From 0fb803895eacab86828a382def96ce5decb9de92 Mon Sep 17 00:00:00 2001 From: Chafik Boukhalfa Date: Fri, 9 Oct 2026 06:28:18 +0400 Subject: [PATCH 1/3] Compose shrunk frames, birth reuse and terminal elimination --- .gitattributes | 5 + .github/workflows/verify.yml | 2 +- Makefile | 5 + NOTICE | 22 + README.md | 14 + certificates/joint-dual-kappa.json | 2 +- certificates/joint-dual-validation.json | 74 +- ...-birth-terminal-repository-validation.json | 31 + formal/lean/AuditAll.lean | 242 + formal/lean/KappaCheck.lean | 1 + .../lean/KappaCheck/ShrunkBirthTerminal.lean | 1248 + formal/lean/SOURCES.md | 3 + formal/lean/sources.py | 6 + research/joint-dual/SOURCE.json | 6 +- research/shrunk-birth-terminal/PROOF.md | 101 + research/shrunk-birth-terminal/README.md | 16 + research/shrunk-birth-terminal/REPRODUCE.md | 35 + research/shrunk-birth-terminal/SOURCE.json | 291 + .../shrunk-birth-terminal/TERMINAL-PROOF.md | 61 + .../shrunk-birth-terminal/arithmetic/PROOF.md | 101 + 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research/shrunk-birth-terminal/selected/construction-sources/compose_terminal.py create mode 100644 research/shrunk-birth-terminal/selected/construction-sources/terminal_inventory.py create mode 100644 research/shrunk-birth-terminal/selected/inputs/BIRTH_MATCHES.json.gz create mode 100644 research/shrunk-birth-terminal/selected/inputs/FRAMES.pkl.gz create mode 100644 research/shrunk-birth-terminal/selected/inputs/READOUTS.pkl.gz create mode 100644 research/shrunk-birth-terminal/selected/inputs/READOUT_COST.json create mode 100644 research/shrunk-birth-terminal/selected/inputs/TERMINAL_ROLES.json create mode 100644 research/shrunk-birth-terminal/selected/inventory.json create mode 100644 research/shrunk-birth-terminal/selected/joint-profile-comparison.json create mode 100644 research/shrunk-birth-terminal/selected/majorization.json create mode 100644 research/shrunk-birth-terminal/selected/physical-audit.json create mode 100644 research/shrunk-birth-terminal/selected/word.json.gz create mode 100644 research/shrunk-birth-terminal/verify.py create mode 100644 tests/test_shrunk_birth_terminal.py diff --git a/.gitattributes b/.gitattributes index 41aef290fd..6b1aac8ce7 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 + +# Preserve exact imported sources and saved compiler-command bytes. +research/shrunk-birth-terminal/arithmetic/references/pr100/binary_frame_math.py -whitespace +research/shrunk-birth-terminal/lean/receipts/compile/command.txt -whitespace +research/shrunk-birth-terminal/references/pr122/research/terminal-elision/verify_portable_118.py -whitespace diff --git a/.github/workflows/verify.yml b/.github/workflows/verify.yml index 6bd374e1ca..44cd939cfc 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, shrunk-terminal] steps: - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 with: diff --git a/Makefile b/Makefile index 84fe8290f3..0f7ee4084e 100644 --- a/Makefile +++ b/Makefile @@ -23,6 +23,7 @@ verify: $(MAKE) verify-positive $(MAKE) verify-joint $(MAKE) verify-pair + $(MAKE) verify-shrunk-terminal $(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 +429,7 @@ 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: verify-shrunk-terminal +verify-shrunk-terminal: + python3 research/shrunk-birth-terminal/verify.py diff --git a/NOTICE b/NOTICE index b565637758..7b9a0d320a 100644 --- a/NOTICE +++ b/NOTICE @@ -302,3 +302,25 @@ 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. + +Selected shrunk-frame / birth-reuse / terminal-elision composition +Copyright 2026 Chafik Boukhalfa + +The portable package research/shrunk-birth-terminal combines the PR117 scalar +DAG by eumemic, PR125 shrunk logical frames by Joel Pulikkan (GamingPuzzled), +PR124 birth-slot reuse by James Chang (jamesyc), and PR122 terminal elimination +by SovereignSteak. It also retains Daniele Corso's PR126 endpoint-search ideas, +Rohan Arun's deferred/signed and unit-shear work, Avi Eisenberg's compiler +contributions, Swapnil Jain's (Swapnil-jain) round-seven bit word, and icekylinx's stopped +product-ring and rational-center interfaces. The paid balanced transfer retains +the Zhihao Chen (jacklightChen) / RaD (hipotures) / James Chang (jamesyc) semantic-layout lineage and Rohan Arun's +deferred/signed integration. Original source-specific notices and Anthropic +Claude and other AI-assistance disclosures are preserved in the archives. + +Chafik Boukhalfa with OpenAI Codex assistance prepared the selected endpoint +and placement composition, joint birth/terminal optimization, full chronological +physical word, exact source/dirty and frame checks, three-stock adaptation, +independent arithmetic, scoped Lean companion and portable package. This is a +conditional research candidate, not human peer review or an OpenAI endorsement. +Its exact finite/rational claims and retained all-size assumptions are stated +in the package proof. Existing contributor notices remain in force. diff --git a/README.md b/README.md index 035c259b68..ea5a6d7d4d 100644 --- a/README.md +++ b/README.md @@ -92,6 +92,20 @@ 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. +## Additional conditional composition + +The separate [shrunk-frame / birth-reuse / terminal-elision package](research/shrunk-birth-terminal/README.md) +certifies `kappa = 112802185097556/10^18 > 2^-14` under the inherited OpenAI #109 +all-size interfaces. It combines Joel Pulikkan's shrunk frames (PR125), James +Chang's birth identity (PR124), SovereignSteak's terminal identity (PR122) and +eumemic's PR117 graph with protected placement, joint matching and a paid +three-stock balanced transfer. The explicit word has 26,216 physical auxiliary +roles. Complete source/dirty and frame audits, two exact arithmetic methods and +240 scoped Lean theorems accompany the [proof](research/shrunk-birth-terminal/PROOF.md) +and [reproduction commands](research/shrunk-birth-terminal/REPRODUCE.md). +Original authorship and assistance disclosures are retained. This separate +candidate does not change the historical maintainer-review ledger above. + ## Reproduce ```sh diff --git a/certificates/joint-dual-kappa.json b/certificates/joint-dual-kappa.json index d92f653fe4..c8d0db8783 100644 --- a/certificates/joint-dual-kappa.json +++ b/certificates/joint-dual-kappa.json @@ -842,7 +842,7 @@ "scripts/experiments/pin_joint_dual_sources.py": "4d31cc0e38b7902709ca5f8f714cba109760d2592346dd7f8dc0b900a2d9fe00", "scripts/experiments/verify_joint_dual.py": "7a31bba1e9c0ded32ae285df2ca9bc91ef20c330f6789fdba361876f3c7a1985" }, - "source_manifest_sha256": "fd1aab7d75753b4b55b2377f26119dae74f367b0b4fab66cba42d944b3042cc9", + "source_manifest_sha256": "900d2c4d716cd547c44e5ea3d0e340e940f431e7e0e809bfffe0851a8b8ee106", "sources": [ { "files": { diff --git a/certificates/joint-dual-validation.json b/certificates/joint-dual-validation.json index 99adb4cf74..64940c84c8 100644 --- a/certificates/joint-dual-validation.json +++ b/certificates/joint-dual-validation.json @@ -46,14 +46,6 @@ "histogram": { "0": 121045, "1": 42027, - "2": 38232, - "3": 6306, - "4": 18054, - "5": 8192, - "6": 4437, - "7": 1089, - "8": 3900, - "9": 331, "10": 2566, "11": 385, "12": 2901, @@ -64,8 +56,16 @@ "17": 187, "18": 8185, "19": 4473, + "2": 38232, "21": 27, - "22": 23 + "22": 23, + "3": 6306, + "4": 18054, + "5": 8192, + "6": 4437, + "7": 1089, + "8": 3900, + "9": 331 }, "output_roles": 5336, "rank_mass": 706330, @@ -81,14 +81,6 @@ "h": 23, "rank_histogram_with_side_growth_split_into_singletons": { "1": 52653, - "2": 32919, - "3": 6306, - "4": 18054, - "5": 8192, - "6": 4437, - "7": 1089, - "8": 3900, - "9": 331, "10": 2566, "11": 385, "12": 2901, @@ -99,8 +91,16 @@ "17": 187, "18": 8185, "19": 4473, + "2": 32919, "21": 27, - "22": 23 + "22": 23, + "3": 6306, + "4": 18054, + "5": 8192, + "6": 4437, + "7": 1089, + "8": 3900, + "9": 331 }, "rank_mass": 706330, "singles": 15939, @@ -157,14 +157,6 @@ "histogram": { "0": 159745, "1": 54602, - "2": 50062, - "3": 8295, - "4": 24232, - "5": 10287, - "6": 4330, - "7": 1843, - "8": 5262, - "9": 860, "10": 3073, "11": 85, "12": 3381, @@ -175,10 +167,18 @@ "17": 630, "18": 2510, "19": 369, + "2": 50062, "20": 10763, "21": 5705, "23": 39, - "24": 25 + "24": 25, + "3": 8295, + "4": 24232, + "5": 10287, + "6": 4330, + "7": 1843, + "8": 5262, + "9": 860 }, "output_roles": 6925, "rank_mass": 1009050, @@ -194,14 +194,6 @@ "h": 25, "rank_histogram_with_side_growth_split_into_singletons": { "1": 68402, - "2": 43162, - "3": 8295, - "4": 24232, - "5": 10287, - "6": 4330, - "7": 1843, - "8": 5262, - "9": 860, "10": 3073, "11": 85, "12": 3381, @@ -212,10 +204,18 @@ "17": 630, "18": 2510, "19": 369, + "2": 43162, "20": 10763, "21": 5705, "23": 39, - "24": 25 + "24": 25, + "3": 8295, + "4": 24232, + "5": 10287, + "6": 4330, + "7": 1843, + "8": 5262, + "9": 860 }, "rank_mass": 1009050, "singles": 20700, @@ -226,7 +226,7 @@ } }, "bit_saving": "2382370177/50000000000000", - "certificate_sha256": "2ed658f05365b28825e24a6e7bac9fc9cc015d5a5d63d9579f4ac6e0640ae559", + "certificate_sha256": "b673aada7e16fd981d5b02c48c8c76e188871c5b05e5dcafc23589d1e709fcc7", "kappa": "4764513337/100000000000000", "margins": 7, "producer_words_regenerated_and_matched": true, diff --git a/certificates/shrunk-birth-terminal-repository-validation.json b/certificates/shrunk-birth-terminal-repository-validation.json new file mode 100644 index 0000000000..9420390606 --- /dev/null +++ b/certificates/shrunk-birth-terminal-repository-validation.json @@ -0,0 +1,31 @@ +{ + "arithmetic_controls": 18, + "canonical_certificate_sha256": "63fe0b3d9d53a18ceb316adbd6053cfc9682e699da1f1d01314d408ee742dd4d", + "focused": { + "command": [ + "make", + "verify-shrunk-terminal" + ], + "elapsed_seconds": 61.742, + "environment": { + "CXX": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/split-dual-main-reconciliation/compiler/cxx.py", + "OMP_NUM_THREADS": "6", + "PR66_BOOST_INCLUDE": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/agent-pr51/deps/boost_1_85_0" + }, + "exit_code": 0, + "finished_at": "2026-10-09T02:27:37.238528+00:00", + "log_sha256": "8430020d5c27b2b20ef04879dd90aebea2ff4f1ceae16237a8dce3b0e73bf13c", + "source_manifest_sha256": "bb0e3fd7aba599f06e25e42516e0d321cd4c9b90aae6c16843c0a60d16028e23", + "source_manifest_unchanged": true, + "started_at": "2026-10-09T02:26:35.496161+00:00", + "tested_commit": "56b66d58297deca1d7dd130247d720e960f77a37" + }, + "focused_controls": 9, + "full_repository_verification": "Pending on a clean source commit; must pass before publication", + "lean_module_sha256": "8c69d10ece16816edaef9df72182c9eecef3b464f88c82e0b8435f09c94ad095", + "remote_ci": "Final publication-head check results are recorded separately to avoid a self-referential receipt commit.", + "scope": "Finite exact construction and rational arithmetic; inherited all-size interfaces remain conditional.", + "selected_physical_word_sha256": "11dfe85123d23c17b4e1f4309b7c5fdfdac55faef7563881f2f3db5b2dfae82e", + "source_manifest_sha256": "bb0e3fd7aba599f06e25e42516e0d321cd4c9b90aae6c16843c0a60d16028e23", + "status": "PASS focused selected portable verification; full repository verification required before publication" +} diff --git a/formal/lean/AuditAll.lean b/formal/lean/AuditAll.lean index a8b5830180..0166694cd9 100644 --- a/formal/lean/AuditAll.lean +++ b/formal/lean/AuditAll.lean @@ -388,3 +388,245 @@ import PRChecksC #print axioms PRChecksC.PR9.constraints_strict #print axioms PRChecksC.PR9.margin_values #print axioms PRChecksC.PR9.kappa_witness + +-- Selected shrunk-frame / birth-reuse / terminal-elision rational companion. +#print axioms KappaCheck.ShrunkBirthTerminal.network_counts +#print axioms KappaCheck.ShrunkBirthTerminal.initial_dimension_count +#print axioms KappaCheck.ShrunkBirthTerminal.rank_mass +#print axioms KappaCheck.ShrunkBirthTerminal.count_1 +#print axioms KappaCheck.ShrunkBirthTerminal.count_2 +#print axioms KappaCheck.ShrunkBirthTerminal.count_3 +#print axioms KappaCheck.ShrunkBirthTerminal.count_4 +#print axioms KappaCheck.ShrunkBirthTerminal.count_5 +#print axioms KappaCheck.ShrunkBirthTerminal.count_6 +#print axioms KappaCheck.ShrunkBirthTerminal.count_7 +#print axioms KappaCheck.ShrunkBirthTerminal.count_8 +#print axioms KappaCheck.ShrunkBirthTerminal.count_9 +#print axioms KappaCheck.ShrunkBirthTerminal.count_10 +#print axioms KappaCheck.ShrunkBirthTerminal.count_11 +#print axioms KappaCheck.ShrunkBirthTerminal.count_12 +#print axioms KappaCheck.ShrunkBirthTerminal.count_13 +#print axioms KappaCheck.ShrunkBirthTerminal.count_14 +#print axioms KappaCheck.ShrunkBirthTerminal.count_15 +#print axioms KappaCheck.ShrunkBirthTerminal.count_16 +#print axioms KappaCheck.ShrunkBirthTerminal.count_17 +#print axioms KappaCheck.ShrunkBirthTerminal.count_18 +#print axioms KappaCheck.ShrunkBirthTerminal.count_19 +#print axioms KappaCheck.ShrunkBirthTerminal.count_20 +#print axioms KappaCheck.ShrunkBirthTerminal.count_21 +#print axioms KappaCheck.ShrunkBirthTerminal.count_22 +#print axioms KappaCheck.ShrunkBirthTerminal.count_23 +#print axioms KappaCheck.ShrunkBirthTerminal.count_529 +#print axioms KappaCheck.ShrunkBirthTerminal.count_552 +#print axioms KappaCheck.ShrunkBirthTerminal.count_554 +#print axioms KappaCheck.ShrunkBirthTerminal.count_556 +#print axioms KappaCheck.ShrunkBirthTerminal.count_558 +#print axioms KappaCheck.ShrunkBirthTerminal.count_560 +#print axioms KappaCheck.ShrunkBirthTerminal.count_562 +#print axioms KappaCheck.ShrunkBirthTerminal.count_571 +#print axioms KappaCheck.ShrunkBirthTerminal.count_572 +#print axioms KappaCheck.ShrunkBirthTerminal.count_573 +#print axioms KappaCheck.ShrunkBirthTerminal.count_574 +#print axioms KappaCheck.ShrunkBirthTerminal.complete_child_support +#print axioms KappaCheck.ShrunkBirthTerminal.strict_child_contraction +#print axioms KappaCheck.ShrunkBirthTerminal.slack_a_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_a_below_b +#print axioms KappaCheck.ShrunkBirthTerminal.slack_b_below_one_over32 +#print axioms KappaCheck.ShrunkBirthTerminal.slack_beta_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_beta_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_phase_leaf_above_bit +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_below_internal +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_below_leaf +#print axioms KappaCheck.ShrunkBirthTerminal.slack_c_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_c_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_below_reservations +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_above_tau +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_above_sigma +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_above_internal +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_prime_above_lambda +#print axioms KappaCheck.ShrunkBirthTerminal.slack_compact_leaf +#print axioms KappaCheck.ShrunkBirthTerminal.slack_compact_reservations +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_prime_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_epsilon_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_epsilon_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_guard_width +#print axioms KappaCheck.ShrunkBirthTerminal.slack_K_geometry +#print axioms KappaCheck.ShrunkBirthTerminal.slack_K_dominates_log +#print axioms KappaCheck.ShrunkBirthTerminal.slack_record_suffix +#print axioms KappaCheck.ShrunkBirthTerminal.slack_phase_local +#print axioms KappaCheck.ShrunkBirthTerminal.slack_phase_boundary +#print axioms KappaCheck.ShrunkBirthTerminal.slack_gamma_sublinear +#print axioms KappaCheck.ShrunkBirthTerminal.slack_cell_above_band +#print axioms KappaCheck.ShrunkBirthTerminal.slack_prime_interval_packing +#print axioms KappaCheck.ShrunkBirthTerminal.slack_alpha_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_alpha_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_alpha_below_one_fourth +#print axioms KappaCheck.ShrunkBirthTerminal.slack_delta_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_delta_below_one_eighth +#print axioms KappaCheck.ShrunkBirthTerminal.slack_short_record_fallback +#print axioms KappaCheck.ShrunkBirthTerminal.slack_small_field_exposure +#print axioms KappaCheck.ShrunkBirthTerminal.slack_artificial_boundary +#print axioms KappaCheck.ShrunkBirthTerminal.slack_literal_scalar_guard +#print axioms KappaCheck.ShrunkBirthTerminal.slack_row_product_gap +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g1_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g2_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g3_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g4_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g5_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g6_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g7_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.margins_strict +#print axioms KappaCheck.ShrunkBirthTerminal.balanced_identities +#print axioms KappaCheck.ShrunkBirthTerminal.stopped_parameter_choice +#print axioms KappaCheck.ShrunkBirthTerminal.controlling_margin +#print axioms KappaCheck.ShrunkBirthTerminal.fixed_profile_grid_exclusion +#print axioms KappaCheck.ShrunkBirthTerminal.gain_over_pinned_bounds +#print axioms KappaCheck.ShrunkBirthTerminal.stock_bit_coarse +#print axioms KappaCheck.ShrunkBirthTerminal.stock_complex +#print axioms KappaCheck.ShrunkBirthTerminal.stock_ordinary_leaf +#print axioms KappaCheck.ShrunkBirthTerminal.row_stock +#print axioms KappaCheck.ShrunkBirthTerminal.semantic_constants +#print axioms KappaCheck.ShrunkBirthTerminal.finite_bridge +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_1 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_1 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_2 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_2 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_3 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_3 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_4 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_4 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_5 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_5 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_6 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_6 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_7 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_7 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_8 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_8 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_9 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_9 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_10 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_10 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_11 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_11 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_12 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_12 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_13 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_13 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_14 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_14 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_15 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_15 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_16 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_16 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_17 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_17 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_18 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_18 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_19 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_19 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_20 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_20 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_21 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_21 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_22 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_22 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_23 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_23 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_529 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_529 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_552 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_552 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_554 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_554 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_556 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_556 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_558 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_558 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_560 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_560 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_562 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_562 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_571 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_571 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_572 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_572 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_573 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_573 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_574 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_574 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_profile_link +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_moment +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_paid_moment +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_1 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_1 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_2 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_2 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_3 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_3 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_4 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_4 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_5 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_5 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_6 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_6 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_7 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_7 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_8 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_8 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_9 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_9 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_10 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_10 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_11 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_11 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_12 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_12 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_13 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_13 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_14 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_14 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_15 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_15 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_16 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_16 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_17 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_17 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_18 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_18 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_19 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_19 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_20 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_20 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_21 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_21 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_22 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_22 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_23 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_23 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_529 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_529 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_552 