reverse-node' + for changed in (wrong_anchor, boolean_group, changed_schedule): + with self.subTest(configuration=changed), patch.object(provider.json, 'loads', return_value=changed): + with self.assertRaises(ValueError): + provider.configuration(23) + for dimension in (True, 22, 24, '23'): + with self.subTest(dimension=dimension), self.assertRaises(ValueError): + provider.configuration(dimension) + + def test_recursive_weighted_exclusions_and_contraction(self): + import split_pair_graph as provider + for h in (23,25): + block_sizes = [] + parent = provider._graph.circuit_class(h) + selected = provider.split_class(parent, provider.configuration(h)['groups']) + case = self + class Audited(selected): + def grouping(self, points): + groups = super().grouping(points) + case.assertEqual([x for group in groups for x in group], list(points)) + case.assertLess(len(groups), len(points)) + return groups + + def _block(self, points, edges, weights, level): + def expected(omitted): + values = [value for pair,value in edges.items() if not set(pair) & omitted] + values += [value for point,value in weights.items() if point not in omitted] + support = 0 + for value in values: + case.assertEqual(support & self.support[value], 0) + support |= self.support[value] + return support + total, single, pairs = super()._block(points, edges, weights, level) + case.assertEqual(self.support[total], expected(set())) + case.assertEqual(set(single), set(points)) + for a in points: + case.assertEqual(self.support[single[a]], expected({a})) + case.assertEqual(set(pairs), set(combinations(points,2))) + for a,b in combinations(points,2): + case.assertEqual(self.support[pairs[a,b]], expected({a,b})) + block_sizes.append(len(points)) + return total, single, pairs + local = Audited(h-1) + block_sizes.clear() + local.pair(list(range(h-1))) + self.assertEqual(sorted(block_sizes, reverse=True), [h-1, 12 if h==23 else 13, 7 if h==23 else 8, 5, 3, 2]) + + def test_next_fine_grid_points_and_old_assembly_controls_reject(self): + from split_pair_arithmetic import refine + current = json.loads((ROOT/'certificates/split-pair-kappa.json').read_text()) + bit = current['bit']; saving = Fraction(current['bit_saving']); kappa = Fraction(current['kappa']) + grid = Fraction(1,10**18) + rows = {int(t): n for t,n in bit['child_multiplicities'].items()} + self.assertLess(refine.exact_moment(bit['m'],bit['W'],rows,saving)['upper'], 1) + self.assertGreater(refine.exact_moment(bit['m'],bit['W'],rows,saving+grid)['lower'], 1) + for label, variant in ( + ('next_kappa', dict(kappa=kappa+grid)), + ('zero_backoff', dict(h=Fraction())), + ('original_prefix', dict(original_prefix=True)), + ('old_guard', dict(old_guard=True)), + ('old_exposures', dict(old_exposures=True))): + call = dict(a_bit=saving, kappa=kappa, h=Fraction(1,10**12));call.update(variant) + with self.subTest(control=label), self.assertRaises(refine.balanced.InvalidAssembly): + refine.balanced.assembly(current['finite_bridge'], **call) + + def test_mass_preserving_profile_mutation_is_rejected(self): + from split_pair_compose import check_sources + profile_path = ROOT/'certificates/split-pair-profiles-23.json' + changed = json.loads(profile_path.read_text()) + before = sum(t*n for t,n in enumerate(changed['blocks'])) + changed['blocks'][2] += 3; changed['blocks'][3] -= 2 + self.assertTrue(all(n >= 0 for n in changed['blocks'])) + self.assertEqual(before, sum(t*n for t,n in enumerate(changed['blocks']))) + forged = (json.dumps(changed)+'\n').encode() + original = Path.read_bytes + def read_bytes(path): + return forged if path == profile_path else original(path) + with patch.object(Path, 'read_bytes', read_bytes), self.assertRaisesRegex(AssertionError, 'split-pair-profiles-23'): + check_sources() + + def test_missing_profile_pin_is_rejected(self): + from split_pair_compose import check_sources + manifest_path = ROOT/'research/split-pair/SOURCE.json' + manifest = json.loads(manifest_path.read_text());manifest['files'].pop('certificates/split-pair-profiles-23.json') + original = Path.read_text + def read_text(path, *args, **kwargs): + return json.dumps(manifest) if path == manifest_path else original(path, *args, **kwargs) + with patch.object(Path, 'read_text', read_text), self.assertRaisesRegex(AssertionError, 'Incomplete'): + check_sources() + + def test_backward_schedule_dependency_and_carrier_rejected(self): + import split_pair_graph as provider + for kind in ('dependency','carrier'): + blocks = [dict(rank=1,nodes=[1],frame=(0,1),inputs=[],candidates=[]), + dict(rank=2,nodes=[2],frame=(0,3),inputs=[],candidates=[])] + if kind == 'dependency': blocks[0]['inputs'] = [5] + else: blocks[1]['candidates'] = [(0,0)] + parts = (None,blocks,[(5,0,None)],None,{5:1},None,[0,1],None) + with self.subTest(kind=kind), self.assertRaises(AssertionError): + provider._schedule.reordered_build(lambda h:parts, 'cover-core')(23) + + def test_optimized_python_is_rejected_by_every_new_entry(self): + for name in ('split_pair_graph.py', 'split_pair_engine.py', 