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_552 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_554 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_554 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_556 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_556 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_558 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_558 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_560 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_560 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_562 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_562 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_571 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_571 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_572 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_572 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_573 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_573 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_574 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_574 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_profile_link +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_moment +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_paid_moment diff --git a/formal/lean/KappaCheck.lean b/formal/lean/KappaCheck.lean index fae11c72de..4c62b280d3 100644 --- a/formal/lean/KappaCheck.lean +++ b/formal/lean/KappaCheck.lean @@ -5,3 +5,4 @@ import KappaCheck.Guard import KappaCheck.Frames import KappaCheck.Movement import KappaCheck.Layout +import KappaCheck.ShrunkBirthTerminal diff --git a/formal/lean/KappaCheck/ShrunkBirthTerminal.lean b/formal/lean/KappaCheck/ShrunkBirthTerminal.lean new file mode 100644 index 0000000000..985b71d41e --- /dev/null +++ b/formal/lean/KappaCheck/ShrunkBirthTerminal.lean @@ -0,0 +1,1248 @@ +import Mathlib.Tactic.NormNum +import Mathlib.Data.Nat.Choose.Basic + +/-! +Exact arithmetic companion for the shrunk-frame / birth-reuse / terminal-elision +composition. Prepared with OpenAI assistance. Upstream construction and analytic +credits are retained in the accompanying proof and source provenance. + +Scope: supplied physical-count arrays, all 47 parameter slacks, seven margins, +three row stocks, scalar guards and independent degree-eight moment arithmetic. +The physical-array derivation, real logarithm / exponential enclosure validity, +and all-size framed-word, stopped-product, tape, prime and recovery hypotheses +remain external. This is not an unconditional integer-multiplication theorem. +No sorry, native_decide or additional axioms are introduced. +-/ +namespace KappaCheck.ShrunkBirthTerminal +set_option maxRecDepth 20000 +set_option maxHeartbeats 8000000 + +-- Source SHA256 89b115978ab95d8e69e58472cde14a588157a3b3a8c577034c39ca0309eab34d: work/r12-audit/canonical-joint-expansion/joint-expansion/certificate.json +-- Source SHA256 3203dcb2709c3c8f1513c9ff31faafe9903f7ba14cdd7bbe1aaa38c9edbfcf43: work/r12-terminal/joint-expansion/READOUT_COST.json +-- Source SHA256 457287cf9986574cef50235644af77c893b3513e7a0872827b1cce352f4b62d5: work/r12-terminal/joint-expansion/physical-audit.json +-- Source SHA256 11dfe85123d23c17b4e1f4309b7c5fdfdac55faef7563881f2f3db5b2dfae82e: work/r12-terminal/joint-expansion/word.json.gz +def h : ℕ := 24 +def m : ℕ := h*h +def v : ℕ := Nat.choose h 3 +def n : ℕ := v*v +def virtualRoles : ℕ := 28705 +def births : ℕ := 2108 +def terminals : ℕ := 381 +def roles : ℕ := virtualRoles-births-terminals +def width : ℕ := 2*n+2*v*roles +def forwardHistogram : List (ℕ × ℕ) := [(1, 106459), (2, 65902), (3, 7179), (4, 14980), (5, 6582), (6, 3788), (7, 2901), (8, 5452), (9, 973), (10, 1911), (11, 1645), (12, 8295), (13, 3257), (14, 450), (15, 800), (16, 156), (17, 100), (18, 50), (19, 77), (20, 136), (21, 302), (22, 16), (23, 2071)] +def initialDimensionHistogram : List (ℕ × ℕ) := [(0, 23980), (2, 854), (4, 366), (6, 589), (8, 110), (10, 12), (19, 183), (20, 25), (21, 7), (22, 90)] +def counts : List (ℕ × ℕ) := + (forwardHistogram.map fun p => (p.1, 2*v*p.2)) ++ + (initialDimensionHistogram.map fun p => (m-h+p.1, 2*v*p.2)) ++ + [((h-1)^2, 2*n), (1, n)] +def count (t : ℕ) : ℕ := (counts.map fun p => if p.1=t then p.2 else 0).sum +def mass : ℕ := (counts.map fun p => p.1*p.2).sum + +theorem network_counts : h = 24 ∧ m = 576 ∧ v = 2024 ∧ n = 4096576 ∧ roles = 26216 ∧ width = 114315520 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose] + +theorem initial_dimension_count : (initialDimensionHistogram.map Prod.snd).sum = roles := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem rank_mass : mass = 65843877440 ∧ m*width-mass = 1862080 ∧ n-2*v*h*(h-1) = 1862080 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_1 : count 1 = 435042608 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_2 : count 2 = 266771296 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_3 : count 3 = 29060592 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_4 : count 4 = 60639040 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_5 : count 5 = 26643936 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_6 : count 6 = 15333824 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_7 : count 7 = 11743248 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_8 : count 8 = 22069696 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_9 : count 9 = 3938704 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_10 : count 10 = 7735728 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_11 : count 11 = 6658960 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_12 : count 12 = 33578160 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_13 : count 13 = 13184336 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_14 : count 14 = 1821600 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_15 : count 15 = 3238400 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_16 : count 16 = 631488 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_17 : count 17 = 404800 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_18 : count 18 = 202400 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_19 : count 19 = 311696 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_20 : count 20 = 550528 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_21 : count 21 = 1222496 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_22 : count 22 = 64768 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_23 : count 23 = 8383408 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_529 : count 529 = 8193152 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_552 : count 552 = 97071040 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_554 : count 554 = 3456992 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_556 : count 556 = 1481568 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_558 : count 558 = 2384272 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_560 : count 560 = 445280 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_562 : count 562 = 48576 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_571 : count 571 = 740784 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_572 : count 572 = 101200 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_573 : count 573 = 28336 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_574 : count 574 = 364320 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +def childSizes : List ℕ := [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 529, 552, 554, 556, 558, 560, 562, 571, 572, 573, 574] +theorem complete_child_support : ∀ p ∈ counts, p.2 ≠ 0 → p.1 ∈ childSizes := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram, childSizes] + +theorem strict_child_contraction : ∀ t ∈ childSizes, 0 < t ∧ t < m := by + norm_num [childSizes, h, m] + +def a : ℚ := (56407455433006738868999943092544566993261131 / 500000000000000000000000000000000000000000000000) +def b : ℚ := (56407455433006738869 / 500000000000000000000000) +def kappa : ℚ := (28200546274389 / 250000000000000000) +def eta : ℚ := (1 / 1000000000000000000000000) +def beta : ℚ := (1 / 1000000000000000000000000) +def backoff : ℚ := (1 / 1000000000000000000000000000000) +def actualBitSaving : ℚ := (1240189553 / 10000000000000) +def tau : ℚ := 1-a +def sigma : ℚ := 1-b +def qParam : ℚ := a*(1-2*eta) +def lp : ℚ := 1-qParam +def c : ℚ := qParam+eta/4 +def epsilon : ℚ := (1-eta)/(1+qParam) +def lam : ℚ := (tau+lp)/2 +def g : ℚ := epsilon*qParam +def r : ℚ := (g+1-epsilon)/2 +def delta : ℚ := eta/8 +def internal : ℚ := tau+(1-beta)*max (sigma-tau) 0 +def leaf : ℚ := sigma+beta*(1-sigma) + +def scalar : ℕ := 3116113870848 +def guardE : ℕ := 64*(width+m+scalar+1)^3 +def guardB : ℕ := mass+guardE +def literal : ℕ := 2*scalar*width^2+8*mass+4*width+4+32*m +def guardC : ℕ := 32*m*guardB^2 +def literalGap : ℚ := (guardE : ℚ)-literal +def rowCoefficient : ℕ := 367*27+200*27+9*28 +def rowGap : ℚ := 32000-(51/25)*rowCoefficient +def margins : List ℚ := [1-epsilon,a,g,a,min (1-epsilon-delta) (r-delta),1-epsilon-delta,epsilon] + +theorem slack_a_positive : (a) = ((56407455433006738868999943092544566993261131 / 500000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (a) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_a_below_b : (b-a) = ((56907455433006738869 / 500000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (b-a) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_b_below_one_over32 : (1/32-b) = ((15568592544566993261131 / 500000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1/32-b) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_beta_positive : (beta) = ((1 / 1000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (beta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_beta_below_one : (1-beta) = ((999999999999999999999999 / 1000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-beta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_phase_leaf_above_bit : ((1-beta)*b-a) = ((1 / 1000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((1-beta)*b-a) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_q_positive : (qParam) = ((28203727716503369434499915138816850489891696500056907455433006738869 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (qParam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_q_below_internal : (1-internal-qParam) = ((56407455433006738868999943092544566993261131 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-internal-qParam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_q_below_leaf : (1-leaf-qParam) = ((56657455433006738868999943092544566993261131 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-leaf-qParam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_c_positive : (c) = ((28203727716503369434562415138816850489891696500056907455433006738869 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (c) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_c_below_one : (1-c) = ((249971796272283496630565437584861183149510108303499943092544566993261131 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-c) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_q_below_reservations : (c-qParam) = ((1 / 4000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (c-qParam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_lambda_above_tau : (lam-tau) = ((56407455433006738868999943092544566993261131 / 500000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lam-tau) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_lambda_above_sigma : (lam-sigma) = ((113314910866013477737999943092544566993261131 / 500000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lam-sigma) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_lambda_above_internal : (lam-internal) = ((56407455433006738868999943092544566993261131 / 500000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lam-internal) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_lambda_prime_above_lambda : (lp-lam) = ((56407455433006738868999943092544566993261131 / 500000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lp-lam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_compact_leaf : (lp-leaf) = ((56657455433006738868999943092544566993261131 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lp-leaf) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_compact_reservations : (lp-(1-c)) = ((1 / 4000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lp-(1-c)) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_lambda_prime_below_one : (qParam) = ((28203727716503369434499915138816850489891696500056907455433006738869 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (qParam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_epsilon_positive : (epsilon) = ((249999750000249999750000000000000000000000000000000000000000000000 / 250027953699762803606630893284245532604957286739213317694137738869) : ℚ) ∧ (0 : ℚ) < (epsilon) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_epsilon_below_one : (1-epsilon) = ((28203699512803856630893284245532604957286739213317694137738869 / 250027953699762803606630893284245532604957286739213317694137738869) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_guard_width : (1-epsilon) = ((28203699512803856630893284245532604957286739213317694137738869 / 250027953699762803606630893284245532604957286739213317694137738869) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_K_geometry : (1-epsilon*(1+c)) = ((187528016199700303669130893284245532604957286739213317694137738869 / 250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon*(1+c)) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_K_dominates_log : (epsilon*c) = ((28203699512803856630705756229332904653617608320033448605133911713260786682305862261131 / 250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (epsilon*c) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_record_suffix : (1-epsilon) = ((28203699512803856630893284245532604957286739213317694137738869 / 250027953699762803606630893284245532604957286739213317694137738869) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_phase_local : (1-epsilon-delta) = ((225629596102430853046896246010561076854687282813257307569305994713260786682305862261131 / 2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon-delta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_phase_boundary : (r-delta) = ((45125919220486170609179226839152405128052151848024065087777233113260786682305862261131 / 400044725919620485770609429254792852167931658782741308310620382190400000000000000000000000) : ℚ) ∧ (0 : ℚ) < (r-delta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_gamma_sublinear : (1-epsilon-r) = ((1 / 2000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon-r) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_cell_above_band : (epsilon-(1-r)/2) = ((499999500000499999499999749972046300237196393369106715754467395042713260786682305862261131 / 1000111814799051214426523573136982130419829146956853270776550955476000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (epsilon-(1-r)/2) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_prime_interval_packing : (1-epsilon) = ((28203699512803856630893284245532604957286739213317694137738869 / 250027953699762803606630893284245532604957286739213317694137738869) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_alpha_positive : (r) = ((56407399025607713261536540537365447110966847533351142742872780713260786682305862261131 / 500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (r) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_alpha_below_one : (1-r) = ((499999500000499999500000250027953699762803606630893284245532604957286739213317694137738869 / 500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-r) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_alpha_below_one_fourth : (1/4-r) = ((124957569450855794090053910101585400855367676522073307704325996653786739213317694137738869 / 500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1/4-r) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_delta_positive : (delta) = ((1 / 8000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (delta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_delta_below_one_eighth : (1/8-delta) = ((999999999999999999999999 / 8000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1/8-delta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_short_record_fallback : (epsilon-a) = ((124985771559469674632287261529685377995480559442484781152571541385040823194886876611665983695762005501567194399161 / 125013976849881401803315446642122766302478643369606658847068869434500000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (epsilon-a) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_small_field_exposure : (1-epsilon-g) = ((1 / 1000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon-g) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_artificial_boundary : (8-epsilon+r-delta-g) = ((14001791036782819432824377920275575186005677171202332185161413102487860217639953082413216607 / 2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (8-epsilon+r-delta-g) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_literal_scalar_guard : (literalGap) = (1936723974066543198917496885658826453564 : ℚ) ∧ (0 : ℚ) < (literalGap) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_row_product_gap : (rowGap) = ((6389 / 25) : ℚ) ∧ (0 : ℚ) < (rowGap) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g1_above_kappa : ((1-epsilon)-kappa) = ((12837801344731479849844430239564663423413902568985912017495473959 / 62506988424940700901657723321061383151239321684803329423534434717250000000000000000) : ℚ) ∧ (0 : ℚ) < ((1-epsilon)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g2_above_kappa : ((a)-kappa) = ((6362884228738868999943092544566993261131 / 500000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((a)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g3_above_kappa : ((g)-kappa) = ((51350955350972219636574114327365369448123005318656908856664201698261131 / 250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((g)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g4_above_kappa : ((a)-kappa) = ((6362884228738868999943092544566993261131 / 500000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((a)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g5_above_kappa : ((min (1-epsilon-delta) (r-delta))-kappa) = ((82161678578327771276200746902320561664316371484223097698653339199861131 / 400044725919620485770609429254792852167931658782741308310620382190400000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((min (1-epsilon-delta) (r-delta))-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g6_above_kappa : ((1-epsilon-delta)-kappa) = ((410809393003453655432218161035175945303712277250262445346537472550261131 / 2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((1-epsilon-delta)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g7_above_kappa : ((epsilon)-kappa) = ((62492886575184298986180078023670096698605108554761333999879467851735912017495473959 / 62506988424940700901657723321061383151239321684803329423534434717250000000000000000) : ℚ) ∧ (0 : ℚ) < ((epsilon)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem margins_strict : ∀ x ∈ margins, kappa < x := by + norm_num [margins, a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem balanced_identities : 1-epsilon-g = eta ∧ 1-epsilon-r = eta/2 ∧ 1-epsilon*(1+c) = eta-epsilon*eta/4 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem stopped_parameter_choice : a = min actualBitSaving ((1-beta)*b-backoff) ∧ 0 < eta ∧ eta < 1/2 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem controlling_margin : kappa < g ∧ g < kappa+1/1000000000000000000 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem fixed_profile_grid_exclusion : (b+1/1000000000000000000000000)/(1+b+1/1000000000000000000000000) < kappa+1/1000000000000000000 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem gain_over_pinned_bounds : kappa > (384569/10000000000 : ℚ) ∧ kappa > (52789616935221/1000000000000000000 : ℚ) ∧ kappa > (111192082577/1000000000000000 : ℚ) ∧ (1/2^14 : ℚ) < kappa ∧ kappa < (1/2^13 : ℚ) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem stock_bit_coarse : (529:ℕ)^367 > 2*528^367 ∧ (529:ℕ)^366 ≤ 2*528^366 ∧ (2:ℕ)^26 ≤ 108516254 ∧ 108516254 < (2:ℕ)^27 := by + norm_num [] + +theorem stock_complex : (576:ℕ)^200 > 2*574^200 ∧ (576:ℕ)^199 ≤ 2*574^199 ∧ (2:ℕ)^26 ≤ 114315520 ∧ 114315520 < (2:ℕ)^27 := by + norm_num [] + +theorem stock_ordinary_leaf : (575:ℕ)^9 > 2*529^9 ∧ (575:ℕ)^8 ≤ 2*529^8 ∧ (2:ℕ)^27 ≤ 188181929 ∧ 188181929 < (2:ℕ)^28 := by + norm_num [] + +theorem row_stock : rowCoefficient = 15561 ∧ rowGap = (6389/25 : ℚ) ∧ 4*(32000:ℕ) = 128000 := by + norm_num [rowCoefficient, rowGap] + +theorem semantic_constants : guardE = 1936723974147986188574068436730358952000 ∧ guardB = 1936723974147986188574068436796202829440 ∧ guardC = 69136584229593344553734547662349298866110568132764137982571664415937240220513075200 ∧ literal = 81442989656571551071532498436 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem finite_bridge : guardE > literal ∧ 2*guardB*(m-574) ≥ mass+guardE ∧ guardC > 2*guardB+18 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +-- The analytic meaning of supplied log intervals is external. These +-- statements prove exact rational Taylor inequalities and complete paid sums. +def taylor8 (x : ℚ) : ℚ := 1+x+x^2/2+x^3/6+x^4/24+x^5/120+x^6/720+x^7/5040+x^8/40320 +def expUpper (x : ℚ) : ℚ := taylor8 x+x^9/362880/(1-x/10) + +def accepted_1 : ℚ := (10007173208708459192443081796658477476273 / 10000000000000000000000000000000000000000) +theorem accepted_interval_1 : (0 : ℚ) ≤ b*(3178053830347945619646941601297 / 500000000000000000000000000000) ∧ b*(3178053830347945619646941601297 / 500000000000000000000000000000) ≤ b*(1271221532139178247858776640519 / 200000000000000000000000000000) ∧ b*(1271221532139178247858776640519 / 200000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_1 : expUpper (b*(1271221532139178247858776640519 / 200000000000000000000000000000)) ≤ accepted_1 := by + norm_num [expUpper, taylor8, b, accepted_1] + +def accepted_2 : ℚ := (2001278141000794096250171811675050044519 / 2000000000000000000000000000000000000000) +theorem accepted_interval_2 : (0 : ℚ) ≤ b*(1132592096027189185975330216227 / 200000000000000000000000000000) ∧ b*(1132592096027189185975330216227 / 200000000000000000000000000000) ≤ b*(353935030008496620617290692571 / 62500000000000000000000000000) ∧ b*(353935030008496620617290692571 / 62500000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_2 : expUpper (b*(353935030008496620617290692571 / 62500000000000000000000000000)) ≤ accepted_2 := by + norm_num [expUpper, taylor8, b, accepted_2] + +def accepted_3 : ℚ := (5002966499022595054406188132806194434321 / 5000000000000000000000000000000000000000) +theorem accepted_interval_3 : (0 : ℚ) ≤ b*(5257495372027781547898637965671 / 1000000000000000000000000000000) ∧ b*(5257495372027781547898637965671 / 1000000000000000000000000000000) ≤ b*(657186921503472693487329745709 / 125000000000000000000000000000) ∧ b*(657186921503472693487329745709 / 125000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_3 : expUpper (b*(657186921503472693487329745709 / 125000000000000000000000000000)) ≤ accepted_3 := by + norm_num [expUpper, taylor8, b, accepted_3] + +def accepted_4 : ℚ := (10005608262486795586682598316938196351633 / 10000000000000000000000000000000000000000) +theorem accepted_interval_4 : (0 : ℚ) ≤ b*(4969813299576000620459418959677 / 1000000000000000000000000000000) ∧ b*(4969813299576000620459418959677 / 1000000000000000000000000000000) ≤ b*(2484906649788000310229709479839 / 500000000000000000000000000000) ∧ b*(2484906649788000310229709479839 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_4 : expUpper (b*(2484906649788000310229709479839 / 500000000000000000000000000000)) ≤ accepted_4 := by + norm_num [expUpper, taylor8, b, accepted_4] + +def accepted_5 : ℚ := (5002678192638354252310939591491486682637 / 5000000000000000000000000000000000000000) +theorem accepted_interval_5 : (0 : ℚ) ≤ b*(4746669748261790864693123869367 / 1000000000000000000000000000000) ∧ b*(4746669748261790864693123869367 / 1000000000000000000000000000000) ≤ b*(593333718532723858086640483671 / 125000000000000000000000000000) ∧ b*(593333718532723858086640483671 / 125000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_5 : expUpper (b*(593333718532723858086640483671 / 