'split_pair_compiler.py', 'split_pair_arithmetic.py', 'split_pair_compose.py', 'verify_split_pair.py'): + with self.subTest(entry=name): + result = subprocess.run([sys.executable, '-O', str(EXPERIMENTS/name), '--help'], capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('Assertions must remain enabled', result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/tests/test_split_pair_pending.py b/tests/test_split_pair_pending.py new file mode 100644 index 0000000000..e6d63f72a4 --- /dev/null +++ b/tests/test_split_pair_pending.py @@ -0,0 +1,101 @@ +"""Adverse fixtures for the actual integrated pending-control source. + +These tests extract the selected nested source functions without running the +full compiler or oracle; complete word replay is a separate focused gate. +Prepared by Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +import ast +import json +import unittest + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT/'scripts/experiments/split_pair_engine.py' +TREE=ast.parse(SOURCE.read_text()) +body=next(n for n in TREE.body if isinstance(n,ast.FunctionDef) and n.name=='compile_').body +functions={n.name:n for n in body if isinstance(n,ast.FunctionDef)} +def check(ok,why): + if not ok: raise ValueError(why) +def contains(a,b): return not(b[0]&~a[0]) and not(a[1]&~b[1]) +def getfn(name,namespace,node=None): + exec(compile(ast.Module(body=[node or functions[name]],type_ignores=[]),str(SOURCE),'exec'),namespace) + return namespace[name] + +def scenario(pending_frame=0, endpoint=2, anchors=False, acquire_node=None): + # F subset E subset G, while H is not an envelope containing E. + blocks=[{'frame':(1,3),'rank':1},{'frame':(1,7),'rank':2},{'frame':(1,15),'rank':3},{'frame':(1,5),'rank':1}] + slots=[1,1];frames=[pending_frame,0];retired={1};pending={0:endpoint};ops=[];stats=Counter() + def new(g): + slots.append(0);frames.append(g);return len(slots)-1 + def xor(a,b,g): + check(a!=b,'noninvertible self XOR') + for s in (a,b): + check(contains(blocks[frames[s]]['frame'],blocks[g]['frame']),'invalid envelope raising') + frames[s]=g + slots[a]^=slots[b];ops.append((a,b,g)) + env=dict(reclaim=True,slots=slots,frames=frames,blocks=blocks,retired=retired,pending=pending,contains=contains,stats=stats,profile_cost=lambda a,g:0,new=new,xor=xor) + result=getfn('acquire',env,acquire_node)(1,[0] if anchors else []) + check(slots[0]==1 and pending=={0:endpoint},'passive pending control changed signal or future use') + return result,slots,frames,ops,stats + + +class PendingControlTests(unittest.TestCase): + def test_current_and_future_containment_and_passive_signal(self): + for name,kwargs,expected in [ + ('legal F subset E subset G',{},1), + ('future endpoint not containing E',{'endpoint':3},2), + ('current pending frame not contained in E',{'pending_frame':2},2), + ('terminal endpoint cannot be overshot',{'endpoint':0},2), + ('same physical control in anchors and pending',{'anchors':True},1), + ]: + with self.subTest(control=name): + result,slots,frames,ops,stats=scenario(**kwargs) + self.assertEqual(result,expected) + if expected==1: + self.assertEqual((slots,frames,ops),([1,0],[1,1],[(1,0,1)])) + self.assertEqual((stats['live_anchor_xors'],stats['clearing_xors'],stats['reclaimed']),(1,1,1)) + else: + self.assertEqual(ops,[]) + self.assertEqual(slots,[1,1,0]) + + def test_next_use_score_and_both_full_space_fallbacks(self): + for use_pending,a,expected_calls in [ + (True,0,[(2,4),(2,3),(3,4)]), + (False,0,[(2,1),(2,3),(3,1)]), + (True,1,[(2,1),(2,3),(3,1)]), + ]: + with self.subTest(pending_cost=use_pending,slot=a): + calls=[] + def entropy(x,y):calls.append((x,y));return 100*x+y + env=dict(frames=[0,0],pending={0:2},PENDING_COST=use_pending,profile_entropy=entropy) + result=getfn('profile_cost',env)(a,1) + self.assertEqual(calls,expected_calls) + self.assertEqual(result,sum(sign*(100*x+y) for sign,(x,y) in zip([1,-1,-1],expected_calls))) + + def test_removing_future_containment_reaches_adverse_fixture(self): + class RemoveFutureBound(ast.NodeTransformer): + def visit_If(self,node): + self.generic_visit(node) + if isinstance(node.test,ast.BoolOp) and isinstance(node.test.op,ast.And) and len(node.test.values)==2 and 'blocks[target]' in ast.unparse(node.test): + node.test=node.test.values[0] + return node + mutant=RemoveFutureBound().visit(ast.parse(ast.unparse(functions['acquire'])).body[0]) + ast.fix_missing_locations(mutant) + original=scenario(endpoint=3)[0] + mutated=scenario(endpoint=3,acquire_node=mutant)[0] + self.assertEqual(original,2) + self.assertEqual(mutated,1) + + def test_selected_words_exercise_pending_controls(self): + record=json.loads((ROOT/'certificates/split-pair-compiler.json').read_text()) + for h in (23,25): + with self.subTest(h=h): + compiled=record['axes'][str(h)]['compiled'] + self.assertTrue(compiled['pending_live_controls']) + self.assertTrue(compiled['pending_cost_uses_next_use_frame']) + self.assertGreater(compiled['stats']['live_anchor_xors'],0) + + +if __name__=='__main__': + unittest.main()