125000000000000000000000000000)) ≤ accepted_5 := by + norm_num [expUpper, taylor8, b, accepted_5] + +def accepted_6 : ℚ := (10005150591318081334437472307882593960501 / 10000000000000000000000000000000000000000) +theorem accepted_interval_6 : (0 : ℚ) ≤ b*(4564348191467836238481405844213 / 1000000000000000000000000000000) ∧ b*(4564348191467836238481405844213 / 1000000000000000000000000000000) ≤ b*(2282174095733918119240702922107 / 500000000000000000000000000000) ∧ b*(2282174095733918119240702922107 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_6 : expUpper (b*(2282174095733918119240702922107 / 500000000000000000000000000000)) ≤ accepted_6 := by + norm_num [expUpper, taylor8, b, accepted_6] + +def accepted_7 : ℚ := (10004976598307617933072074586029358175999 / 10000000000000000000000000000000000000000) +theorem accepted_interval_7 : (0 : ℚ) ≤ b*(88203950232811558683770609183 / 20000000000000000000000000000) ∧ b*(88203950232811558683770609183 / 20000000000000000000000000000) ≤ b*(4410197511640577934188530459151 / 1000000000000000000000000000000) ∧ b*(4410197511640577934188530459151 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_7 : expUpper (b*(4410197511640577934188530459151 / 1000000000000000000000000000000)) ≤ accepted_7 := by + norm_num [expUpper, taylor8, b, accepted_7] + +def accepted_8 : ℚ := (1250603235144018751348201924633183002973 / 1250000000000000000000000000000000000000) +theorem accepted_interval_8 : (0 : ℚ) ≤ b*(4276666119016055311042186838219 / 1000000000000000000000000000000) ∧ b*(4276666119016055311042186838219 / 1000000000000000000000000000000) ≤ b*(213833305950802765552109341911 / 50000000000000000000000000000) ∧ b*(213833305950802765552109341911 / 50000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_8 : expUpper (b*(213833305950802765552109341911 / 50000000000000000000000000000)) ≤ accepted_8 := by + norm_num [expUpper, taylor8, b, accepted_8] + +def accepted_9 : ℚ := (10004692941083916304711037875234252480853 / 10000000000000000000000000000000000000000) +theorem accepted_interval_9 : (0 : ℚ) ≤ b*(4158883083359671856503392728749 / 1000000000000000000000000000000) ∧ b*(4158883083359671856503392728749 / 1000000000000000000000000000000) ≤ b*(3327106466687737485202714183 / 800000000000000000000000000) ∧ b*(3327106466687737485202714183 / 800000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_9 : expUpper (b*(3327106466687737485202714183 / 800000000000000000000000000)) ≤ accepted_9 := by + norm_num [expUpper, taylor8, b, accepted_9] + +def accepted_10 : ℚ := (2000914804727484006991228354413582185253 / 2000000000000000000000000000000000000000) +theorem accepted_interval_10 : (0 : ℚ) ≤ b*(4053522567701845555275891747909 / 1000000000000000000000000000000) ∧ b*(4053522567701845555275891747909 / 1000000000000000000000000000000) ≤ b*(405352256770184555527589174791 / 100000000000000000000000000000) ∧ b*(405352256770184555527589174791 / 100000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_10 : expUpper (b*(405352256770184555527589174791 / 100000000000000000000000000000)) ≤ accepted_10 := by + norm_num [expUpper, taylor8, b, accepted_10] + +def accepted_11 : ℚ := (10004466450939586496552205020318496489341 / 10000000000000000000000000000000000000000) +theorem accepted_interval_11 : (0 : ℚ) ≤ b*(989553096974380173807984906157 / 250000000000000000000000000000) ∧ b*(989553096974380173807984906157 / 250000000000000000000000000000) ≤ b*(3958212387897520695231939624629 / 1000000000000000000000000000000) ∧ b*(3958212387897520695231939624629 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_11 : expUpper (b*(3958212387897520695231939624629 / 1000000000000000000000000000000)) ≤ accepted_11 := by + norm_num [expUpper, taylor8, b, accepted_11] + +def accepted_12 : ℚ := (2501092061442675825070071222311488555861 / 2500000000000000000000000000000000000000) +theorem accepted_interval_12 : (0 : ℚ) ≤ b*(774240202181578185812834744551 / 200000000000000000000000000000) ∧ b*(774240202181578185812834744551 / 200000000000000000000000000000) ≤ b*(967800252726972732266043430689 / 250000000000000000000000000000) ∧ b*(967800252726972732266043430689 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_12 : expUpper (b*(967800252726972732266043430689 / 250000000000000000000000000000)) ≤ accepted_12 := by + norm_num [expUpper, taylor8, b, accepted_12] + +def accepted_13 : ℚ := (1000427790662396194996233470122394286203 / 1000000000000000000000000000000000000000) +theorem accepted_interval_13 : (0 : ℚ) ≤ b*(947789575808588625810098940257 / 250000000000000000000000000000) ∧ b*(947789575808588625810098940257 / 250000000000000000000000000000) ≤ b*(3791158303234354503240395761029 / 1000000000000000000000000000000) ∧ b*(3791158303234354503240395761029 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_13 : expUpper (b*(3791158303234354503240395761029 / 1000000000000000000000000000000)) ≤ accepted_13 := by + norm_num [expUpper, taylor8, b, accepted_13] + +def accepted_14 : ℚ := (1250524283295687260942300726950585983367 / 1250000000000000000000000000000000000000) +theorem accepted_interval_14 : (0 : ℚ) ≤ b*(929262582770158156192824584423 / 250000000000000000000000000000) ∧ b*(929262582770158156192824584423 / 250000000000000000000000000000) ≤ b*(3717050331080632624771298337693 / 1000000000000000000000000000000) ∧ b*(3717050331080632624771298337693 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_14 : expUpper (b*(3717050331080632624771298337693 / 1000000000000000000000000000000)) ≤ accepted_14 := by + norm_num [expUpper, taylor8, b, accepted_14] + +def accepted_15 : ℚ := (10004116399776304731797587454524115614907 / 10000000000000000000000000000000000000000) +theorem accepted_interval_15 : (0 : ℚ) ≤ b*(729611491918736234659575726489 / 200000000000000000000000000000) ∧ b*(729611491918736234659575726489 / 200000000000000000000000000000) ≤ b*(1824028729796840586648939316223 / 500000000000000000000000000000) ∧ b*(1824028729796840586648939316223 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_15 : expUpper (b*(1824028729796840586648939316223 / 500000000000000000000000000000)) ≤ accepted_15 := by + norm_num [expUpper, taylor8, b, accepted_15] + +def accepted_16 : ℚ := (5002021780497624814863799490608923226717 / 5000000000000000000000000000000000000000) +theorem accepted_interval_16 : (0 : ℚ) ≤ b*(3583518938456110001624954716761 / 1000000000000000000000000000000) ∧ b*(3583518938456110001624954716761 / 1000000000000000000000000000000) ≤ b*(1791759469228055000812477358381 / 500000000000000000000000000000) ∧ b*(1791759469228055000812477358381 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_16 : expUpper (b*(1791759469228055000812477358381 / 500000000000000000000000000000)) ≤ accepted_16 := by + norm_num [expUpper, taylor8, b, accepted_16] + +def accepted_17 : ℚ := (1000397513996078830412133154494488397217 / 1000000000000000000000000000000000000000) +theorem accepted_interval_17 : (0 : ℚ) ≤ b*(44036178957995939488054357309 / 12500000000000000000000000000) ∧ b*(44036178957995939488054357309 / 12500000000000000000000000000) ≤ b*(3522894316639675159044348584721 / 1000000000000000000000000000000) ∧ b*(3522894316639675159044348584721 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_17 : expUpper (b*(3522894316639675159044348584721 / 1000000000000000000000000000000)) ≤ accepted_17 := by + norm_num [expUpper, taylor8, b, accepted_17] + +def accepted_18 : ℚ := (2500977657830542212572203647666043033353 / 2500000000000000000000000000000000000000) +theorem accepted_interval_18 : (0 : ℚ) ≤ b*(346573590279972654708616060729 / 100000000000000000000000000000) ∧ b*(346573590279972654708616060729 / 100000000000000000000000000000) ≤ b*(3465735902799726547086160607291 / 1000000000000000000000000000000) ∧ b*(3465735902799726547086160607291 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_18 : expUpper (b*(3465735902799726547086160607291 / 1000000000000000000000000000000)) ≤ accepted_18 := by + norm_num [expUpper, taylor8, b, accepted_18] + +def accepted_19 : ℚ := (10003849611767539530251041249190273494001 / 10000000000000000000000000000000000000000) +theorem accepted_interval_19 : (0 : ℚ) ≤ b*(1705834340764725389642427885353 / 500000000000000000000000000000) ∧ b*(1705834340764725389642427885353 / 500000000000000000000000000000) ≤ b*(3411668681529450779284855770707 / 1000000000000000000000000000000) ∧ b*(3411668681529450779284855770707 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_19 : expUpper (b*(3411668681529450779284855770707 / 1000000000000000000000000000000)) ≤ accepted_19 := by + norm_num [expUpper, taylor8, b, accepted_19] + +def accepted_20 : ℚ := (10003791723174336695859928379092107147311 / 10000000000000000000000000000000000000000) +theorem accepted_interval_20 : (0 : ℚ) ≤ b*(3360375387141900245858659626451 / 1000000000000000000000000000000) ∧ b*(3360375387141900245858659626451 / 1000000000000000000000000000000) ≤ b*(840093846785475061464664906613 / 250000000000000000000000000000) ∧ b*(840093846785475061464664906613 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_20 : expUpper (b*(840093846785475061464664906613 / 250000000000000000000000000000)) ≤ accepted_20 := by + norm_num [expUpper, taylor8, b, accepted_20] + +def accepted_21 : ℚ := (10003736659875036312749799798518888013029 / 10000000000000000000000000000000000000000) +theorem accepted_interval_21 : (0 : ℚ) ≤ b*(827896305743117060698321305557 / 250000000000000000000000000000) ∧ b*(827896305743117060698321305557 / 250000000000000000000000000000) ≤ b*(3311585222972468242793285222229 / 1000000000000000000000000000000) ∧ b*(3311585222972468242793285222229 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_21 : expUpper (b*(3311585222972468242793285222229 / 1000000000000000000000000000000)) ≤ accepted_21 := by + norm_num [expUpper, taylor8, b, accepted_21] + +def accepted_22 : ℚ := (5001842079444036409320152786470891628601 / 5000000000000000000000000000000000000000) +theorem accepted_interval_22 : (0 : ℚ) ≤ b*(326506520733757538581470750317 / 100000000000000000000000000000) ∧ b*(326506520733757538581470750317 / 100000000000000000000000000000) ≤ b*(3265065207337575385814707503171 / 1000000000000000000000000000000) ∧ b*(3265065207337575385814707503171 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_22 : expUpper (b*(3265065207337575385814707503171 / 1000000000000000000000000000000)) ≤ accepted_22 := by + norm_num [expUpper, taylor8, b, accepted_22] + +def accepted_23 : ℚ := (10003633992322138767059090899422809010713 / 10000000000000000000000000000000000000000) +theorem accepted_interval_23 : (0 : ℚ) ≤ b*(3220613444766741548487130370783 / 1000000000000000000000000000000) ∧ b*(3220613444766741548487130370783 / 1000000000000000000000000000000) ≤ b*(100644170148960673390222824087 / 31250000000000000000000000000) ∧ b*(100644170148960673390222824087 / 31250000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_23 : expUpper (b*(100644170148960673390222824087 / 31250000000000000000000000000)) ≤ accepted_23 := by + norm_num [expUpper, taylor8, b, accepted_23] + +def accepted_529 : ℚ := (2500024006910801357156667820225605837451 / 2500000000000000000000000000000000000000) +theorem accepted_interval_529 : (0 : ℚ) ≤ b*(85119228837591857680377538973 / 1000000000000000000000000000000) ∧ b*(85119228837591857680377538973 / 1000000000000000000000000000000) ≤ b*(42559614418795928840188769487 / 500000000000000000000000000000) ∧ b*(42559614418795928840188769487 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_529 : expUpper (b*(42559614418795928840188769487 / 500000000000000000000000000000)) ≤ accepted_529 := by + norm_num [expUpper, taylor8, b, accepted_529] + +def accepted_552 : ℚ := (10000048013706336914502962445538143648637 / 10000000000000000000000000000000000000000) +theorem accepted_interval_552 : (0 : ℚ) ≤ b*(21279807209397964420094384743 / 500000000000000000000000000000) ∧ b*(21279807209397964420094384743 / 500000000000000000000000000000) ≤ b*(42559614418795928840188769487 / 1000000000000000000000000000000) ∧ b*(42559614418795928840188769487 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_552 : expUpper (b*(42559614418795928840188769487 / 1000000000000000000000000000000)) ≤ accepted_552 := by + norm_num [expUpper, taylor8, b, accepted_552] + +def accepted_554 : ℚ := (400001757343114255072912651180621264047 / 400000000000000000000000000000000000000) +theorem accepted_interval_554 : (0 : ℚ) ≤ b*(38942973948607430007253531611 / 1000000000000000000000000000000) ∧ b*(38942973948607430007253531611 / 1000000000000000000000000000000) ≤ b*(9735743487151857501813382903 / 250000000000000000000000000000) ∧ b*(9735743487151857501813382903 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_554 : expUpper (b*(9735743487151857501813382903 / 250000000000000000000000000000)) ≤ accepted_554 := by + norm_num [expUpper, taylor8, b, accepted_554] + +def accepted_556 : ℚ := (5000019934077114581960794678319392907493 / 5000000000000000000000000000000000000000) +theorem accepted_interval_556 : (0 : ℚ) ≤ b*(17669683222654431635317020401 / 500000000000000000000000000000) ∧ b*(17669683222654431635317020401 / 500000000000000000000000000000) ≤ b*(35339366445308863270634040803 / 1000000000000000000000000000000) ∧ b*(35339366445308863270634040803 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_556 : expUpper (b*(35339366445308863270634040803 / 1000000000000000000000000000000)) ≤ accepted_556 := by + norm_num [expUpper, taylor8, b, accepted_556] + +def accepted_558 : ℚ := (10000035817329848616000090876431682424381 / 10000000000000000000000000000000000000000) +theorem accepted_interval_558 : (0 : ℚ) ≤ b*(7937174578645075289249070687 / 250000000000000000000000000000) ∧ b*(7937174578645075289249070687 / 250000000000000000000000000000) ≤ b*(31748698314580301156996282749 / 1000000000000000000000000000000) ∧ b*(31748698314580301156996282749 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_558 : expUpper (b*(31748698314580301156996282749 / 1000000000000000000000000000000)) ≤ accepted_558 := by + norm_num [expUpper, taylor8, b, accepted_558] + +def accepted_560 : ℚ := (2000006356200048328919135749948149107147 / 2000000000000000000000000000000000000000) +theorem accepted_interval_560 : (0 : ℚ) ≤ b*(7042719241674080479710660023 / 250000000000000000000000000000) ∧ b*(7042719241674080479710660023 / 250000000000000000000000000000) ≤ b*(28170876966696321918842640093 / 1000000000000000000000000000000) ∧ b*(28170876966696321918842640093 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_560 : expUpper (b*(28170876966696321918842640093 / 1000000000000000000000000000000)) ≤ accepted_560 := by + norm_num [expUpper, taylor8, b, accepted_560] + +def accepted_562 : ℚ := (5000013879531026283516616597127113348633 / 5000000000000000000000000000000000000000) +theorem accepted_interval_562 : (0 : ℚ) ≤ b*(12302905401100082385006378221 / 500000000000000000000000000000) ∧ b*(12302905401100082385006378221 / 500000000000000000000000000000) ≤ b*(24605810802200164770012756443 / 1000000000000000000000000000000) ∧ b*(24605810802200164770012756443 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_562 : expUpper (b*(24605810802200164770012756443 / 1000000000000000000000000000000)) ≤ accepted_562 := by + norm_num [expUpper, taylor8, b, accepted_562] + +def accepted_571 : ℚ := (2500002458929401650667719229571399047519 / 2500000000000000000000000000000000000000) +theorem accepted_interval_571 : (0 : ℚ) ≤ b*(4359225519940511281958503327 / 500000000000000000000000000000) ∧ b*(4359225519940511281958503327 / 500000000000000000000000000000) ≤ b*(1743690207976204512783401331 / 200000000000000000000000000000) ∧ b*(1743690207976204512783401331 / 200000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_571 : expUpper (b*(1743690207976204512783401331 / 200000000000000000000000000000)) ≤ accepted_571 := by + norm_num [expUpper, taylor8, b, accepted_571] + +def accepted_572 : ℚ := (2500001965425291953393961431121574574217 / 2500000000000000000000000000000000000000) +theorem accepted_interval_572 : (0 : ℚ) ≤ b*(6968669316093340343987940147 / 1000000000000000000000000000000) ∧ b*(6968669316093340343987940147 / 1000000000000000000000000000000) ≤ b*(1742167329023335085996985037 / 250000000000000000000000000000) ∧ b*(1742167329023335085996985037 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_572 : expUpper (b*(1742167329023335085996985037 / 250000000000000000000000000000)) ≤ accepted_572 := by + norm_num [expUpper, taylor8, b, accepted_572] + +def accepted_573 : ℚ := (5000002945566591540622685978536652726911 / 5000000000000000000000000000000000000000) +theorem accepted_interval_573 : (0 : ℚ) ≤ b*(5221943981151675048688013469 / 1000000000000000000000000000000) ∧ b*(5221943981151675048688013469 / 1000000000000000000000000000000) ≤ b*(522194398115167504868801347 / 100000000000000000000000000000) ∧ b*(522194398115167504868801347 / 100000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_573 : expUpper (b*(522194398115167504868801347 / 100000000000000000000000000000)) ≤ accepted_573 := by + norm_num [expUpper, taylor8, b, accepted_573] + +def accepted_574 : ℚ := (5000001962000812862191416361841862291317 / 5000000000000000000000000000000000000000) +theorem accepted_interval_574 : (0 : ℚ) ≤ b*(695652875264964180906992931 / 200000000000000000000000000000) ∧ b*(695652875264964180906992931 / 200000000000000000000000000000) ≤ b*(217391523520301306533435291 / 62500000000000000000000000000) ∧ b*(217391523520301306533435291 / 62500000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_574 : expUpper (b*(217391523520301306533435291 / 62500000000000000000000000000)) ≤ accepted_574 := by + norm_num [expUpper, taylor8, b, accepted_574] + +def acceptedMoment : ℚ := + ((1*435042608 : ℚ)/(576*114315520))*accepted_1 + + ((2*266771296 : ℚ)/(576*114315520))*accepted_2 + + ((3*29060592 : ℚ)/(576*114315520))*accepted_3 + + ((4*60639040 : ℚ)/(576*114315520))*accepted_4 + + ((5*26643936 : ℚ)/(576*114315520))*accepted_5 + + ((6*15333824 : ℚ)/(576*114315520))*accepted_6 + + ((7*11743248 : ℚ)/(576*114315520))*accepted_7 + + ((8*22069696 : ℚ)/(576*114315520))*accepted_8 + + ((9*3938704 : ℚ)/(576*114315520))*accepted_9 + + ((10*7735728 : ℚ)/(576*114315520))*accepted_10 + + ((11*6658960 : ℚ)/(576*114315520))*accepted_11 + + ((12*33578160 : ℚ)/(576*114315520))*accepted_12 + + ((13*13184336 : ℚ)/(576*114315520))*accepted_13 + + ((14*1821600 : ℚ)/(576*114315520))*accepted_14 + + ((15*3238400 : ℚ)/(576*114315520))*accepted_15 + + ((16*631488 : ℚ)/(576*114315520))*accepted_16 + + ((17*404800 : ℚ)/(576*114315520))*accepted_17 + + ((18*202400 : ℚ)/(576*114315520))*accepted_18 + + ((19*311696 : ℚ)/(576*114315520))*accepted_19 + + ((20*550528 : ℚ)/(576*114315520))*accepted_20 + + ((21*1222496 : ℚ)/(576*114315520))*accepted_21 + + ((22*64768 : ℚ)/(576*114315520))*accepted_22 + + ((23*8383408 : ℚ)/(576*114315520))*accepted_23 + + ((529*8193152 : ℚ)/(576*114315520))*accepted_529 + + ((552*97071040 : ℚ)/(576*114315520))*accepted_552 + + ((554*3456992 : ℚ)/(576*114315520))*accepted_554 + + ((556*1481568 : ℚ)/(576*114315520))*accepted_556 + + ((558*2384272 : ℚ)/(576*114315520))*accepted_558 + + ((560*445280 : ℚ)/(576*114315520))*accepted_560 + + ((562*48576 : ℚ)/(576*114315520))*accepted_562 + + ((571*740784 : ℚ)/(576*114315520))*accepted_571 + + ((572*101200 : ℚ)/(576*114315520))*accepted_572 + + ((573*28336 : ℚ)/(576*114315520))*accepted_573 + + ((574*364320 : ℚ)/(576*114315520))*accepted_574 +def acceptedFromCounts : ℚ := + ((1*(count 1 : ℚ))/(m*width))*accepted_1 + + ((2*(count 2 : ℚ))/(m*width))*accepted_2 + + ((3*(count 3 : ℚ))/(m*width))*accepted_3 + + ((4*(count 4 : ℚ))/(m*width))*accepted_4 + + ((5*(count 5 : ℚ))/(m*width))*accepted_5 + + ((6*(count 6 : ℚ))/(m*width))*accepted_6 + + ((7*(count 7 : ℚ))/(m*width))*accepted_7 + + ((8*(count 8 : ℚ))/(m*width))*accepted_8 + + ((9*(count 9 : ℚ))/(m*width))*accepted_9 + + ((10*(count 10 : ℚ))/(m*width))*accepted_10 + + ((11*(count 11 : ℚ))/(m*width))*accepted_11 + + ((12*(count 12 : ℚ))/(m*width))*accepted_12 + + ((13*(count 13 : ℚ))/(m*width))*accepted_13 + + ((14*(count 14 : ℚ))/(m*width))*accepted_14 + + ((15*(count 15 : ℚ))/(m*width))*accepted_15 + + ((16*(count 16 : ℚ))/(m*width))*accepted_16 + + ((17*(count 17 : ℚ))/(m*width))*accepted_17 + + ((18*(count 18 : ℚ))/(m*width))*accepted_18 + + ((19*(count 19 : ℚ))/(m*width))*accepted_19 + + ((20*(count 20 : ℚ))/(m*width))*accepted_20 + + ((21*(count 21 : ℚ))/(m*width))*accepted_21 + + ((22*(count 22 : ℚ))/(m*width))*accepted_22 + + ((23*(count 23 : ℚ))/(m*width))*accepted_23 + + ((529*(count 529 : ℚ))/(m*width))*accepted_529 + + ((552*(count 552 : ℚ))/(m*width))*accepted_552 + + ((554*(count 554 : ℚ))/(m*width))*accepted_554 + + ((556*(count 556 : ℚ))/(m*width))*accepted_556 + + ((558*(count 558 : ℚ))/(m*width))*accepted_558 + + ((560*(count 560 : ℚ))/(m*width))*accepted_560 + + ((562*(count 562 : ℚ))/(m*width))*accepted_562 + + ((571*(count 571 : ℚ))/(m*width))*accepted_571 + + ((572*(count 572 : ℚ))/(m*width))*accepted_572 + + ((573*(count 573 : ℚ))/(m*width))*accepted_573 + + ((574*(count 574 : ℚ))/(m*width))*accepted_574 +theorem accepted_profile_link : acceptedFromCounts = acceptedMoment := by + norm_num [acceptedFromCounts, acceptedMoment, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, count_1, count_10, count_11, count_12, count_13, count_14, count_15, count_16, count_17, count_18, count_19, count_2, count_20, count_21, count_22, count_23, count_3, count_4, count_5, count_529, count_552, count_554, count_556, count_558, count_560, count_562, count_571, count_572, count_573, count_574, count_6, count_7, count_8, count_9] + +theorem accepted_moment : acceptedMoment < 1 ∧ acceptedMoment = (40665599999999999999999992105609200772387856393 / 40665600000000000000000000000000000000000000000) := by + norm_num [acceptedMoment, accepted_1, accepted_10, accepted_11, accepted_12, accepted_13, accepted_14, accepted_15, accepted_16, accepted_17, accepted_18, accepted_19, accepted_2, accepted_20, accepted_21, accepted_22, accepted_23, accepted_3, accepted_4, accepted_5, accepted_529, accepted_552, accepted_554, accepted_556, accepted_558, accepted_560, accepted_562, accepted_571, accepted_572, accepted_573, accepted_574, accepted_6, accepted_7, accepted_8, accepted_9] + +theorem accepted_paid_moment : acceptedFromCounts < 1 := by + rw [accepted_profile_link] + exact accepted_moment.1 + +def rejected_1 : ℚ := (5003586604354229596221572701664384374267 / 5000000000000000000000000000000000000000) +theorem rejected_interval_1 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(3178053830347945619646941601297 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3178053830347945619646941601297 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(1271221532139178247858776640519 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1271221532139178247858776640519 / 200000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_1 : rejected_1 ≤ taylor8 ((b+1/1000000000000000000000000)*(3178053830347945619646941601297 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_1] + +def rejected_2 : ℚ := (10006390705003970481250915724170359842273 / 10000000000000000000000000000000000000000) +theorem rejected_interval_2 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(1132592096027189185975330216227 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1132592096027189185975330216227 / 200000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(353935030008496620617290692571 / 62500000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(353935030008496620617290692571 / 62500000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_2 : rejected_2 ≤ taylor8 ((b+1/1000000000000000000000000)*(1132592096027189185975330216227 / 200000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_2] + +def rejected_3 : ℚ := (10005932998045190108812428871758817532111 / 10000000000000000000000000000000000000000) +theorem rejected_interval_3 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(5257495372027781547898637965671 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(5257495372027781547898637965671 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(657186921503472693487329745709 / 125000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(657186921503472693487329745709 / 125000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_3 : rejected_3 ≤ taylor8 ((b+1/1000000000000000000000000)*(5257495372027781547898637965671 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_3] + +def rejected_4 : ℚ := (1000560826248679558668264804294320832637 / 1000000000000000000000000000000000000000) +theorem rejected_interval_4 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4969813299576000620459418959677 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4969813299576000620459418959677 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(2484906649788000310229709479839 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(2484906649788000310229709479839 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_4 : rejected_4 ≤ taylor8 ((b+1/1000000000000000000000000)*(4969813299576000620459418959677 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_4] + +def rejected_5 : ℚ := (10005356385276708504621926675105446707631 / 10000000000000000000000000000000000000000) +theorem rejected_interval_5 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4746669748261790864693123869367 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4746669748261790864693123869367 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(593333718532723858086640483671 / 125000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(593333718532723858086640483671 / 125000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_5 : rejected_5 ≤ taylor8 ((b+1/1000000000000000000000000)*(4746669748261790864693123869367 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_5] + +def rejected_6 : ℚ := (5002575295659040667218758987436799803833 / 5000000000000000000000000000000000000000) +theorem rejected_interval_6 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4564348191467836238481405844213 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4564348191467836238481405844213 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(2282174095733918119240702922107 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(2282174095733918119240702922107 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_6 : rejected_6 ≤ taylor8 ((b+1/1000000000000000000000000)*(4564348191467836238481405844213 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_6] + +def rejected_7 : ℚ := (5002488299153808966536059354976127437137 / 5000000000000000000000000000000000000000) +theorem rejected_interval_7 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(88203950232811558683770609183 / 20000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(88203950232811558683770609183 / 20000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(4410197511640577934188530459151 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4410197511640577934188530459151 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_7 : rejected_7 ≤ taylor8 ((b+1/1000000000000000000000000)*(88203950232811558683770609183 / 20000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_7] + +def rejected_8 : ℚ := (10004825881152150010785658184365335434401 / 10000000000000000000000000000000000000000) +theorem rejected_interval_8 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4276666119016055311042186838219 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4276666119016055311042186838219 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(213833305950802765552109341911 / 50000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(213833305950802765552109341911 / 50000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_8 : rejected_8 ≤ taylor8 ((b+1/1000000000000000000000000)*(4276666119016055311042186838219 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_8] + +def rejected_9 : ℚ := (625293308817744769044442467723904887727 / 625000000000000000000000000000000000000) +theorem rejected_interval_9 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4158883083359671856503392728749 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4158883083359671856503392728749 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3327106466687737485202714183 / 800000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3327106466687737485202714183 / 800000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_9 : rejected_9 ≤ taylor8 ((b+1/1000000000000000000000000)*(4158883083359671856503392728749 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_9] + +def rejected_10 : ℚ := (10004574023637420034956182325834494831437 / 10000000000000000000000000000000000000000) +theorem rejected_interval_10 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4053522567701845555275891747909 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4053522567701845555275891747909 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(405352256770184555527589174791 / 100000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(405352256770184555527589174791 / 100000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_10 : rejected_10 ≤ taylor8 ((b+1/1000000000000000000000000)*(4053522567701845555275891747909 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_10] + +def rejected_11 : ℚ := (5002233225469793248276122310060767877723 / 5000000000000000000000000000000000000000) +theorem rejected_interval_11 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(989553096974380173807984906157 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(989553096974380173807984906157 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3958212387897520695231939624629 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3958212387897520695231939624629 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_11 : rejected_11 ≤ taylor8 ((b+1/1000000000000000000000000)*(989553096974380173807984906157 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_11] + +def rejected_12 : ℚ := (10004368245770703300280323618166419601223 / 10000000000000000000000000000000000000000) +theorem rejected_interval_12 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(774240202181578185812834744551 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(774240202181578185812834744551 / 200000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(967800252726972732266043430689 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(967800252726972732266043430689 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_12 : rejected_12 ≤ taylor8 ((b+1/1000000000000000000000000)*(774240202181578185812834744551 / 200000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_12] + +def rejected_13 : ℚ := (10004277906623961949962372629025195281639 / 10000000000000000000000000000000000000000) +theorem rejected_interval_13 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(947789575808588625810098940257 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(947789575808588625810098940257 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3791158303234354503240395761029 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3791158303234354503240395761029 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_13 : rejected_13 ≤ taylor8 ((b+1/1000000000000000000000000)*(947789575808588625810098940257 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_13] + +def rejected_14 : ℚ := (2000838853273099617507688600339659343221 / 2000000000000000000000000000000000000000) +theorem rejected_interval_14 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(929262582770158156192824584423 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(929262582770158156192824584423 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3717050331080632624771298337693 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3717050331080632624771298337693 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_14 : rejected_14 ≤ taylor8 ((b+1/1000000000000000000000000)*(929262582770158156192824584423 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_14] + +def rejected_15 : ℚ := (10004116399776304731797623950115573324387 / 10000000000000000000000000000000000000000) +theorem rejected_interval_15 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(729611491918736234659575726489 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(729611491918736234659575726489 / 200000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(1824028729796840586648939316223 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1824028729796840586648939316223 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_15 : rejected_15 ≤ taylor8 ((b+1/1000000000000000000000000)*(729611491918736234659575726489 / 200000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_15] + +def rejected_16 : ℚ := (5002021780497624814863817415448703641629 / 5000000000000000000000000000000000000000) +theorem rejected_interval_16 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(3583518938456110001624954716761 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3583518938456110001624954716761 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(1791759469228055000812477358381 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1791759469228055000812477358381 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_16 : rejected_16 ≤ taylor8 ((b+1/1000000000000000000000000)*(3583518938456110001624954716761 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_16] + +def rejected_17 : ℚ := (10003975139960788304121366787892047209213 / 10000000000000000000000000000000000000000) +theorem rejected_interval_17 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(44036178957995939488054357309 / 12500000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(44036178957995939488054357309 / 12500000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3522894316639675159044348584721 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3522894316639675159044348584721 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_17 : rejected_17 ≤ taylor8 ((b+1/1000000000000000000000000)*(44036178957995939488054357309 / 12500000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_17] + +def rejected_18 : ℚ := (1250488828915271106286106157697051796507 / 1250000000000000000000000000000000000000) +theorem rejected_interval_18 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(346573590279972654708616060729 / 100000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(346573590279972654708616060729 / 100000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3465735902799726547086160607291 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3465735902799726547086160607291 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_18 : rejected_18 ≤ taylor8 ((b+1/1000000000000000000000000)*(346573590279972654708616060729 / 100000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_18] + +def rejected_19 : ℚ := (5001924805883769765125537689505343779089 / 5000000000000000000000000000000000000000) +theorem rejected_interval_19 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(1705834340764725389642427885353 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1705834340764725389642427885353 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3411668681529450779284855770707 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3411668681529450779284855770707 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_19 : rejected_19 ≤ taylor8 ((b+1/1000000000000000000000000)*(1705834340764725389642427885353 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_19] + +def rejected_20 : ℚ := (400151668926973467834398479823503626527 / 400000000000000000000000000000000000000) +theorem rejected_interval_20 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(3360375387141900245858659626451 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3360375387141900245858659626451 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(840093846785475061464664906613 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(840093846785475061464664906613 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_20 : rejected_20 ≤ taylor8 ((b+1/1000000000000000000000000)*(3360375387141900245858659626451 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_20] + +def rejected_21 : ℚ := (10003736659875036312749832926745384230677 / 10000000000000000000000000000000000000000) +theorem rejected_interval_21 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(827896305743117060698321305557 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(827896305743117060698321305557 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3311585222972468242793285222229 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3311585222972468242793285222229 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_21 : rejected_21 ≤ taylor8 ((b+1/1000000000000000000000000)*(827896305743117060698321305557 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_21] + +def rejected_22 : ℚ := (100036841588880728186403382356228745047 / 100000000000000000000000000000000000000) +theorem rejected_interval_22 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(326506520733757538581470750317 / 100000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(326506520733757538581470750317 / 100000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3265065207337575385814707503171 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3265065207337575385814707503171 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_22 : rejected_22 ≤ taylor8 ((b+1/1000000000000000000000000)*(326506520733757538581470750317 / 100000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_22] + +def rejected_23 : ℚ := (5001816996161069383529561558630470038693 / 5000000000000000000000000000000000000000) +theorem rejected_interval_23 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(3220613444766741548487130370783 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3220613444766741548487130370783 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(100644170148960673390222824087 / 31250000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(100644170148960673390222824087 / 31250000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_23 : rejected_23 ≤ taylor8 ((b+1/1000000000000000000000000)*(3220613444766741548487130370783 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_23] + +def rejected_529 : ℚ := (10000096027643205428626672132102884396499 / 10000000000000000000000000000000000000000) +theorem rejected_interval_529 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(85119228837591857680377538973 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(85119228837591857680377538973 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(42559614418795928840188769487 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(42559614418795928840188769487 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_529 : rejected_529 ≤ taylor8 ((b+1/1000000000000000000000000)*(85119228837591857680377538973 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_529] + +def rejected_552 : ℚ := (10000048013706336914502962871136330153269 / 10000000000000000000000000000000000000000) +theorem rejected_interval_552 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(21279807209397964420094384743 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(21279807209397964420094384743 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(42559614418795928840188769487 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(42559614418795928840188769487 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_552 : rejected_552 ≤ taylor8 ((b+1/1000000000000000000000000)*(21279807209397964420094384743 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_552] + +def rejected_554 : ℚ := (1250005491697232047102852083618372607909 / 1250000000000000000000000000000000000000) +theorem rejected_interval_554 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(38942973948607430007253531611 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(38942973948607430007253531611 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(9735743487151857501813382903 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(9735743487151857501813382903 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_554 : rejected_554 ≤ taylor8 ((b+1/1000000000000000000000000)*(38942973948607430007253531611 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_554] + +def rejected_556 : ℚ := (156250622939909830686274839219279032113 / 156250000000000000000000000000000000000) +theorem rejected_interval_556 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(17669683222654431635317020401 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(17669683222654431635317020401 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(35339366445308863270634040803 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(35339366445308863270634040803 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_556 : rejected_556 ≤ taylor8 ((b+1/1000000000000000000000000)*(17669683222654431635317020401 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_556] + +def rejected_558 : ℚ := (1000003581732984861600009119391980159563 / 1000000000000000000000000000000000000000) +theorem rejected_interval_558 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(7937174578645075289249070687 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(7937174578645075289249070687 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(31748698314580301156996282749 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(31748698314580301156996282749 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_558 : rejected_558 ≤ taylor8 ((b+1/1000000000000000000000000)*(7937174578645075289249070687 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_558] + +def rejected_560 : ℚ := (10000031781000241644595679031450409373193 / 10000000000000000000000000000000000000000) +theorem rejected_interval_560 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(7042719241674080479710660023 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(7042719241674080479710660023 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(28170876966696321918842640093 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(28170876966696321918842640093 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_560 : rejected_560 ≤ taylor8 ((b+1/1000000000000000000000000)*(7042719241674080479710660023 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_560] + +def rejected_562 : ℚ := (10000027759062052567033233440313016625343 / 10000000000000000000000000000000000000000) +theorem rejected_interval_562 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(12302905401100082385006378221 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(12302905401100082385006378221 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(24605810802200164770012756443 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(24605810802200164770012756443 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_562 : rejected_562 ≤ taylor8 ((b+1/1000000000000000000000000)*(12302905401100082385006378221 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_562] + +def rejected_571 : ℚ := (10000009835717606602670877005470191212957 / 10000000000000000000000000000000000000000) +theorem rejected_interval_571 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4359225519940511281958503327 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4359225519940511281958503327 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(1743690207976204512783401331 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1743690207976204512783401331 / 200000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_571 : rejected_571 ≤ taylor8 ((b+1/1000000000000000000000000)*(4359225519940511281958503327 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_571] + +def rejected_572 : ℚ := (5000003930850583906787922897086522557623 / 5000000000000000000000000000000000000000) +theorem rejected_interval_572 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(6968669316093340343987940147 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(6968669316093340343987940147 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(1742167329023335085996985037 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1742167329023335085996985037 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_572 : rejected_572 ≤ taylor8 ((b+1/1000000000000000000000000)*(6968669316093340343987940147 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_572] + +def rejected_573 : ℚ := (2000001178226636616249074401858554980071 / 2000000000000000000000000000000000000000) +theorem rejected_interval_573 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(5221943981151675048688013469 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(5221943981151675048688013469 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(522194398115167504868801347 / 100000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(522194398115167504868801347 / 100000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_573 : rejected_573 ≤ taylor8 ((b+1/1000000000000000000000000)*(5221943981151675048688013469 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_573] + +def rejected_574 : ℚ := (10000003924001625724382832758466380866447 / 10000000000000000000000000000000000000000) +theorem rejected_interval_574 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(695652875264964180906992931 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(695652875264964180906992931 / 200000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(217391523520301306533435291 / 62500000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(217391523520301306533435291 / 62500000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_574 : rejected_574 ≤ taylor8 ((b+1/1000000000000000000000000)*(695652875264964180906992931 / 200000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_574] + +def rejectedMoment : ℚ := + ((1*435042608 : ℚ)/(576*114315520))*rejected_1 + + ((2*266771296 : ℚ)/(576*114315520))*rejected_2 + + ((3*29060592 : ℚ)/(576*114315520))*rejected_3 + + ((4*60639040 : ℚ)/(576*114315520))*rejected_4 + + ((5*26643936 : ℚ)/(576*114315520))*rejected_5 + + ((6*15333824 : ℚ)/(576*114315520))*rejected_6 + + ((7*11743248 : ℚ)/(576*114315520))*rejected_7 + + ((8*22069696 : ℚ)/(576*114315520))*rejected_8 + + ((9*3938704 : ℚ)/(576*114315520))*rejected_9 + + ((10*7735728 : ℚ)/(576*114315520))*rejected_10 + + ((11*6658960 : ℚ)/(576*114315520))*rejected_11 + + ((12*33578160 : ℚ)/(576*114315520))*rejected_12 + + ((13*13184336 : ℚ)/(576*114315520))*rejected_13 + + ((14*1821600 : ℚ)/(576*114315520))*rejected_14 + + ((15*3238400 : ℚ)/(576*114315520))*rejected_15 + + ((16*631488 : ℚ)/(576*114315520))*rejected_16 + + ((17*404800 : ℚ)/(576*114315520))*rejected_17 + + ((18*202400 : ℚ)/(576*114315520))*rejected_18 + + ((19*311696 : ℚ)/(576*114315520))*rejected_19 + + ((20*550528 : ℚ)/(576*114315520))*rejected_20 + + ((21*1222496 : ℚ)/(576*114315520))*rejected_21 + + ((22*64768 : ℚ)/(576*114315520))*rejected_22 + + ((23*8383408 : ℚ)/(576*114315520))*rejected_23 + + ((529*8193152 : ℚ)/(576*114315520))*rejected_529 + + ((552*97071040 : ℚ)/(576*114315520))*rejected_552 + + ((554*3456992 : ℚ)/(576*114315520))*rejected_554 + + ((556*1481568 : ℚ)/(576*114315520))*rejected_556 + + ((558*2384272 : ℚ)/(576*114315520))*rejected_558 + + ((560*445280 : ℚ)/(576*114315520))*rejected_560 + + ((562*48576 : ℚ)/(576*114315520))*rejected_562 + + ((571*740784 : ℚ)/(576*114315520))*rejected_571 + + ((572*101200 : ℚ)/(576*114315520))*rejected_572 + + ((573*28336 : ℚ)/(576*114315520))*rejected_573 + + ((574*364320 : ℚ)/(576*114315520))*rejected_574 +def rejectedFromCounts : ℚ := + ((1*(count 1 : ℚ))/(m*width))*rejected_1 + + ((2*(count 2 : ℚ))/(m*width))*rejected_2 + + ((3*(count 3 : ℚ))/(m*width))*rejected_3 + + ((4*(count 4 : ℚ))/(m*width))*rejected_4 + + ((5*(count 5 : ℚ))/(m*width))*rejected_5 + + ((6*(count 6 : ℚ))/(m*width))*rejected_6 + + ((7*(count 7 : ℚ))/(m*width))*rejected_7 + + ((8*(count 8 : ℚ))/(m*width))*rejected_8 + + ((9*(count 9 : ℚ))/(m*width))*rejected_9 + + ((10*(count 10 : ℚ))/(m*width))*rejected_10 + + ((11*(count 11 : ℚ))/(m*width))*rejected_11 + + ((12*(count 12 : ℚ))/(m*width))*rejected_12 + + ((13*(count 13 : ℚ))/(m*width))*rejected_13 + + ((14*(count 14 : ℚ))/(m*width))*rejected_14 + + ((15*(count 15 : ℚ))/(m*width))*rejected_15 + + ((16*(count 16 : ℚ))/(m*width))*rejected_16 + + ((17*(count 17 : ℚ))/(m*width))*rejected_17 + + ((18*(count 18 : ℚ))/(m*width))*rejected_18 + + ((19*(count 19 : ℚ))/(m*width))*rejected_19 + + ((20*(count 20 : ℚ))/(m*width))*rejected_20 + + ((21*(count 21 : ℚ))/(m*width))*rejected_21 + + ((22*(count 22 : ℚ))/(m*width))*rejected_22 + + ((23*(count 23 : ℚ))/(m*width))*rejected_23 + + ((529*(count 529 : ℚ))/(m*width))*rejected_529 + + ((552*(count 552 : ℚ))/(m*width))*rejected_552 + + ((554*(count 554 : ℚ))/(m*width))*rejected_554 + + ((556*(count 556 : ℚ))/(m*width))*rejected_556 + + ((558*(count 558 : ℚ))/(m*width))*rejected_558 + + ((560*(count 560 : ℚ))/(m*width))*rejected_560 + + ((562*(count 562 : ℚ))/(m*width))*rejected_562 + + ((571*(count 571 : ℚ))/(m*width))*rejected_571 + + ((572*(count 572 : ℚ))/(m*width))*rejected_572 + + ((573*(count 573 : ℚ))/(m*width))*rejected_573 + + ((574*(count 574 : ℚ))/(m*width))*rejected_574 +theorem rejected_profile_link : rejectedFromCounts = rejectedMoment := by + norm_num [rejectedFromCounts, rejectedMoment, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, count_1, count_10, count_11, count_12, count_13, count_14, count_15, count_16, count_17, count_18, count_19, count_2, count_20, count_21, count_22, count_23, count_3, count_4, count_5, count_529, count_552, count_554, count_556, count_558, count_560, count_562, count_571, count_572, count_573, count_574, count_6, count_7, count_8, count_9] + +theorem rejected_moment : 1 < rejectedMoment ∧ rejectedMoment = (40665600000000000000000002301675639985445787697 / 40665600000000000000000000000000000000000000000) := by + norm_num [rejectedMoment, rejected_1, rejected_10, rejected_11, rejected_12, rejected_13, rejected_14, rejected_15, rejected_16, rejected_17, rejected_18, rejected_19, rejected_2, rejected_20, rejected_21, rejected_22, rejected_23, rejected_3, rejected_4, rejected_5, rejected_529, rejected_552, rejected_554, rejected_556, rejected_558, rejected_560, rejected_562, rejected_571, rejected_572, rejected_573, rejected_574, rejected_6, rejected_7, rejected_8, rejected_9] + +theorem rejected_paid_moment : 1 < rejectedFromCounts := by + rw [rejected_profile_link] + exact rejected_moment.1 + +end KappaCheck.ShrunkBirthTerminal +#print axioms KappaCheck.ShrunkBirthTerminal.network_counts +#print axioms KappaCheck.ShrunkBirthTerminal.initial_dimension_count +#print axioms KappaCheck.ShrunkBirthTerminal.rank_mass +#print axioms KappaCheck.ShrunkBirthTerminal.count_1 +#print axioms KappaCheck.ShrunkBirthTerminal.count_2 +#print axioms KappaCheck.ShrunkBirthTerminal.count_3 +#print axioms KappaCheck.ShrunkBirthTerminal.count_4 +#print axioms KappaCheck.ShrunkBirthTerminal.count_5 +#print axioms KappaCheck.ShrunkBirthTerminal.count_6 +#print axioms KappaCheck.ShrunkBirthTerminal.count_7 +#print axioms KappaCheck.ShrunkBirthTerminal.count_8 +#print axioms KappaCheck.ShrunkBirthTerminal.count_9 +#print axioms KappaCheck.ShrunkBirthTerminal.count_10 +#print axioms KappaCheck.ShrunkBirthTerminal.count_11 +#print axioms KappaCheck.ShrunkBirthTerminal.count_12 +#print axioms KappaCheck.ShrunkBirthTerminal.count_13 +#print axioms KappaCheck.ShrunkBirthTerminal.count_14 +#print axioms KappaCheck.ShrunkBirthTerminal.count_15 +#print axioms KappaCheck.ShrunkBirthTerminal.count_16 +#print axioms KappaCheck.ShrunkBirthTerminal.count_17 +#print axioms KappaCheck.ShrunkBirthTerminal.count_18 +#print axioms KappaCheck.ShrunkBirthTerminal.count_19 +#print axioms KappaCheck.ShrunkBirthTerminal.count_20 +#print axioms KappaCheck.ShrunkBirthTerminal.count_21 +#print axioms KappaCheck.ShrunkBirthTerminal.count_22 +#print axioms KappaCheck.ShrunkBirthTerminal.count_23 +#print axioms KappaCheck.ShrunkBirthTerminal.count_529 +#print axioms KappaCheck.ShrunkBirthTerminal.count_552 +#print axioms KappaCheck.ShrunkBirthTerminal.count_554 +#print axioms KappaCheck.ShrunkBirthTerminal.count_556 +#print axioms KappaCheck.ShrunkBirthTerminal.count_558 +#print axioms KappaCheck.ShrunkBirthTerminal.count_560 +#print axioms KappaCheck.ShrunkBirthTerminal.count_562 +#print axioms KappaCheck.ShrunkBirthTerminal.count_571 +#print axioms KappaCheck.ShrunkBirthTerminal.count_572 +#print axioms KappaCheck.ShrunkBirthTerminal.count_573 +#print axioms KappaCheck.ShrunkBirthTerminal.count_574 +#print axioms KappaCheck.ShrunkBirthTerminal.complete_child_support +#print axioms KappaCheck.ShrunkBirthTerminal.strict_child_contraction +#print axioms KappaCheck.ShrunkBirthTerminal.slack_a_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_a_below_b +#print axioms KappaCheck.ShrunkBirthTerminal.slack_b_below_one_over32 +#print axioms KappaCheck.ShrunkBirthTerminal.slack_beta_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_beta_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_phase_leaf_above_bit +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_below_internal +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_below_leaf +#print axioms KappaCheck.ShrunkBirthTerminal.slack_c_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_c_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_below_reservations +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_above_tau +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_above_sigma +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_above_internal +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_prime_above_lambda +#print axioms KappaCheck.ShrunkBirthTerminal.slack_compact_leaf +#print axioms KappaCheck.ShrunkBirthTerminal.slack_compact_reservations +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_prime_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_epsilon_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_epsilon_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_guard_width +#print axioms KappaCheck.ShrunkBirthTerminal.slack_K_geometry +#print axioms KappaCheck.ShrunkBirthTerminal.slack_K_dominates_log +#print axioms KappaCheck.ShrunkBirthTerminal.slack_record_suffix +#print axioms KappaCheck.ShrunkBirthTerminal.slack_phase_local +#print axioms KappaCheck.ShrunkBirthTerminal.slack_phase_boundary +#print axioms KappaCheck.ShrunkBirthTerminal.slack_gamma_sublinear +#print axioms KappaCheck.ShrunkBirthTerminal.slack_cell_above_band +#print axioms KappaCheck.ShrunkBirthTerminal.slack_prime_interval_packing +#print axioms KappaCheck.ShrunkBirthTerminal.slack_alpha_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_alpha_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_alpha_below_one_fourth +#print axioms KappaCheck.ShrunkBirthTerminal.slack_delta_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_delta_below_one_eighth +#print axioms KappaCheck.ShrunkBirthTerminal.slack_short_record_fallback +#print axioms KappaCheck.ShrunkBirthTerminal.slack_small_field_exposure +#print axioms KappaCheck.ShrunkBirthTerminal.slack_artificial_boundary +#print axioms KappaCheck.ShrunkBirthTerminal.slack_literal_scalar_guard +#print axioms KappaCheck.ShrunkBirthTerminal.slack_row_product_gap +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g1_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g2_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g3_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g4_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g5_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g6_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g7_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.margins_strict +#print axioms KappaCheck.ShrunkBirthTerminal.balanced_identities +#print axioms KappaCheck.ShrunkBirthTerminal.stopped_parameter_choice +#print axioms KappaCheck.ShrunkBirthTerminal.controlling_margin +#print axioms KappaCheck.ShrunkBirthTerminal.fixed_profile_grid_exclusion +#print axioms KappaCheck.ShrunkBirthTerminal.gain_over_pinned_bounds +#print axioms KappaCheck.ShrunkBirthTerminal.stock_bit_coarse +#print axioms KappaCheck.ShrunkBirthTerminal.stock_complex +#print axioms KappaCheck.ShrunkBirthTerminal.stock_ordinary_leaf +#print axioms KappaCheck.ShrunkBirthTerminal.row_stock +#print axioms KappaCheck.ShrunkBirthTerminal.semantic_constants +#print axioms KappaCheck.ShrunkBirthTerminal.finite_bridge +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_1 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_1 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_2 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_2 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_3 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_3 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_4 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_4 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_5 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_5 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_6 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_6 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_7 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_7 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_8 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_8 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_9 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_9 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_10 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_10 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_11 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_11 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_12 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_12 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_13 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_13 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_14 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_14 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_15 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_15 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_16 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_16 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_17 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_17 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_18 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_18 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_19 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_19 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_20 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_20 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_21 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_21 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_22 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_22 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_23 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_23 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_529 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_529 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_552 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_552 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_554 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_554 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_556 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_556 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_558 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_558 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_560 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_560 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_562 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_562 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_571 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_571 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_572 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_572 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_573 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_573 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_574 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_574 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_profile_link +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_moment +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_paid_moment +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_1 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_1 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_2 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_2 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_3 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_3 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_4 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_4 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_5 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_5 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_6 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_6 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_7 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_7 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_8 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_8 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_9 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_9 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_10 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_10 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_11 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_11 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_12 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_12 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_13 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_13 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_14 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_14 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_15 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_15 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_16 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_16 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_17 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_17 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_18 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_18 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_19 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_19 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_20 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_20 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_21 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_21 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_22 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_22 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_23 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_23 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_529 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_529 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_552 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_552 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_554 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_554 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_556 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_556 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_558 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_558 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_560 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_560 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_562 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_562 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_571 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_571 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_572 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_572 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_573 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_573 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_574 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_574 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_profile_link +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_moment +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_paid_moment diff --git a/formal/lean/SOURCES.md b/formal/lean/SOURCES.md index f2203fb62d..0970a107c1 100644 --- a/formal/lean/SOURCES.md +++ b/formal/lean/SOURCES.md @@ -79,3 +79,6 @@ Line numbers refer to this branch, based on `6e56487`. | [`scoped_ceiling_exact`](KappaCheck/CrocSwap.lean#L559) | κ < U for every admissible choice with this motif | [compact-control-note.tex:143–146](../../notes/compact-control-note.tex#L143-L146)
[compact-control-note.tex:146](../../notes/compact-control-note.tex#L146) | — | — | | | [`ceiling_facts`](KappaCheck/CrocSwap.lean#L585) | U < 8.369598075·10⁻¹¹ < 2⁻³³; κ > 0.99 U | [compact-control-note.tex:146](../../notes/compact-control-note.tex#L146)
[compact-control-note.tex:148](../../notes/compact-control-note.tex#L148) | — | — | | | [`witness_meets_ceiling`](KappaCheck/CrocSwap.lean#L590) | their witness satisfies every hypothesis | — | — | — | Non-vacuity check for `scoped_ceiling_exact`; no source line. | +| [`h`](KappaCheck/ShrunkBirthTerminal.lean#L24), [`m`](KappaCheck/ShrunkBirthTerminal.lean#L25), [`v`](KappaCheck/ShrunkBirthTerminal.lean#L26), [`n`](KappaCheck/ShrunkBirthTerminal.lean#L27), [`virtualRoles`](KappaCheck/ShrunkBirthTerminal.lean#L28), [`births`](KappaCheck/ShrunkBirthTerminal.lean#L29), [`terminals`](KappaCheck/ShrunkBirthTerminal.lean#L30), [`roles`](KappaCheck/ShrunkBirthTerminal.lean#L31), [`width`](KappaCheck/ShrunkBirthTerminal.lean#L32), [`forwardHistogram`](KappaCheck/ShrunkBirthTerminal.lean#L33), [`initialDimensionHistogram`](KappaCheck/ShrunkBirthTerminal.lean#L34), [`counts`](KappaCheck/ShrunkBirthTerminal.lean#L35), [`count`](KappaCheck/ShrunkBirthTerminal.lean#L39), [`mass`](KappaCheck/ShrunkBirthTerminal.lean#L40), [`network_counts`](KappaCheck/ShrunkBirthTerminal.lean#L42), [`initial_dimension_count`](KappaCheck/ShrunkBirthTerminal.lean#L45), [`rank_mass`](KappaCheck/ShrunkBirthTerminal.lean#L48), [`count_1`](KappaCheck/ShrunkBirthTerminal.lean#L51), [`count_2`](KappaCheck/ShrunkBirthTerminal.lean#L54), [`count_3`](KappaCheck/ShrunkBirthTerminal.lean#L57), [`count_4`](KappaCheck/ShrunkBirthTerminal.lean#L60), [`count_5`](KappaCheck/ShrunkBirthTerminal.lean#L63), [`count_6`](KappaCheck/ShrunkBirthTerminal.lean#L66), [`count_7`](KappaCheck/ShrunkBirthTerminal.lean#L69), [`count_8`](KappaCheck/ShrunkBirthTerminal.lean#L72), [`count_9`](KappaCheck/ShrunkBirthTerminal.lean#L75), [`count_10`](KappaCheck/ShrunkBirthTerminal.lean#L78), [`count_11`](KappaCheck/ShrunkBirthTerminal.lean#L81), [`count_12`](KappaCheck/ShrunkBirthTerminal.lean#L84), [`count_13`](KappaCheck/ShrunkBirthTerminal.lean#L87), [`count_14`](KappaCheck/ShrunkBirthTerminal.lean#L90), [`count_15`](KappaCheck/ShrunkBirthTerminal.lean#L93), [`count_16`](KappaCheck/ShrunkBirthTerminal.lean#L96), [`count_17`](KappaCheck/ShrunkBirthTerminal.lean#L99), [`count_18`](KappaCheck/ShrunkBirthTerminal.lean#L102), [`count_19`](KappaCheck/ShrunkBirthTerminal.lean#L105), [`count_20`](KappaCheck/ShrunkBirthTerminal.lean#L108), [`count_21`](KappaCheck/ShrunkBirthTerminal.lean#L111), [`count_22`](KappaCheck/ShrunkBirthTerminal.lean#L114), [`count_23`](KappaCheck/ShrunkBirthTerminal.lean#L117), [`count_529`](KappaCheck/ShrunkBirthTerminal.lean#L120), [`count_552`](KappaCheck/ShrunkBirthTerminal.lean#L123), [`count_554`](KappaCheck/ShrunkBirthTerminal.lean#L126), [`count_556`](KappaCheck/ShrunkBirthTerminal.lean#L129), [`count_558`](KappaCheck/ShrunkBirthTerminal.lean#L132), [`count_560`](KappaCheck/ShrunkBirthTerminal.lean#L135), [`count_562`](KappaCheck/ShrunkBirthTerminal.lean#L138), [`count_571`](KappaCheck/ShrunkBirthTerminal.lean#L141), [`count_572`](KappaCheck/ShrunkBirthTerminal.lean#L144), [`count_573`](KappaCheck/ShrunkBirthTerminal.lean#L147), [`count_574`](KappaCheck/ShrunkBirthTerminal.lean#L150), [`childSizes`](KappaCheck/ShrunkBirthTerminal.lean#L153), [`complete_child_support`](KappaCheck/ShrunkBirthTerminal.lean#L154), [`strict_child_contraction`](KappaCheck/ShrunkBirthTerminal.lean#L157) | Complete physical-count arrays and paid histogram | — | — | [generate.py:34–56](../../research/shrunk-birth-terminal/lean/generate.py#L34-L56) | Exact input derivation and full generated-byte linkage are checked by research/shrunk-birth-terminal/audit_lean.py; general analytic and physical interfaces remain external. | +| [`a`](KappaCheck/ShrunkBirthTerminal.lean#L160), [`b`](KappaCheck/ShrunkBirthTerminal.lean#L161), [`kappa`](KappaCheck/ShrunkBirthTerminal.lean#L162), [`eta`](KappaCheck/ShrunkBirthTerminal.lean#L163), [`beta`](KappaCheck/ShrunkBirthTerminal.lean#L164), [`backoff`](KappaCheck/ShrunkBirthTerminal.lean#L165), [`actualBitSaving`](KappaCheck/ShrunkBirthTerminal.lean#L166), [`tau`](KappaCheck/ShrunkBirthTerminal.lean#L167), [`sigma`](KappaCheck/ShrunkBirthTerminal.lean#L168), [`qParam`](KappaCheck/ShrunkBirthTerminal.lean#L169), [`lp`](KappaCheck/ShrunkBirthTerminal.lean#L170), [`c`](KappaCheck/ShrunkBirthTerminal.lean#L171), [`epsilon`](KappaCheck/ShrunkBirthTerminal.lean#L172), [`lam`](KappaCheck/ShrunkBirthTerminal.lean#L173), [`g`](KappaCheck/ShrunkBirthTerminal.lean#L174), [`r`](KappaCheck/ShrunkBirthTerminal.lean#L175), [`delta`](KappaCheck/ShrunkBirthTerminal.lean#L176), [`internal`](KappaCheck/ShrunkBirthTerminal.lean#L177), [`leaf`](KappaCheck/ShrunkBirthTerminal.lean#L178), [`scalar`](KappaCheck/ShrunkBirthTerminal.lean#L180), [`guardE`](KappaCheck/ShrunkBirthTerminal.lean#L181), [`guardB`](KappaCheck/ShrunkBirthTerminal.lean#L182), [`literal`](KappaCheck/ShrunkBirthTerminal.lean#L183), [`guardC`](KappaCheck/ShrunkBirthTerminal.lean#L184), [`literalGap`](KappaCheck/ShrunkBirthTerminal.lean#L185), [`rowCoefficient`](KappaCheck/ShrunkBirthTerminal.lean#L186), [`rowGap`](KappaCheck/ShrunkBirthTerminal.lean#L187), [`margins`](KappaCheck/ShrunkBirthTerminal.lean#L188), [`slack_a_positive`](KappaCheck/ShrunkBirthTerminal.lean#L190), [`slack_a_below_b`](KappaCheck/ShrunkBirthTerminal.lean#L193), [`slack_b_below_one_over32`](KappaCheck/ShrunkBirthTerminal.lean#L196), [`slack_beta_positive`](KappaCheck/ShrunkBirthTerminal.lean#L199), [`slack_beta_below_one`](KappaCheck/ShrunkBirthTerminal.lean#L202), [`slack_phase_leaf_above_bit`](KappaCheck/ShrunkBirthTerminal.lean#L205), [`slack_q_positive`](KappaCheck/ShrunkBirthTerminal.lean#L208), [`slack_q_below_internal`](KappaCheck/ShrunkBirthTerminal.lean#L211), [`slack_q_below_leaf`](KappaCheck/ShrunkBirthTerminal.lean#L214), [`slack_c_positive`](KappaCheck/ShrunkBirthTerminal.lean#L217), [`slack_c_below_one`](KappaCheck/ShrunkBirthTerminal.lean#L220), [`slack_q_below_reservations`](KappaCheck/ShrunkBirthTerminal.lean#L223), [`slack_lambda_above_tau`](KappaCheck/ShrunkBirthTerminal.lean#L226), [`slack_lambda_above_sigma`](KappaCheck/ShrunkBirthTerminal.lean#L229), [`slack_lambda_above_internal`](KappaCheck/ShrunkBirthTerminal.lean#L232), [`slack_lambda_prime_above_lambda`](KappaCheck/ShrunkBirthTerminal.lean#L235), [`slack_compact_leaf`](KappaCheck/ShrunkBirthTerminal.lean#L238), [`slack_compact_reservations`](KappaCheck/ShrunkBirthTerminal.lean#L241), [`slack_lambda_prime_below_one`](KappaCheck/ShrunkBirthTerminal.lean#L244), [`slack_epsilon_positive`](KappaCheck/ShrunkBirthTerminal.lean#L247), [`slack_epsilon_below_one`](KappaCheck/ShrunkBirthTerminal.lean#L250), [`slack_guard_width`](KappaCheck/ShrunkBirthTerminal.lean#L253), [`slack_K_geometry`](KappaCheck/ShrunkBirthTerminal.lean#L256), [`slack_K_dominates_log`](KappaCheck/ShrunkBirthTerminal.lean#L259), [`slack_record_suffix`](KappaCheck/ShrunkBirthTerminal.lean#L262), [`slack_phase_local`](KappaCheck/ShrunkBirthTerminal.lean#L265), [`slack_phase_boundary`](KappaCheck/ShrunkBirthTerminal.lean#L268), [`slack_gamma_sublinear`](KappaCheck/ShrunkBirthTerminal.lean#L271), [`slack_cell_above_band`](KappaCheck/ShrunkBirthTerminal.lean#L274), [`slack_prime_interval_packing`](KappaCheck/ShrunkBirthTerminal.lean#L277), [`slack_alpha_positive`](KappaCheck/ShrunkBirthTerminal.lean#L280), [`slack_alpha_below_one`](KappaCheck/ShrunkBirthTerminal.lean#L283), [`slack_alpha_below_one_fourth`](KappaCheck/ShrunkBirthTerminal.lean#L286), [`slack_delta_positive`](KappaCheck/ShrunkBirthTerminal.lean#L289), [`slack_delta_below_one_eighth`](KappaCheck/ShrunkBirthTerminal.lean#L292), [`slack_short_record_fallback`](KappaCheck/ShrunkBirthTerminal.lean#L295), [`slack_small_field_exposure`](KappaCheck/ShrunkBirthTerminal.lean#L298), [`slack_artificial_boundary`](KappaCheck/ShrunkBirthTerminal.lean#L301), [`slack_literal_scalar_guard`](KappaCheck/ShrunkBirthTerminal.lean#L304), [`slack_row_product_gap`](KappaCheck/ShrunkBirthTerminal.lean#L307), [`slack_g1_above_kappa`](KappaCheck/ShrunkBirthTerminal.lean#L310), [`slack_g2_above_kappa`](KappaCheck/ShrunkBirthTerminal.lean#L313), [`slack_g3_above_kappa`](KappaCheck/ShrunkBirthTerminal.lean#L316), [`slack_g4_above_kappa`](KappaCheck/ShrunkBirthTerminal.lean#L319), [`slack_g5_above_kappa`](KappaCheck/ShrunkBirthTerminal.lean#L322), [`slack_g6_above_kappa`](KappaCheck/ShrunkBirthTerminal.lean#L325), [`slack_g7_above_kappa`](KappaCheck/ShrunkBirthTerminal.lean#L328), [`margins_strict`](KappaCheck/ShrunkBirthTerminal.lean#L331), [`balanced_identities`](KappaCheck/ShrunkBirthTerminal.lean#L334), [`stopped_parameter_choice`](KappaCheck/ShrunkBirthTerminal.lean#L337), [`controlling_margin`](KappaCheck/ShrunkBirthTerminal.lean#L340), [`fixed_profile_grid_exclusion`](KappaCheck/ShrunkBirthTerminal.lean#L343), [`gain_over_pinned_bounds`](KappaCheck/ShrunkBirthTerminal.lean#L346), [`stock_bit_coarse`](KappaCheck/ShrunkBirthTerminal.lean#L349), [`stock_complex`](KappaCheck/ShrunkBirthTerminal.lean#L352), [`stock_ordinary_leaf`](KappaCheck/ShrunkBirthTerminal.lean#L355), [`row_stock`](KappaCheck/ShrunkBirthTerminal.lean#L358), [`semantic_constants`](KappaCheck/ShrunkBirthTerminal.lean#L361), [`finite_bridge`](KappaCheck/ShrunkBirthTerminal.lean#L364) | Exact transfer parameters, all 47 inequalities, seven margins and three row stocks | — | — | [generate.py:57–101](../../research/shrunk-birth-terminal/lean/generate.py#L57-L101) | Exact input derivation and full generated-byte linkage are checked by research/shrunk-birth-terminal/audit_lean.py; general analytic and physical interfaces remain external. | +| [`taylor8`](KappaCheck/ShrunkBirthTerminal.lean#L369), [`expUpper`](KappaCheck/ShrunkBirthTerminal.lean#L370), [`accepted_1`](KappaCheck/ShrunkBirthTerminal.lean#L372), [`accepted_interval_1`](KappaCheck/ShrunkBirthTerminal.lean#L373), [`accepted_taylor_1`](KappaCheck/ShrunkBirthTerminal.lean#L376), [`accepted_2`](KappaCheck/ShrunkBirthTerminal.lean#L379), [`accepted_interval_2`](KappaCheck/ShrunkBirthTerminal.lean#L380), [`accepted_taylor_2`](KappaCheck/ShrunkBirthTerminal.lean#L383), [`accepted_3`](KappaCheck/ShrunkBirthTerminal.lean#L386), [`accepted_interval_3`](KappaCheck/ShrunkBirthTerminal.lean#L387), [`accepted_taylor_3`](KappaCheck/ShrunkBirthTerminal.lean#L390), [`accepted_4`](KappaCheck/ShrunkBirthTerminal.lean#L393), [`accepted_interval_4`](KappaCheck/ShrunkBirthTerminal.lean#L394), [`accepted_taylor_4`](KappaCheck/ShrunkBirthTerminal.lean#L397), [`accepted_5`](KappaCheck/ShrunkBirthTerminal.lean#L400), [`accepted_interval_5`](KappaCheck/ShrunkBirthTerminal.lean#L401), [`accepted_taylor_5`](KappaCheck/ShrunkBirthTerminal.lean#L404), [`accepted_6`](KappaCheck/ShrunkBirthTerminal.lean#L407), [`accepted_interval_6`](KappaCheck/ShrunkBirthTerminal.lean#L408), [`accepted_taylor_6`](KappaCheck/ShrunkBirthTerminal.lean#L411), [`accepted_7`](KappaCheck/ShrunkBirthTerminal.lean#L414), [`accepted_interval_7`](KappaCheck/ShrunkBirthTerminal.lean#L415), [`accepted_taylor_7`](KappaCheck/ShrunkBirthTerminal.lean#L418), [`accepted_8`](KappaCheck/ShrunkBirthTerminal.lean#L421), [`accepted_interval_8`](KappaCheck/ShrunkBirthTerminal.lean#L422), [`accepted_taylor_8`](KappaCheck/ShrunkBirthTerminal.lean#L425), [`accepted_9`](KappaCheck/ShrunkBirthTerminal.lean#L428), [`accepted_interval_9`](KappaCheck/ShrunkBirthTerminal.lean#L429), [`accepted_taylor_9`](KappaCheck/ShrunkBirthTerminal.lean#L432), [`accepted_10`](KappaCheck/ShrunkBirthTerminal.lean#L435), [`accepted_interval_10`](KappaCheck/ShrunkBirthTerminal.lean#L436), [`accepted_taylor_10`](KappaCheck/ShrunkBirthTerminal.lean#L439), [`accepted_11`](KappaCheck/ShrunkBirthTerminal.lean#L442), [`accepted_interval_11`](KappaCheck/ShrunkBirthTerminal.lean#L443), [`accepted_taylor_11`](KappaCheck/ShrunkBirthTerminal.lean#L446), [`accepted_12`](KappaCheck/ShrunkBirthTerminal.lean#L449), [`accepted_interval_12`](KappaCheck/ShrunkBirthTerminal.lean#L450), [`accepted_taylor_12`](KappaCheck/ShrunkBirthTerminal.lean#L453), [`accepted_13`](KappaCheck/ShrunkBirthTerminal.lean#L456), [`accepted_interval_13`](KappaCheck/ShrunkBirthTerminal.lean#L457), [`accepted_taylor_13`](KappaCheck/ShrunkBirthTerminal.lean#L460), [`accepted_14`](KappaCheck/ShrunkBirthTerminal.lean#L463), [`accepted_interval_14`](KappaCheck/ShrunkBirthTerminal.lean#L464), [`accepted_taylor_14`](KappaCheck/ShrunkBirthTerminal.lean#L467), [`accepted_15`](KappaCheck/ShrunkBirthTerminal.lean#L470), [`accepted_interval_15`](KappaCheck/ShrunkBirthTerminal.lean#L471), [`accepted_taylor_15`](KappaCheck/ShrunkBirthTerminal.lean#L474), [`accepted_16`](KappaCheck/ShrunkBirthTerminal.lean#L477), [`accepted_interval_16`](KappaCheck/ShrunkBirthTerminal.lean#L478), [`accepted_taylor_16`](KappaCheck/ShrunkBirthTerminal.lean#L481), [`accepted_17`](KappaCheck/ShrunkBirthTerminal.lean#L484), [`accepted_interval_17`](KappaCheck/ShrunkBirthTerminal.lean#L485), [`accepted_taylor_17`](KappaCheck/ShrunkBirthTerminal.lean#L488), [`accepted_18`](KappaCheck/ShrunkBirthTerminal.lean#L491), [`accepted_interval_18`](KappaCheck/ShrunkBirthTerminal.lean#L492), [`accepted_taylor_18`](KappaCheck/ShrunkBirthTerminal.lean#L495), [`accepted_19`](KappaCheck/ShrunkBirthTerminal.lean#L498), [`accepted_interval_19`](KappaCheck/ShrunkBirthTerminal.lean#L499), [`accepted_taylor_19`](KappaCheck/ShrunkBirthTerminal.lean#L502), [`accepted_20`](KappaCheck/ShrunkBirthTerminal.lean#L505), [`accepted_interval_20`](KappaCheck/ShrunkBirthTerminal.lean#L506), [`accepted_taylor_20`](KappaCheck/ShrunkBirthTerminal.lean#L509), [`accepted_21`](KappaCheck/ShrunkBirthTerminal.lean#L512), [`accepted_interval_21`](KappaCheck/ShrunkBirthTerminal.lean#L513), [`accepted_taylor_21`](KappaCheck/ShrunkBirthTerminal.lean#L516), [`accepted_22`](KappaCheck/ShrunkBirthTerminal.lean#L519), [`accepted_interval_22`](KappaCheck/ShrunkBirthTerminal.lean#L520), [`accepted_taylor_22`](KappaCheck/ShrunkBirthTerminal.lean#L523), [`accepted_23`](KappaCheck/ShrunkBirthTerminal.lean#L526), [`accepted_interval_23`](KappaCheck/ShrunkBirthTerminal.lean#L527), [`accepted_taylor_23`](KappaCheck/ShrunkBirthTerminal.lean#L530), [`accepted_529`](KappaCheck/ShrunkBirthTerminal.lean#L533), [`accepted_interval_529`](KappaCheck/ShrunkBirthTerminal.lean#L534), [`accepted_taylor_529`](KappaCheck/ShrunkBirthTerminal.lean#L537), [`accepted_552`](KappaCheck/ShrunkBirthTerminal.lean#L540), [`accepted_interval_552`](KappaCheck/ShrunkBirthTerminal.lean#L541), [`accepted_taylor_552`](KappaCheck/ShrunkBirthTerminal.lean#L544), [`accepted_554`](KappaCheck/ShrunkBirthTerminal.lean#L547), [`accepted_interval_554`](KappaCheck/ShrunkBirthTerminal.lean#L548), [`accepted_taylor_554`](KappaCheck/ShrunkBirthTerminal.lean#L551), [`accepted_556`](KappaCheck/ShrunkBirthTerminal.lean#L554), [`accepted_interval_556`](KappaCheck/ShrunkBirthTerminal.lean#L555), [`accepted_taylor_556`](KappaCheck/ShrunkBirthTerminal.lean#L558), [`accepted_558`](KappaCheck/ShrunkBirthTerminal.lean#L561), [`accepted_interval_558`](KappaCheck/ShrunkBirthTerminal.lean#L562), [`accepted_taylor_558`](KappaCheck/ShrunkBirthTerminal.lean#L565), [`accepted_560`](KappaCheck/ShrunkBirthTerminal.lean#L568), [`accepted_interval_560`](KappaCheck/ShrunkBirthTerminal.lean#L569), [`accepted_taylor_560`](KappaCheck/ShrunkBirthTerminal.lean#L572), [`accepted_562`](KappaCheck/ShrunkBirthTerminal.lean#L575), [`accepted_interval_562`](KappaCheck/ShrunkBirthTerminal.lean#L576), [`accepted_taylor_562`](KappaCheck/ShrunkBirthTerminal.lean#L579), [`accepted_571`](KappaCheck/ShrunkBirthTerminal.lean#L582), [`accepted_interval_571`](KappaCheck/ShrunkBirthTerminal.lean#L583), [`accepted_taylor_571`](KappaCheck/ShrunkBirthTerminal.lean#L586), [`accepted_572`](KappaCheck/ShrunkBirthTerminal.lean#L589), [`accepted_interval_572`](KappaCheck/ShrunkBirthTerminal.lean#L590), [`accepted_taylor_572`](KappaCheck/ShrunkBirthTerminal.lean#L593), [`accepted_573`](KappaCheck/ShrunkBirthTerminal.lean#L596), [`accepted_interval_573`](KappaCheck/ShrunkBirthTerminal.lean#L597), [`accepted_taylor_573`](KappaCheck/ShrunkBirthTerminal.lean#L600), [`accepted_574`](KappaCheck/ShrunkBirthTerminal.lean#L603), [`accepted_interval_574`](KappaCheck/ShrunkBirthTerminal.lean#L604), [`accepted_taylor_574`](KappaCheck/ShrunkBirthTerminal.lean#L607), [`acceptedMoment`](KappaCheck/ShrunkBirthTerminal.lean#L610), [`acceptedFromCounts`](KappaCheck/ShrunkBirthTerminal.lean#L645), [`accepted_profile_link`](KappaCheck/ShrunkBirthTerminal.lean#L680), [`accepted_moment`](KappaCheck/ShrunkBirthTerminal.lean#L683), [`accepted_paid_moment`](KappaCheck/ShrunkBirthTerminal.lean#L686), [`rejected_1`](KappaCheck/ShrunkBirthTerminal.lean#L690), [`rejected_interval_1`](KappaCheck/ShrunkBirthTerminal.lean#L691), [`rejected_taylor_1`](KappaCheck/ShrunkBirthTerminal.lean#L694), [`rejected_2`](KappaCheck/ShrunkBirthTerminal.lean#L697), [`rejected_interval_2`](KappaCheck/ShrunkBirthTerminal.lean#L698), [`rejected_taylor_2`](KappaCheck/ShrunkBirthTerminal.lean#L701), [`rejected_3`](KappaCheck/ShrunkBirthTerminal.lean#L704), [`rejected_interval_3`](KappaCheck/ShrunkBirthTerminal.lean#L705), [`rejected_taylor_3`](KappaCheck/ShrunkBirthTerminal.lean#L708), [`rejected_4`](KappaCheck/ShrunkBirthTerminal.lean#L711), [`rejected_interval_4`](KappaCheck/ShrunkBirthTerminal.lean#L712), [`rejected_taylor_4`](KappaCheck/ShrunkBirthTerminal.lean#L715), [`rejected_5`](KappaCheck/ShrunkBirthTerminal.lean#L718), [`rejected_interval_5`](KappaCheck/ShrunkBirthTerminal.lean#L719), [`rejected_taylor_5`](KappaCheck/ShrunkBirthTerminal.lean#L722), [`rejected_6`](KappaCheck/ShrunkBirthTerminal.lean#L725), [`rejected_interval_6`](KappaCheck/ShrunkBirthTerminal.lean#L726), [`rejected_taylor_6`](KappaCheck/ShrunkBirthTerminal.lean#L729), [`rejected_7`](KappaCheck/ShrunkBirthTerminal.lean#L732), [`rejected_interval_7`](KappaCheck/ShrunkBirthTerminal.lean#L733), [`rejected_taylor_7`](KappaCheck/ShrunkBirthTerminal.lean#L736), [`rejected_8`](KappaCheck/ShrunkBirthTerminal.lean#L739), [`rejected_interval_8`](KappaCheck/ShrunkBirthTerminal.lean#L740), [`rejected_taylor_8`](KappaCheck/ShrunkBirthTerminal.lean#L743), [`rejected_9`](KappaCheck/ShrunkBirthTerminal.lean#L746), [`rejected_interval_9`](KappaCheck/ShrunkBirthTerminal.lean#L747), [`rejected_taylor_9`](KappaCheck/ShrunkBirthTerminal.lean#L750), [`rejected_10`](KappaCheck/ShrunkBirthTerminal.lean#L753), [`rejected_interval_10`](KappaCheck/ShrunkBirthTerminal.lean#L754), [`rejected_taylor_10`](KappaCheck/ShrunkBirthTerminal.lean#L757), [`rejected_11`](KappaCheck/ShrunkBirthTerminal.lean#L760), [`rejected_interval_11`](KappaCheck/ShrunkBirthTerminal.lean#L761), [`rejected_taylor_11`](KappaCheck/ShrunkBirthTerminal.lean#L764), [`rejected_12`](KappaCheck/ShrunkBirthTerminal.lean#L767), [`rejected_interval_12`](KappaCheck/ShrunkBirthTerminal.lean#L768), [`rejected_taylor_12`](KappaCheck/ShrunkBirthTerminal.lean#L771), [`rejected_13`](KappaCheck/ShrunkBirthTerminal.lean#L774), [`rejected_interval_13`](KappaCheck/ShrunkBirthTerminal.lean#L775), [`rejected_taylor_13`](KappaCheck/ShrunkBirthTerminal.lean#L778), [`rejected_14`](KappaCheck/ShrunkBirthTerminal.lean#L781), [`rejected_interval_14`](KappaCheck/ShrunkBirthTerminal.lean#L782), [`rejected_taylor_14`](KappaCheck/ShrunkBirthTerminal.lean#L785), [`rejected_15`](KappaCheck/ShrunkBirthTerminal.lean#L788), [`rejected_interval_15`](KappaCheck/ShrunkBirthTerminal.lean#L789), [`rejected_taylor_15`](KappaCheck/ShrunkBirthTerminal.lean#L792), [`rejected_16`](KappaCheck/ShrunkBirthTerminal.lean#L795), [`rejected_interval_16`](KappaCheck/ShrunkBirthTerminal.lean#L796), [`rejected_taylor_16`](KappaCheck/ShrunkBirthTerminal.lean#L799), [`rejected_17`](KappaCheck/ShrunkBirthTerminal.lean#L802), [`rejected_interval_17`](KappaCheck/ShrunkBirthTerminal.lean#L803), [`rejected_taylor_17`](KappaCheck/ShrunkBirthTerminal.lean#L806), [`rejected_18`](KappaCheck/ShrunkBirthTerminal.lean#L809), [`rejected_interval_18`](KappaCheck/ShrunkBirthTerminal.lean#L810), [`rejected_taylor_18`](KappaCheck/ShrunkBirthTerminal.lean#L813), [`rejected_19`](KappaCheck/ShrunkBirthTerminal.lean#L816), [`rejected_interval_19`](KappaCheck/ShrunkBirthTerminal.lean#L817), [`rejected_taylor_19`](KappaCheck/ShrunkBirthTerminal.lean#L820), [`rejected_20`](KappaCheck/ShrunkBirthTerminal.lean#L823), [`rejected_interval_20`](KappaCheck/ShrunkBirthTerminal.lean#L824), [`rejected_taylor_20`](KappaCheck/ShrunkBirthTerminal.lean#L827), [`rejected_21`](KappaCheck/ShrunkBirthTerminal.lean#L830), [`rejected_interval_21`](KappaCheck/ShrunkBirthTerminal.lean#L831), [`rejected_taylor_21`](KappaCheck/ShrunkBirthTerminal.lean#L834), [`rejected_22`](KappaCheck/ShrunkBirthTerminal.lean#L837), [`rejected_interval_22`](KappaCheck/ShrunkBirthTerminal.lean#L838), [`rejected_taylor_22`](KappaCheck/ShrunkBirthTerminal.lean#L841), [`rejected_23`](KappaCheck/ShrunkBirthTerminal.lean#L844), [`rejected_interval_23`](KappaCheck/ShrunkBirthTerminal.lean#L845), [`rejected_taylor_23`](KappaCheck/ShrunkBirthTerminal.lean#L848), [`rejected_529`](KappaCheck/ShrunkBirthTerminal.lean#L851), [`rejected_interval_529`](KappaCheck/ShrunkBirthTerminal.lean#L852), [`rejected_taylor_529`](KappaCheck/ShrunkBirthTerminal.lean#L855), [`rejected_552`](KappaCheck/ShrunkBirthTerminal.lean#L858), [`rejected_interval_552`](KappaCheck/ShrunkBirthTerminal.lean#L859), [`rejected_taylor_552`](KappaCheck/ShrunkBirthTerminal.lean#L862), [`rejected_554`](KappaCheck/ShrunkBirthTerminal.lean#L865), [`rejected_interval_554`](KappaCheck/ShrunkBirthTerminal.lean#L866), [`rejected_taylor_554`](KappaCheck/ShrunkBirthTerminal.lean#L869), [`rejected_556`](KappaCheck/ShrunkBirthTerminal.lean#L872), [`rejected_interval_556`](KappaCheck/ShrunkBirthTerminal.lean#L873), [`rejected_taylor_556`](KappaCheck/ShrunkBirthTerminal.lean#L876), [`rejected_558`](KappaCheck/ShrunkBirthTerminal.lean#L879), [`rejected_interval_558`](KappaCheck/ShrunkBirthTerminal.lean#L880), [`rejected_taylor_558`](KappaCheck/ShrunkBirthTerminal.lean#L883), [`rejected_560`](KappaCheck/ShrunkBirthTerminal.lean#L886), [`rejected_interval_560`](KappaCheck/ShrunkBirthTerminal.lean#L887), [`rejected_taylor_560`](KappaCheck/ShrunkBirthTerminal.lean#L890), [`rejected_562`](KappaCheck/ShrunkBirthTerminal.lean#L893), [`rejected_interval_562`](KappaCheck/ShrunkBirthTerminal.lean#L894), [`rejected_taylor_562`](KappaCheck/ShrunkBirthTerminal.lean#L897), [`rejected_571`](KappaCheck/ShrunkBirthTerminal.lean#L900), [`rejected_interval_571`](KappaCheck/ShrunkBirthTerminal.lean#L901), [`rejected_taylor_571`](KappaCheck/ShrunkBirthTerminal.lean#L904), [`rejected_572`](KappaCheck/ShrunkBirthTerminal.lean#L907), [`rejected_interval_572`](KappaCheck/ShrunkBirthTerminal.lean#L908), [`rejected_taylor_572`](KappaCheck/ShrunkBirthTerminal.lean#L911), [`rejected_573`](KappaCheck/ShrunkBirthTerminal.lean#L914), [`rejected_interval_573`](KappaCheck/ShrunkBirthTerminal.lean#L915), [`rejected_taylor_573`](KappaCheck/ShrunkBirthTerminal.lean#L918), [`rejected_574`](KappaCheck/ShrunkBirthTerminal.lean#L921), [`rejected_interval_574`](KappaCheck/ShrunkBirthTerminal.lean#L922), [`rejected_taylor_574`](KappaCheck/ShrunkBirthTerminal.lean#L925), [`rejectedMoment`](KappaCheck/ShrunkBirthTerminal.lean#L928), [`rejectedFromCounts`](KappaCheck/ShrunkBirthTerminal.lean#L963), [`rejected_profile_link`](KappaCheck/ShrunkBirthTerminal.lean#L998), [`rejected_moment`](KappaCheck/ShrunkBirthTerminal.lean#L1001), [`rejected_paid_moment`](KappaCheck/ShrunkBirthTerminal.lean#L1004) | Independent rational Taylor enclosure arithmetic | — | — | [generate.py:102–125](../../research/shrunk-birth-terminal/lean/generate.py#L102-L125) | Exact input derivation and full generated-byte linkage are checked by research/shrunk-birth-terminal/audit_lean.py; general analytic and physical interfaces remain external. | diff --git a/formal/lean/sources.py b/formal/lean/sources.py index eedaedad3b..600c2a9a22 100644 --- a/formal/lean/sources.py +++ b/formal/lean/sources.py @@ -414,6 +414,12 @@ def main_(*k): STOP = re.compile(r'^(?:theorem|def|noncomputable|/-|end |namespace|section)', re.M) +# Scoped rational arithmetic for the selected portable composition. +ROWS.append(('ShrunkBirthTerminal', ['h', 'm', 'v', 'n', 'virtualRoles', 'births', 'terminals', 'roles', 'width', 'forwardHistogram', 'initialDimensionHistogram', 'counts', 'count', 'mass', 'network_counts', 'initial_dimension_count', 'rank_mass', 'count_1', 'count_2', 'count_3', 'count_4', 'count_5', 'count_6', 'count_7', 'count_8', 'count_9', 'count_10', 'count_11', 'count_12', 'count_13', 'count_14', 'count_15', 'count_16', 'count_17', 'count_18', 'count_19', 'count_20', 'count_21', 'count_22', 'count_23', 'count_529', 'count_552', 'count_554', 'count_556', 'count_558', 'count_560', 'count_562', 'count_571', 'count_572', 'count_573', 'count_574', 'childSizes', 'complete_child_support', 'strict_child_contraction'], 'Complete physical-count arrays and paid histogram', [Line('research/shrunk-birth-terminal/lean/generate.py', 34, 56, 'complete_child_support')], 'Exact input derivation and full generated-byte linkage are checked by research/shrunk-birth-terminal/audit_lean.py; general analytic and physical interfaces remain external.')) +ROWS.append(('ShrunkBirthTerminal', ['a', 'b', 'kappa', 'eta', 'beta', 'backoff', 'actualBitSaving', 'tau', 'sigma', 'qParam', 'lp', 'c', 'epsilon', 'lam', 'g', 'r', 'delta', 'internal', 'leaf', 'scalar', 'guardE', 'guardB', 'literal', 'guardC', 'literalGap', 'rowCoefficient', 'rowGap', 'margins', 'slack_a_positive', 'slack_a_below_b', 'slack_b_below_one_over32', 'slack_beta_positive', 'slack_beta_below_one', 'slack_phase_leaf_above_bit', 'slack_q_positive', 'slack_q_below_internal', 'slack_q_below_leaf', 'slack_c_positive', 'slack_c_below_one', 'slack_q_below_reservations', 'slack_lambda_above_tau', 'slack_lambda_above_sigma', 'slack_lambda_above_internal', 'slack_lambda_prime_above_lambda', 'slack_compact_leaf', 'slack_compact_reservations', 'slack_lambda_prime_below_one', 'slack_epsilon_positive', 'slack_epsilon_below_one', 'slack_guard_width', 'slack_K_geometry', 'slack_K_dominates_log', 'slack_record_suffix', 'slack_phase_local', 'slack_phase_boundary', 'slack_gamma_sublinear', 'slack_cell_above_band', 'slack_prime_interval_packing', 'slack_alpha_positive', 'slack_alpha_below_one', 'slack_alpha_below_one_fourth', 'slack_delta_positive', 'slack_delta_below_one_eighth', 'slack_short_record_fallback', 'slack_small_field_exposure', 'slack_artificial_boundary', 'slack_literal_scalar_guard', 'slack_row_product_gap', 'slack_g1_above_kappa', 'slack_g2_above_kappa', 'slack_g3_above_kappa', 'slack_g4_above_kappa', 'slack_g5_above_kappa', 'slack_g6_above_kappa', 'slack_g7_above_kappa', 'margins_strict', 'balanced_identities', 'stopped_parameter_choice', 'controlling_margin', 'fixed_profile_grid_exclusion', 'gain_over_pinned_bounds', 'stock_bit_coarse', 'stock_complex', 'stock_ordinary_leaf', 'row_stock', 'semantic_constants', 'finite_bridge'], 'Exact transfer parameters, all 47 inequalities, seven margins and three row stocks', [Line('research/shrunk-birth-terminal/lean/generate.py', 57, 101, 'slacks')], 'Exact input derivation and full generated-byte linkage are checked by research/shrunk-birth-terminal/audit_lean.py; general analytic and physical interfaces remain external.')) +ROWS.append(('ShrunkBirthTerminal', ['taylor8', 'expUpper', 'accepted_1', 'accepted_interval_1', 'accepted_taylor_1', 'accepted_2', 'accepted_interval_2', 'accepted_taylor_2', 'accepted_3', 'accepted_interval_3', 'accepted_taylor_3', 'accepted_4', 'accepted_interval_4', 'accepted_taylor_4', 'accepted_5', 'accepted_interval_5', 'accepted_taylor_5', 'accepted_6', 'accepted_interval_6', 'accepted_taylor_6', 'accepted_7', 'accepted_interval_7', 'accepted_taylor_7', 'accepted_8', 'accepted_interval_8', 'accepted_taylor_8', 'accepted_9', 'accepted_interval_9', 'accepted_taylor_9', 'accepted_10', 'accepted_interval_10', 'accepted_taylor_10', 'accepted_11', 'accepted_interval_11', 'accepted_taylor_11', 'accepted_12', 'accepted_interval_12', 'accepted_taylor_12', 'accepted_13', 'accepted_interval_13', 'accepted_taylor_13', 'accepted_14', 'accepted_interval_14', 'accepted_taylor_14', 'accepted_15', 'accepted_interval_15', 'accepted_taylor_15', 'accepted_16', 'accepted_interval_16', 'accepted_taylor_16', 'accepted_17', 'accepted_interval_17', 'accepted_taylor_17', 'accepted_18', 'accepted_interval_18', 'accepted_taylor_18', 'accepted_19', 'accepted_interval_19', 'accepted_taylor_19', 'accepted_20', 'accepted_interval_20', 'accepted_taylor_20', 'accepted_21', 'accepted_interval_21', 'accepted_taylor_21', 'accepted_22', 'accepted_interval_22', 'accepted_taylor_22', 'accepted_23', 'accepted_interval_23', 'accepted_taylor_23', 'accepted_529', 'accepted_interval_529', 'accepted_taylor_529', 'accepted_552', 'accepted_interval_552', 'accepted_taylor_552', 'accepted_554', 'accepted_interval_554', 'accepted_taylor_554', 'accepted_556', 'accepted_interval_556', 'accepted_taylor_556', 'accepted_558', 'accepted_interval_558', 'accepted_taylor_558', 'accepted_560', 'accepted_interval_560', 'accepted_taylor_560', 'accepted_562', 'accepted_interval_562', 'accepted_taylor_562', 'accepted_571', 'accepted_interval_571', 'accepted_taylor_571', 'accepted_572', 'accepted_interval_572', 'accepted_taylor_572', 'accepted_573', 'accepted_interval_573', 'accepted_taylor_573', 'accepted_574', 'accepted_interval_574', 'accepted_taylor_574', 'acceptedMoment', 'acceptedFromCounts', 'accepted_profile_link', 'accepted_moment', 'accepted_paid_moment', 'rejected_1', 'rejected_interval_1', 'rejected_taylor_1', 'rejected_2', 'rejected_interval_2', 'rejected_taylor_2', 'rejected_3', 'rejected_interval_3', 'rejected_taylor_3', 'rejected_4', 'rejected_interval_4', 'rejected_taylor_4', 'rejected_5', 'rejected_interval_5', 'rejected_taylor_5', 'rejected_6', 'rejected_interval_6', 'rejected_taylor_6', 'rejected_7', 'rejected_interval_7', 'rejected_taylor_7', 'rejected_8', 'rejected_interval_8', 'rejected_taylor_8', 'rejected_9', 'rejected_interval_9', 'rejected_taylor_9', 'rejected_10', 'rejected_interval_10', 'rejected_taylor_10', 'rejected_11', 'rejected_interval_11', 'rejected_taylor_11', 'rejected_12', 'rejected_interval_12', 'rejected_taylor_12', 'rejected_13', 'rejected_interval_13', 'rejected_taylor_13', 'rejected_14', 'rejected_interval_14', 'rejected_taylor_14', 'rejected_15', 'rejected_interval_15', 'rejected_taylor_15', 'rejected_16', 'rejected_interval_16', 'rejected_taylor_16', 'rejected_17', 'rejected_interval_17', 'rejected_taylor_17', 'rejected_18', 'rejected_interval_18', 'rejected_taylor_18', 'rejected_19', 'rejected_interval_19', 'rejected_taylor_19', 'rejected_20', 'rejected_interval_20', 'rejected_taylor_20', 'rejected_21', 'rejected_interval_21', 'rejected_taylor_21', 'rejected_22', 'rejected_interval_22', 'rejected_taylor_22', 'rejected_23', 'rejected_interval_23', 'rejected_taylor_23', 'rejected_529', 'rejected_interval_529', 'rejected_taylor_529', 'rejected_552', 'rejected_interval_552', 'rejected_taylor_552', 'rejected_554', 'rejected_interval_554', 'rejected_taylor_554', 'rejected_556', 'rejected_interval_556', 'rejected_taylor_556', 'rejected_558', 'rejected_interval_558', 'rejected_taylor_558', 'rejected_560', 'rejected_interval_560', 'rejected_taylor_560', 'rejected_562', 'rejected_interval_562', 'rejected_taylor_562', 'rejected_571', 'rejected_interval_571', 'rejected_taylor_571', 'rejected_572', 'rejected_interval_572', 'rejected_taylor_572', 'rejected_573', 'rejected_interval_573', 'rejected_taylor_573', 'rejected_574', 'rejected_interval_574', 'rejected_taylor_574', 'rejectedMoment', 'rejectedFromCounts', 'rejected_profile_link', 'rejected_moment', 'rejected_paid_moment'], 'Independent rational Taylor enclosure arithmetic', [Line('research/shrunk-birth-terminal/lean/generate.py', 102, 125, 'taylor8')], 'Exact input derivation and full generated-byte linkage are checked by research/shrunk-birth-terminal/audit_lean.py; general analytic and physical interfaces remain external.')) + + def lean_decls(): out = {} for f in sorted((LEAN/'KappaCheck').glob('*.lean')): diff --git a/research/joint-dual/SOURCE.json b/research/joint-dual/SOURCE.json index 80c0f29dc4..ccbdfeb1ed 100644 --- a/research/joint-dual/SOURCE.json +++ b/research/joint-dual/SOURCE.json @@ -3,9 +3,9 @@ "base_pr57_commit": "cd350f76c9bc01489ec83568bded532cb69be938", "base_pr58_commit": "bc2f7ed4c20dc18898305ab17165c0c995cbb804", "files": { - "Makefile": "97620e0205736d9c0fce736e8ac6ab67f8ed0e490c381f6cac152cc6a003dca7", - "NOTICE": "1c53970fb4face631a1b331ec66d33111eccd280a129f9b64c2da6df96861c3f", - "README.md": "fd92de31aece76b1f5ff897e6e0dbc38dd3bf67c140579bbcb03a1a11a792668", + "Makefile": "8c201787bf9d1bf119c0e28edcffd44fefd2f496d763e9ef749f266dfa477952", + "NOTICE": "c11074a7ac34c16520ec6d0d7fb9380ee72f2a4fe3e7f2d8c69d5bc0f751a296", + "README.md": "9f3dac26471dbcdc034313b3af13d23452a13ebe17975d0db174ea13ea574c94", "certificates/joint-dual-compiler.json": "516c4d85158553dabd0a98216a064b2a7397957a9d5dd0df1d6e5aec53a4e805", "certificates/joint-dual-profiles-23.json": "159fa8fee175fc1d24f63e72d3c2f1dc9f4fcd78b938c5e7d2f735fd0fd37209", "certificates/joint-dual-profiles-25.json": "8d190ce42d097e828c5756918c52f2963df576cf4c6600b0fc7f2b7fdb6ad223", diff --git a/research/shrunk-birth-terminal/PROOF.md b/research/shrunk-birth-terminal/PROOF.md new file mode 100644 index 0000000000..2aedd92746 --- /dev/null +++ b/research/shrunk-birth-terminal/PROOF.md @@ -0,0 +1,101 @@ +# A shrunk-frame, birth-reuse and terminal-elision composition + +Under the retained OpenAI #109 all-size framework and the paid interfaces stated below, this composition gives + +\[ +T(n)=O\bigl(n(\log n)^{1-\kappa}\bigr),\qquad +\kappa=\frac{112802185097556}{10^{18}} + =0.000112802185097556>2^{-14}. +\] + +The dyadic corollary is therefore `kappa = 2^-14`. The decimal display `kappa ≈ 2^-13.113917365014208` is descriptive; the certificate uses only integers and exact rational strings. This is an asymptotic exponent saving, with no practical multiplication-speed claim. The finite checks and 240 Lean arithmetic theorems do not replace the inherited all-size proofs or expert review. + +## Construction and what is new + +The scalar graph is eumemic's PR117, the initial shrunk logical frames are Joel Pulikkan's PR125, the dirty-slot birth identity is James Chang's PR124, and the terminal identity is SovereignSteak's PR122. Original source files, author disclosures and notices are retained in `references/` and `search/original-runtime/`. The finite composition here optimizes the two endpoint frames, applies explicit legal deferral moves while protecting live births, and selects birth reuse and terminal elimination jointly. A complete physical word, independently reconstructed paid profile and exact rational source/dirty responses are emitted after those choices. A three-stock balanced positional transfer then uses that complete profile. + +The selected geometry has 28,705 virtual auxiliary roles and 4,725 deferred virtual roles. Its disjoint matching reuses 2,108 birth slots and eliminates 381 ordinary terminals on distinct target coordinates. The resulting physical auxiliary count is + + R = 28705 - 2108 - 381 = 26216. + +The endpoint and placement choices are finite witnesses, not assumptions about the optimizer. `search/reproduce_geometry.py` reconstructs every mathematical geometry field from pinned source and the recorded moves. The canonical geometry digest omits only descriptive `base_profile` metadata and normalizes empty target lists and list ordering. It neither assumes the saved pickle nor needs to rerun a heuristic search. The selected pickle is also independently hash-bound to the physical compiler. + +## Dirty-slot reuse and terminal elimination + +A birth recipient has no earlier active use. Its donor has finished all active uses in the center phase and has a nondegenerate endpoint frame A contained in the recipient's nondegenerate birth frame F. The explicit birth compensation read cancels the donor's current dirty value, including any correlations and earlier source signals. The subsequent recipient operations use that same physical slot. Cleanup reverses the actual chronological sequence of source and workspace events. All 2,108 donors and recipients are distinct and no eliminated terminal is a donor or recipient. + +For e=dim(A) and s=dim(F), the complete paid reuse comparison replaces the two old widths `h-e` and `m-h+s` by the new residual width `s-e`, while removing one physical auxiliary role. Adding a dummy width-m child to the new side conserves mass. The padded new packet majorizes the old packet. For a strictly concave power, this improves the unnormalized feasibility slack; normalized-moment improvement is asserted only at an already feasible exponent. The stored word and profile, not a role-count approximation, determine the final moment. + +Each selected terminal u has exact ordinary readout coefficient alpha=+/-1/2 on one target, never controls an auxiliary update, is untouched in the center phase, and has only late updates. If its initial dirty value is z_u, then + + -alpha*z_u + alpha*(z_u + sum_j a_j(t_j)) + = sum_j alpha*a_j(t_j). + +The compiler removes u and redirects each update at its original index to that target, using the same source value and the same gate frame. It retains target promotions even when the corresponding old terminal read is omitted. Targets never control workspace operations. One selected terminal per target ensures that simultaneous rewrites have disjoint target-front packets. The actual reverse cleanup includes only the retained workspace and source operations. + +The selected first incoming frame, final old target front and initial terminal frame coincide: sigma=M=F0. With h=24 and m=576, the general padded comparison is + + old: [m-h+sigma, 1, F0-sigma, h-1-M] + new: [m, F0-M, 0, 0]. + +All entries are nonnegative and masses agree. Complete-profile reconstruction checks the sum of these packets and every integer concavity hinge from 1 through 576. The detailed terminal proof and its assumptions are in [TERMINAL-PROOF.md](TERMINAL-PROOF.md). Deleting an aliased birth recipient is expressly forbidden; the joint optimizer instead chooses between its real donor edge and its terminal edge. + +## Complete word, frames and scalar charge + +The serialized word contains 276,608 blocks. Exact signed integer bit-plane arithmetic over the rationals, with common denominator 42, checks every source and physical dirty column simultaneously. Its forward response is +I on all 2,024 source coordinates and zero on all 26,216 dirty coordinates. The signed reflected word reverses the actual event order, negates shears, exchanges the data banks and complements frames; its response is -I with every dirty response zero. Both words receive complete frame, containment and nondegeneracy scans. Actual omitted-redirect, wrong-sign and illegal-frame mutations are rejected. + +A direct terminal update +/-1/2 is exactly 21 same-frame shears of coefficient +/-1/42. It creates no new role, source copy or frame incidence. The retained old readout numerator 55 is likewise 55 such unit shears; no false coefficient-at-most-one test is applied to the grouped 55/42 expression. The scalar bill keeps the entire old virtual-word bound, without credit for removed work, then adds 29 groups for each of the 1,167 direct updates: 21 actual shears and eight conservative bookkeeping groups. It gives + + local = 48069997 + 29*1167 = 48103840, + G = 16*(2*2024*local + 8*2024^2) = 3116113870848. + +The old billing snapshot's descriptive deferred-support count 9,732 is explicitly labeled inherited. Recounting exact signed supports on the selected geometry gives 11,884 terms across all 4,725 deferred virtual roles and 11,503 across the 4,344 retained deferred roles. These diagnostics do not reduce the conservative scalar charge. Original input and execution receipts remain unchanged in the audit archive; the corrected bill is independently bound by the portable certificate. + +The resulting complete two-factor profile is + +| Quantity | Exact value | +|---|---:| +| h, v, m | 24, 2024, 576 | +| N = v^2 | 4096576 | +| Physical auxiliary roles R | 26216 | +| W = 2N+2vR | 114315520 | +| Total recursive rank | 65843877440 | +| mW-rank | 1862080 | +| Largest child | 574 | +| Distinct child widths | 34 | + +The full histogram includes both orientations, source and target fronts, auxiliary exteriors, copied-center losses and the final data endpoint correction. It is reconstructed from the emitted word and separately from the birth/terminal packets. The Lean input derives its forward and exterior count arrays from the same actual word, then independently proves their paid total. + +## Exact transfer and its boundary + +The stopped product-ring ordinary wrapper and common odd-21 grid remain as in icekylinx's PR104. The bit input is the round-seven word attributed to Swapnil Jain, with its original sources retained. The older ordinary leaf supplier stays present. The paid balanced positional layout follows the PR23/29, RaD and James Chang/PR34 lineage as applied to deferred signed words by Rohan Arun in PR100/103. It pays the coordinate regrouping and preserves complete active, spectator, scratch, control and phase fields. This changes the proved outer work margin, not the physical word or its histogram. + +All three simultaneous row stocks are retained. Their exact halving-degree/role-bit contributions are 9909+5400+252=15561. A degree-32000 reserve has strict gap 6389/25 and suffix slope 128000. The literal scalar guard, completed-child induction, all 47 strict inequalities and all seven exponent margins are recomputed. Removing the ordinary-leaf stock or reinstating the old repeated-prefix work margin is rejected by explicit controls. + +Two independent rational log/exp enclosure methods certify + + complex saving b = 112814910866013477738/10^24 + +and reject b+10^-24. With beta=eta=10^-24 and strict backoff 10^-30, the minimum final margin is the balanced Gaussian/layer margin g, and the largest accepted 10^-18-grid kappa is the value stated above. The rejected complex point also bounds every member of this fixed-profile, fixed-bit-supplier balanced family below the next kappa grid point. This is a scoped grid ceiling, not a global optimum over other networks or transfer methods. The complete argument, exact parameter formulas and comparison at identical backoff values are in [arithmetic/PROOF.md](arithmetic/PROOF.md). + +The remaining inherited obligations are the all-size realization of the paid residuals and completed tensor primitive; the simultaneous generic basis, common odd-grid and semantic induction interfaces; and the stopped product-ring, routing, prime supply, precision, recovery and fixed-tape analytic transfer. The concrete word and finite arithmetic constrain their parameters but do not prove those general interfaces anew. The Lean module proves supplied rational/count identities only; the analytic meaning of the logarithm intervals and the derivation of the physical arrays remain separately checked or inherited. + +## Attribution and exact provenance + +Chafik Boukhalfa (@chafreaky) with OpenAI Codex assistance prepared this composition, joint optimization, explicit word, independent accounting and portable verification. GitHub author accounts were checked against the submitted PR metadata and repository owner; the evidence is in `references/CONTRIBUTOR-PINS.json`. + +| Contributor | Retained work and source | +|---|---| +| [@GamingPuzzled](https://github.com/GamingPuzzled), Joel Pulikkan | Shrunk frames, [PR125](https://github.com/CrocSwap/integer-mult-bounds/pull/125) | +| [@jamesyc](https://github.com/jamesyc), James Chang | Birth reuse and balanced-layout lineage, [PR124](https://github.com/CrocSwap/integer-mult-bounds/pull/124), [PR34](https://github.com/CrocSwap/integer-mult-bounds/pull/34) | +| [@SovereignSteak](https://github.com/SovereignSteak) | Terminal identity and majorization, [PR122](https://github.com/CrocSwap/integer-mult-bounds/pull/122) | +| [@eumemic](https://github.com/eumemic) | Scalar DAG and earlier compiler, [PR117](https://github.com/CrocSwap/integer-mult-bounds/pull/117) | +| [@DanieleCorso](https://github.com/DanieleCorso) | Endpoint-frame search and marginal placement costs, [PR126](https://github.com/CrocSwap/integer-mult-bounds/pull/126) | +| [@rohanarun](https://github.com/rohanarun), Rohan Arun | Deferred/signed balanced transfer and unit readouts, [PR100](https://github.com/CrocSwap/integer-mult-bounds/pull/100), [PR103](https://github.com/CrocSwap/integer-mult-bounds/pull/103), [PR118](https://github.com/CrocSwap/integer-mult-bounds/pull/118) | +| [@ikeboy](https://github.com/ikeboy), Avi Eisenberg | Deferred physical compiler, [PR110](https://github.com/CrocSwap/integer-mult-bounds/pull/110) and earlier work | +| [@icekylinx](https://github.com/icekylinx) | Stopped product ring, rational centers and ordinary wrapper, [PR104](https://github.com/CrocSwap/integer-mult-bounds/pull/104) | +| [@Swapnil-jain](https://github.com/Swapnil-jain), Swapnil Jain | Round-seven bit word, [integer-mult-kappa](https://github.com/Swapnil-jain/integer-mult-kappa) | +| [@jacklightChen](https://github.com/jacklightChen), Zhihao Chen | Semantic and controlled-basis interfaces, [PR23](https://github.com/CrocSwap/integer-mult-bounds/pull/23), [PR29](https://github.com/CrocSwap/integer-mult-bounds/pull/29) | +| [@hipotures](https://github.com/hipotures), RaD project | Paid positional, routing and semantic machinery, [PR41](https://github.com/CrocSwap/integer-mult-bounds/pull/41) and retained sources | + +Earlier authors remain credited in the original notices. Original Anthropic Claude and other assistance disclosures are preserved verbatim in archived sources. These accounts identify contributors to distinct dependencies, not reviewers of this new composition. diff --git a/research/shrunk-birth-terminal/README.md b/research/shrunk-birth-terminal/README.md new file mode 100644 index 0000000000..dc737e9e30 --- /dev/null +++ b/research/shrunk-birth-terminal/README.md @@ -0,0 +1,16 @@ +# Shrunk frames with joint birth reuse and terminal elimination + +The selected conditional bound is `kappa = 112802185097556/10^18`, with dyadic corollary `2^-14`, under the inherited OpenAI #109 all-size framework. The complete profile has 26,216 physical auxiliary roles, width 114,315,520, total rank 65,843,877,440, largest child 574 and conservative scalar charge 3,116,113,870,848. + +- [Proof and inherited hypotheses](PROOF.md) +- [Exact certificate](certificate.json) +- [Reproduction commands](REPRODUCE.md) +- [Terminal identity and complete packet argument](TERMINAL-PROOF.md) +- [Three-stock balanced transfer](arithmetic/PROOF.md) +- [Source and input hashes](SOURCE.json) +- [Independent prepackage certificate](audit/independent-prepackage-certificate.json) +- [Scoped Lean arithmetic companion](lean/ShrunkBirthTerminal.lean) + +The new composition retains 2,108 dirty-slot births and eliminates 381 unaliased terminals. The portable verifier reconstructs the complete geometry and physical word, checks all 2,024 source and 26,216 dirty columns in both orientations, and independently assembles the full paid histogram. Two exact arithmetic implementations and 240 Lean theorems check the stated finite/rational claims. All-size realization, analytic and fixed-tape interfaces remain explicit inherited hypotheses. + +Chafik Boukhalfa with OpenAI Codex assistance. Original contributors, licenses, source-specific notices and AI-assistance disclosures are preserved; see the proof and archived credit records. diff --git a/research/shrunk-birth-terminal/REPRODUCE.md b/research/shrunk-birth-terminal/REPRODUCE.md new file mode 100644 index 0000000000..5c666b6355 --- /dev/null +++ b/research/shrunk-birth-terminal/REPRODUCE.md @@ -0,0 +1,35 @@ +# Reproduce the selected composition + +From the repository root, run: + +```sh +make verify-shrunk-terminal +``` + +This uses Python's standard library. It verifies the frozen source closure, losslessly decompresses the exact selected inputs, reproduces the entire geometry from pinned source and recorded legal moves, compares it directly with every mathematical field of the actual selected input fixture, reconstructs the complete physical word, checks both orientations over Q, compares the complete paid profile and scalar bill, recomputes both exact arithmetic enclosures and all transfer inequalities, runs 18 arithmetic adverse controls, audits independent birth/terminal accounting, and checks the unchanged Lean input/generator/compile provenance. All reconstruction writes occur in a new temporary directory; frozen inputs and certificates remain unchanged. The geometry replay is a selected witness replay, not a rerun of the heuristic optimization. + +The complete repository check required before publication is: + +```sh +make -j1 verify +``` + +Historical compiler groups need a C++17 compiler and Boost headers. CI uses Ubuntu; the exported local verification receipt records the macOS compiler adapter and environment. The selected group itself requires no compiler, external package, network request, downloaded model or account credential. + +Fresh formal compilation uses the repository's pinned Lean 4.21.0 and Mathlib configuration: + +```sh +make formal-historical-verify +``` + +The `formal/lean/KappaCheck/ShrunkBirthTerminal.lean` module is byte-identical to the separately compiled 240-theorem companion. The formal target builds all integrated modules and checks every listed theorem's axiom dependencies. It permits only `propext`, `Classical.choice` and `Quot.sound`. `audit_lean.py` reproduces the generated source from its saved input and links all mathematical values to the selected exact certificate; that check is not itself a fresh Lean compilation. + +The authoritative current certificate is `certificate.json`. `arithmetic/certificate.json` and `audit/independent-prepackage-certificate.json` preserve the independent witnesses before the descriptive scalar-count correction. The exact equivalence and original byte hashes are recorded in `audit/lean-portable-equivalence.json` and `audit/scalar-metadata-correction.json`. No bound, physical word, paid histogram, scalar charge or Lean theorem changed during that correction. + +For a fresh optional receipt outside the frozen package: + +```sh +python3 research/shrunk-birth-terminal/verify.py --output build/shrunk-birth-terminal-verification.json +``` + +`SOURCE.json` binds all portable construction, exact arithmetic, saved inputs, original references, Lean sources and repository integration. `selected/INPUTS.json` binds both the stored compressed bytes and the original uncompressed input bytes. The full word comparison uses the decompressed canonical payload, avoiding platform-specific gzip-header differences; the supplied archived file also has its own exact SHA256. Assertions must be enabled. Timing and RSS belong only to diagnostic receipts; the mathematical certificate forbids floating-point values recursively. diff --git a/research/shrunk-birth-terminal/SOURCE.json b/research/shrunk-birth-terminal/SOURCE.json new file mode 100644 index 0000000000..c77e99bbcf --- /dev/null +++ b/research/shrunk-birth-terminal/SOURCE.json @@ -0,0 +1,291 @@ +{ + "author": "Chafik Boukhalfa with OpenAI Codex assistance", + "base_commit": "56b66d58297deca1d7dd130247d720e960f77a37", + "package_files": { + "PROOF.md": "b2852ec95798b137ef96d3723a69090f37fcdd2a5089d10712a4f1f2691cea5d", + "README.md": "21964e8a40e4847e42a513cd5bc103c966e517f783e86369cc1958380d6eb9cf", + "REPRODUCE.md": "13f94f66d588d9629af06009859cc402c597add91cefeccba9e8b018f0f1936b", + "TERMINAL-PROOF.md": "b16b3025ba29103d331a19c7e70c95848b8576772bbe5197708af649fbdf3432", + "arithmetic/PROOF.md": "2309aafdeecc7a432aa485f1cd4a5392fda3542ec8a3ea193ad1557f049becdb", + "arithmetic/README.md": 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Repository-validation receipts are derived and excluded from this freeze." +} diff --git a/research/shrunk-birth-terminal/TERMINAL-PROOF.md b/research/shrunk-birth-terminal/TERMINAL-PROOF.md new file mode 100644 index 0000000000..ebe1515ac7 --- /dev/null +++ b/research/shrunk-birth-terminal/TERMINAL-PROOF.md @@ -0,0 +1,61 @@ +# Terminal elimination after shrunk frames and birth-slot reuse + +This is a finite composition of PR125's shrunk frames, PR124's birth-slot reuse, and PR122's terminal-accumulator identity. The code and physical word are new composition artifacts. PR117's graph, the ordinary rational-center decoder and the inherited stopped-product, analytic, fixed-tape and all-size transfer remain assumptions. No new final kappa is asserted here; complete numerical assembly is a separate check. + +## Selection and noninterference + +A selected virtual role u is an ordinary terminal, has no outgoing auxiliary use, has exact old and terminal readout column alpha times one target with alpha=+/-1/2, is deferred and untouched during the retained-center phase, and receives every update after centers and all old readouts. This bounded pass excludes clean-input-start roles. + +A role is also excluded if it is either endpoint of a selected birth reuse. In particular, deleting a terminal that occupies an earlier donor's physical slot would not remove that physical slot and would require a different cost argument. The current selection preserves every birth pair and all existing birth compensation reads. Since selected terminals never control a retained auxiliary update, all retained auxiliary values, donor liveness, recipient birth values and compensation-read times remain identical. + +For each selected terminal, all old readout frames of its target are contained in its first incoming-update frame; its entire incoming frame chain is nested through the final target hyperplane. One role is selected per target, preventing two terminal rewrites from competing for the same target-front interval. The builder emits the old target advances even when their accompanying terminal read is deleted. Every new target subdivision is charged by the full chronological scan. + +## Exact arbitrary-dirty identity + +Write z_u for u's initial dirty value. Its contribution is + + -alpha*z_u + alpha*(z_u + sum_j a_j(t_j)) + = sum_j alpha*a_j(t_j). + +Delete u, its initial and final reads, its destination updates and their inverse cleanup. At each original update index t_j, add alpha times the same source's current value directly to the target. No source is read early, late, or from an uncharged snapshot. Every retained auxiliary update and source injection keeps its exact original order. Cleanup is the exact reverse of the actual retained workspace and source events; direct target updates are not cleaned up. Targets never control workspace gates. + +The complete emitted word is checked over Q using exact signed integer bit planes with common denominator 42. The audit propagates every target response backward through the actual aliased word and checks all source and physical dirty columns simultaneously. The forward source response is +I and every dirty response is zero. The reflected signed inverse, with the two data banks swapped and frames complemented, is checked independently for source response -I and zero dirty responses. Omitted redirects and changed redirect signs fail this exact all-column audit. + +## Frames, complete profile and cost + +Every redirect uses the source's original gate frame. Its target is promoted at that exact operation index. Full forward and reflected frame scans verify actual containment, nondegenerate endpoints, both data-bank paths, center-copy losses, auxiliary exteriors and final endpoint charges. An illegal redirect-frame mutation is rejected. The reflected event involution and the full paid histograms agree exactly. + +Let h=24, m=h^2=576 and v=2024. For one selected role, sigma is its initial deferred dimension, M is the target's final old-readout dimension and F0 is its first incoming frame dimension. Eligibility establishes 0<=sigma<=M<=F0<=h-1. The exact complete cost comparison, after adding one dummy width-m child to the new side, is + + old: [m-h+sigma, 1, F0-sigma, h-1-M] + new: [m, F0-M, 0, 0]. + +The masses coincide. The new packet strictly majorizes the old one; it therefore has smaller strictly concave power sum. The full profile emitted from the actual physical word equals the sum of these packets, with replication 2v. All 576 integer hinge functions are checked against the complete histogram, not only against isolated packets. + +For all completed variants below, sigma=M=F0. After the paid target subdivisions, each elimination therefore removes 2v copies of widths [m-h+sigma, 1, h-1-sigma], with zero-width entries omitted. All counts stay nonnegative. Removing q unshared physical roles changes W by -2vq and recursive rank by -2vqm, preserving deficit 1,862,080. Largest child remains read from the complete histogram. + +If the old power numerator is below W_old*m^p, padded concave dominance implies that the new numerator is below W_new*m^p. This establishes preservation and strict improvement of each previously feasible power moment. It does not assert unrestricted monotonicity of normalized moments at infeasible exponents, nor does it determine the final assembly bottleneck. + +## Explicit scalar charge + +Every direct update has numerator +/-21 over denominator 42 and is expanded literally into 21 same-frame shears of coefficient +/-1/42. This introduces no new role, source copy or frame incidence. The new bill keeps the entire inherited scalar bound without taking credit for any removed work, then adds 29 groups per direct update: the 21 actual shears and eight additional groups of conservative bookkeeping allowance. The allowance creates no additional physical operation or frame charge. The fixed odd-21 grid and maximum coefficient bound do not increase. The global bound is recomputed as 16*(2v*local+8v^2), with this larger local bill. This conservative bound is exported separately for numerical recertification. + +## Reproduction and provenance + +Run `compose_terminal.py --frames PATH/FRAMES.pkl --matches PATH/BIRTH_MATCHES.json.gz --readouts PATH/READOUTS.pkl --scalar-bill PATH/READOUT_COST.json --out NEW_DIRECTORY`. Inputs are copied and hashed before use. An optional `--terminal-roles PATH/TERMINAL_ROLES.json` supplies a bare JSON list of integer role IDs; the builder validates that it is a duplicate-free subset of eligible unshared roles with distinct targets and no birth alias before reconstructing the whole word. `terminal_inventory.py` accepts the same three witness paths and optional selection. Its separate `--include-birth-recipients` mode exposes virtual options with sigma=M=F0 for joint optimization; these options are explicitly not a legal simultaneous elimination selection until the real birth matching is adjusted and the default checks rerun. No upstream or root research directory is written. + +Each output retains input copies, exact selected roles, full chronological word, full child profile, exact scalar bill, both frame/response audits, actual mutation results, 576 hinge values, source hashes and original operation-index bindings. The final joint runs contain immutable construction-source copies under `construction-sources`; their inventory runs use those copies and reject generator drift during execution. Both final emitted histograms also equal the independently predicted joint-optimization histograms. The original PR122 source archive is retained under `references/pr122`, pinned to b1a6f24e57141637b3ff040d6f2ce9d896ffb9bb. + +Credit: SovereignSteak for PR122's terminal-elision identity and packet argument; Joel Pulikkan and Anthropic Claude assistance for PR125 shrunk frames; James Chang for PR124 birth reuse and corrected feasible-moment qualification; eumemic for PR117's replayed graph; Avi Eisenberg, Rohan Arun, Swapnil Jain and inherited contributors for compiler, deferral, rational-center and stopped-product ingredients. This disjoint composition, explicit word, conservative added scalar bill and both-orientation all-column audits were prepared with OpenAI Codex assistance. Original source notices are preserved with the references. + +## Completed finite variants + +| Variant | Birth pairs retained | Terminal roles removed | Physical R | W | Rank | Conservative G | +|---|---:|---:|---:|---:|---:|---:| +| cost-weighted | 2108 | 266 | 26331 | 114781040 | 66112016960 | 3115182247936 | +| original-greedy | 2108 | 253 | 26344 | 114833664 | 66142328384 | 3115140925952 | +| protected-prune | 2108 | 309 | 26288 | 114606976 | 66011756096 | 3115484649728 | +| protected-expansion | 2108 | 309 | 26288 | 114606976 | 66011756096 | 3115484649728 | +| weighted | 2108 | 309 | 26288 | 114606976 | 66011756096 | 3115484649728 | +| joint-base | 2108 | 381 | 26216 | 114315520 | 65843877440 | 3116113870848 | +| joint-expansion | 2108 | 381 | 26216 | 114315520 | 65843877440 | 3116113870848 | diff --git a/research/shrunk-birth-terminal/arithmetic/PROOF.md b/research/shrunk-birth-terminal/arithmetic/PROOF.md new file mode 100644 index 0000000000..2cca3a12e1 --- /dev/null +++ b/research/shrunk-birth-terminal/arithmetic/PROOF.md @@ -0,0 +1,101 @@ +# Balanced positional transfer of the stopped product-ring composition + +This is an additional paid layout composition. It is not an omission of the old prefix cost or a claim that a favorable child histogram by itself proves an all-size multiplication theorem. + +## Contracts that have to survive the composition + +The supplied finite word must return every dirty auxiliary coordinate, compute the exact signed complex source map, use legal common frames on both ports, and account for every transition, source/target front, exterior, center copy and endpoint correction. Its signed reflected word reverses the literal operation order, negates shears, exchanges data banks and complements every frame. The complete paid histogram and literal scalar upper bound are inputs to this arithmetic layer. Reflection and scalar-identity evidence are separately hash-bound. + +PR104's opposite-bank product-ring construction makes each proper projector residual of rank r one reversed child of width r. Its global conjugation, common generic basis, full involution factorization and paid atom adapters remain required. It supplies an ordinary interchange only after the constant-size outer wrapper. That completed wrapper has arbitrary-width, complete-spectator and restored-row guarantees. Its constant number of calls is outside the recursive moment and does not multiply the child histogram. The atom exponent remains theta=1/1000, with old ordinary saving 384599/10^10. Thus the round-seven coarse bit saving 620523/(5*10^9) gives ordinary saving 1240189553/10^13, and theta exceeds this saving, so paid atom loops are lower order. + +The complex primitive retains the completed exact tensor contract, translated endpoint gauges, inverse phase correction, and common odd-21 grid. It must preserve a completed child's incoming odd denominator. No boundary rounding, characteristic-two substitution for signed arithmetic, free address reversal, or uncharged coefficient multiplication is introduced. + +Readout n/42 may be realized by |n| consecutive same-frame shears with coefficient sign(n)/42. Each has magnitude at most one, their exact sum is n/42, and their inverse negates the pieces in reverse order. They require no new source copy or frame transition. The supplied conservative L1 scalar bill may include unused copy/scan allowance, but its local/global bound must still cover the actual selected literal word. This observation does not authorize ignoring repeated scalar occurrences or a wrong inverse sign. + +## Why the balanced layout applies + +Use the inherited PR34/RaD paid positional layout as made explicit for deferred/signed networks in PR100 and PR103. Separate the extra top bit of each long FFT axis, and use common named low-coordinate groups K_j in [K,2K). The axis-major/group-major permutation and inverse are paid by the ordinary arbitrary-coordinate router. The resulting extra prefix work is O(T p d), with saving margin 1-epsilon. Complete active, spectator, scratch, phase, control and row fields travel with their descriptors; FFT order, twiddle order and forward/inverse alignment are preserved. No local scalar operation or physical residual is moved across another operation by this outer regrouping. + +The stopped ordinary wrapper exposes precisely the ordinary interchange contract consumed by that router. The complex word exposes the same completed tensor contract required by the semantic C1=1 induction. Therefore the stopped product-ring implementation can instantiate the same balanced layout, under the inherited all-size contracts. The original geometric condition 1-epsilon(1+c)>0 remains in the constraint list; only the work margin changes from the old repeated-prefix charge to the proved paid layout's 1-epsilon. A negative control reinstates the old work margin at the new parameters and rejects them. + +## All three row stocks remain present + +Along any active nested call chain, reserve + + W_complex^D_complex * W_coarse^D_coarse * W_old^D_old. + +After a complex and coarse division, the old ordinary stock remains available to every stopped leaf or peeled atom. Sequential wrappers and copies reuse restored rows. They create no additional simultaneous factor, and also do not remove the old factor. + +For each family, d is the least positive integer with m^d > 2*r_max^d, so its depth is at most d*ceil(log2(max(2,e))) plus a fixed constant. The selected dimensions give: + +| Family | m | largest child | role bits | d | row coefficient | +|---|---:|---:|---:|---:|---:| +| Coarse bit | 529 | 528 | 27 | 367 | 9909 | +| Complex | 576 | 574 | 27 | 200 | 5400 | +| Old ordinary leaf | 575 | 529 | 28 | 9 | 252 | + +The total is 15561. A p^32000 stock leaves strict gap + + 32000 - (51/25)*15561 = 6389/25 > 0. + +The suffix slope is 128000. The validator recomputes all three minimal halving degrees, every wire-bit count, the old-stock contribution, the total coefficient, the degree gap and the suffix slope. It does not reuse the original balanced helper's two-family row formula. Semantic E, literal charge, B, C0, C1=1 and the completed-child induction are also recomputed from the supplied scalar upper bound. + +## Exact parameters and all retained inequalities + +Let b be the certified complex saving, A the proved ordinary bit saving, beta>0 the complex stopping parameter, eta>0 the balanced backoff, and zeta>0 a strict weakening. Set + + a = min(A, (1-beta)*b-zeta), + q = a*(1-2*eta), + c = q+eta/4, + epsilon = (1-eta)/(1+q), + lambda' = 1-q, + lambda = ((1-a)+lambda')/2, + g = epsilon*q, + r = (g+1-epsilon)/2, + delta = eta/8. + +The seven margins are + + 1-epsilon, a, g, a, + min(1-epsilon-delta, r-delta), + 1-epsilon-delta, epsilon. + +The minimum is g. The identities + + 1-epsilon-g = eta, + 1-epsilon-r = eta/2, + 1-epsilon*(1+c) = eta-epsilon*eta/4 > 0 + +retain the scalar, Gaussian and geometric gaps. The stopped internal exponent and complex leaf exponent remain exactly those in PR104; (1-beta)*b>a ensures the leaf ordering. All 47 strict inequalities are retained. Source normalization shows the full adapter differs from the pinned balanced implementation only in three-stock validation, explicit old-leaf argument plumbing and inclusion of the old leaf in cutoff maxima. No constraint or cost margin is deleted. + +## Selected finite arithmetic and grid ceiling + +The selected joint-expansion profile retains 2108 birth reuses, eliminates 381 nonaliased terminal roles, and has R=26216, m=576, W=114315520, rank=65843877440 and deficit=1862080. Its scalar group bound is G=3116113870848. The actual emitted physical profile, both-orientation frame/scalar audits, and literal word are separate SHA-bound construction evidence. Its entire histogram is supplied, not inferred from role reduction or an unrestricted majorization claim. Two separate rational enclosures accept the greatest 10^-24-grid complex saving + + b = 112814910866013477738/10^24 + +and reject b+10^-24. The first enclosure reduces logarithms by 4/3 with 80 atanh terms and uses degree-12 exponentials with outward 10^-45 rounding. The independent pinned PR65/100 method reduces by 2 with 32 atanh terms and uses a degree-eight exponential bound with outward 10^-40 rounding. Every first-method log/exponential interval lies inside the second, and both separate the accepted and rejected moments from one. + +Taking beta=eta=10^-24 and zeta=10^-30 gives + + kappa = 112802185097556/10^18. + +The next 10^-18 point is rejected. More strongly, let b_plus be the rejected complex point. The moment is strictly increasing in b, so the true profile root is below b_plus. Every member of this balanced family has a= 14000000000000000000000000. This is only a sufficient numeric-comparison threshold. Prime supply, fixed-basis setup, descriptor/catalogue domination, logarithm absorption and exact recovery retain their inherited eventual conditions; this value is not a practical runtime threshold. + +Original authorship remains attached: icekylinx for stopped product-ring accounting and the ordinary wrapper; PR23/29 Zhihao Chen, RaD/hipotures and James Chang/PR34 for the semantic/balanced layout; PR100/103 Rohan Arun for its deferred/signed integration; Swapnil Jain and the relevant complex producer/frame/recycling authors for the finite inputs. This three-stock adapter and independent certificate were prepared with OpenAI Codex assistance. The supplied physical word, all-size frame implementation, simultaneous basis, atom streaming, routing, prime/precision/recovery and analytic fixed-tape transfer remain separate inherited obligations. + +## Portable exact boundary + +The portable certificate generator admits only explicit integer mathematical profile fields and canonical integer child counts. It derives h, v, m, N, L, W and deficit relations before arithmetic, recursively rejects floating-point values before serialization and after readback, and binds the raw physical profile and scalar-bill bytes by SHA256. Discovery timings stay outside the mathematical certificate. The independent secondary enclosure executes only three verbatim arithmetic function bodies from the pinned source. The selected validation applies 18 adverse controls and compares every controlling quantity, moment enclosure, assembly and cutoff against the separately generated prepackage witness. The two certificates agree exactly on these mathematical fields. diff --git a/research/shrunk-birth-terminal/arithmetic/README.md b/research/shrunk-birth-terminal/arithmetic/README.md new file mode 100644 index 0000000000..304230a378 --- /dev/null +++ b/research/shrunk-birth-terminal/arithmetic/README.md @@ -0,0 +1,23 @@ +# Portable exact arithmetic + +Python 3 standard library only. No producer, external service, dependency install or upstream baseline execution is required. Keep this directory layout and filenames intact. + +Generate the deterministic mathematical certificate from the selected complete profile and paid scalar bill: + +```sh +python3 certificate.py --profile PATH/complex-profile.json --scalar-bill PATH/READOUT_COST.json --certificate PATH/certificate.json --record +``` + +Verify exact regeneration by omitting `--record`. The generator checks the copied upstream sources against SHA256 and Git blob pins, canonicalizes the supplied mathematical profile, rejects floats recursively, recomputes both rational moment enclosures, all 47 inequalities, seven margins, three row stocks, semantic constants, cutoffs and the fixed-profile next-grid exclusion. It also recomputes the stopped coarse-bit supplier with both enclosures. + +Run the source-adaptation and selected mutation checks: + +```sh +python3 validate.py --certificate PATH/certificate.json --receipt PATH/validation.json +``` + +For the independent prepackage witness, add `--reference-certificate PATH/independent-prepackage-certificate.json`. The validator compares all controlling mathematical fields, including both full moment records, the complete assembly and cutoffs. Its receipt is deterministic and float-free. Normal Python assertion execution is required; optimized mode is rejected. + +`references/pr100/refine.py` is a pinned source document. Only its three exact arithmetic function bodies are selected through AST; its application and foreign producer entry points are never imported or executed. `REFERENCE_PINS.json` retains original repositories, commits, file paths and Git blobs. The full original notices remain in copied source files. + +Raw discovery timings and source metadata are excluded from the mathematical certificate. Only the raw profile/bill SHA256 values enter it. Retain physical generation, both-orientation scalar/frame audits, proofs, Lean input/source/compiler receipts, raw metadata, and their source manifest separately. This arithmetic layer does not replace those obligations or claim a global optimum or practical speedup. diff --git a/research/shrunk-birth-terminal/arithmetic/REFERENCE_PINS.json b/research/shrunk-birth-terminal/arithmetic/REFERENCE_PINS.json new file mode 100644 index 0000000000..f39c72e7db --- /dev/null +++ b/research/shrunk-birth-terminal/arithmetic/REFERENCE_PINS.json @@ -0,0 +1,52 @@ +{ + "balanced_stopped.py": { + "derivation": "Exact pinned PR104 balanced helper with explicit old-leaf argument, third simultaneous row factor and cutoff maximum; validate.py normalizes the complete source back to its pinned upstream bytes.", + "sha256": "03f5f012ab4eb306320ab8a209c2041addd75b84aa43f45ab80595c8989ce781" + }, + "inputs/bit-profile.json": { + "commit": "6ec868e8568ca9a74b7245494de1b187c7be78fe", + "git_blob": "36105e819aed9576d5397cbb151d09fb97878324", + "path": "research/cyclic-deferred/bit-profile.json", + "repository": "rohanarun/integer-mult-bounds", + "sha256": "7293f330518b78650bd86d76b93681e43f3a55541cdb8110993714148a4b4a6a" + }, + "interval_moment.py": { + "derivation": "Independent rational enclosure using 4/3 range reduction, 80 atanh terms, degree12 Taylor exponential and outward10^-45 rounding; prepared with OpenAI Codex assistance.", + "sha256": "9d3d1d28bfb3375958995205179b171fb65c70a3792cf9f7a21ef5ee54f5460b" + }, + "references/pr100/binary_frame_math.py": { + "commit": "22dc19dd7123dd582110a912a6ca687e31e2243f", + "git_blob": "b87855e808802c6b5dbdfb845f2328370ff8a4f0", + "path": "research/deferred-balanced/arithmetic-sources/binary_frame_math.py", + "repository": "rohanarun/integer-mult-bounds", + "sha256": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0" + }, + "references/pr100/refine.py": { + "commit": "22dc19dd7123dd582110a912a6ca687e31e2243f", + "git_blob": "399299089e26a77a81d11365c829f4cb6cb05e49", + "path": "research/deferred-balanced/arithmetic-sources/refine.py", + "repository": "rohanarun/integer-mult-bounds", + "sha256": "e0488c919e76850313ff93d7da704a7fcc14a316eee2cac81e2b8dff9c145b5d" + }, + "references/pr104/balanced_assembly.py": { + "commit": "948ce1510df750f4c18b96bdaef436a86f8bf834", + "git_blob": "c7fd42867d741939db6a41529bfdbb136f03191b", + "path": "research/copied-fixed/balanced_assembly.py", + "repository": "icekylinx/integer-mult-bounds", + "sha256": "4d27575dcad2b45a281a34054d311409ecd954f373c0c3a62c29bcc843f06a86" + }, + "references/pr104/copied-centers-network.json": { + "commit": "948ce1510df750f4c18b96bdaef436a86f8bf834", + "git_blob": "20bbb6806ce0611e481512894d1fd73d97c2970f", + "path": "certificates/copied-centers-network.json", + "repository": "icekylinx/integer-mult-bounds", + "sha256": "7dbd675e42e22ac076280360f8750031851564bb7a56079e66236fee5d0a6cdf" + }, + "references/pr104/structured_bulk_assembly.py": { + "commit": "948ce1510df750f4c18b96bdaef436a86f8bf834", + "git_blob": "b76f9cb5a452fb637f3a8aec0748da6d2d81968a", + "path": "scripts/structured_bulk_assembly.py", + "repository": "icekylinx/integer-mult-bounds", + "sha256": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + } +} diff --git a/research/shrunk-birth-terminal/arithmetic/balanced_stopped.py b/research/shrunk-birth-terminal/arithmetic/balanced_stopped.py new file mode 100644 index 0000000000..5b02fb6948 --- /dev/null +++ b/research/shrunk-birth-terminal/arithmetic/balanced_stopped.py @@ -0,0 +1,204 @@ +# Three-reserve stopped-product adaptation of the inherited PR34/RaD/PR23 balanced +# positional assembly retained in PR104 and proved applicable to deferred words +# in PR100/103. Original attribution below is preserved. This module verifies +# arithmetic only; scalar-word/profile provenance and all-size interfaces remain +# separate obligations. Prepared with OpenAI Codex assistance, Apache-2.0. +"""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, ordinary_leaf): + """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_coarse', 'complex', 'ordinary_leaf'): + data = ordinary_leaf if name == 'ordinary_leaf' else 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'] + leaf_degree = result['ordinary_leaf']['halving_degree']*result['ordinary_leaf']['wire_bits'] + require(integer(finite_bridge['ordinary_leaf_row_degree']) == leaf_degree, + 'ordinary leaf stock missing or stale') + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit_coarse', 'complex', 'ordinary_leaf')) + 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, ordinary_leaf, 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, ordinary_leaf) + 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, ordinary_leaf, 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, ordinary_leaf) + 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[name]['m'] for name in ('bit_coarse','complex','ordinary_leaf')) + 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/research/shrunk-birth-terminal/arithmetic/certificate.json b/research/shrunk-birth-terminal/arithmetic/certificate.json new file mode 100644 index 0000000000..119b6c8b07 --- /dev/null +++ b/research/shrunk-birth-terminal/arithmetic/certificate.json @@ -0,0 +1,2524 @@ +{ + "actual_bit_saving": "1240189553/10000000000000", + "assembly": { + "absorption_gap": "51350955350972219636574114327365369448123005318656908856664201698261131/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000", + "constraints": { + "K_dominates_log": 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'-28203699512803805279500377303413505275896650061379754949523635769612716700410026261131/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000'}", + "ordinary_leaf_bridge": { + "W": 188181929, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "ordinary_leaf_saving": "384599/10000000000", + "profile": { + "L": 2234496, + "N": 4096576, + "R": 26216, + "W": 114315520, + "child_multiplicities": { + "1": 435042608, + "10": 7735728, + "11": 6658960, + "12": 33578160, + "13": 13184336, + "14": 1821600, + "15": 3238400, + "16": 631488, + "17": 404800, + "18": 202400, + "19": 311696, + "2": 266771296, + "20": 550528, + "21": 1222496, + "22": 64768, + "23": 8383408, + "3": 29060592, + "4": 60639040, + "5": 26643936, + "529": 8193152, + "552": 97071040, + "554": 3456992, + "556": 1481568, + "558": 2384272, + "560": 445280, + "562": 48576, + "571": 740784, + "572": 101200, + "573": 28336, + "574": 364320, + "6": 15333824, + "7": 11743248, + "8": 22069696, + "9": 3938704 + }, + "deficit": 1862080, + "h": 24, + "m": 576, + "maxchild": 574, + "total_rank": 65843877440, + "v": 2024 + }, + "raw_discovery_metadata_in_certificate": false, + "scope": "Exact arithmetic on the supplied complete physical profile. Physical source/dirty/reflection identities, paid positional layout, all-size interfaces and fixed-tape analytic transfer remain separately verified or inherited obligations. Grid optimality is only within this fixed-profile balanced transfer family.", + "source_sha256": { + "REFERENCE_PINS.json": "fbf75766c9112483e43e9cfca5e339044fe80f1d41481c1d7146080ed4970e6f", + "balanced_stopped.py": "03f5f012ab4eb306320ab8a209c2041addd75b84aa43f45ab80595c8989ce781", + "certificate.py": "30f143d6b2e05dc284b773fafbe831080207ef070d07f222cf2e5b87c9746142", + "inputs/bit-profile.json": "7293f330518b78650bd86d76b93681e43f3a55541cdb8110993714148a4b4a6a", + "interval_moment.py": "9d3d1d28bfb3375958995205179b171fb65c70a3792cf9f7a21ef5ee54f5460b", + "references/pr100/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "references/pr100/refine.py": "e0488c919e76850313ff93d7da704a7fcc14a316eee2cac81e2b8dff9c145b5d", + "references/pr104/balanced_assembly.py": "4d27575dcad2b45a281a34054d311409ecd954f373c0c3a62c29bcc843f06a86", + "references/pr104/copied-centers-network.json": "7dbd675e42e22ac076280360f8750031851564bb7a56079e66236fee5d0a6cdf", + "references/pr104/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d", + "validate.py": "f61d6d19fcfe1e3974a16da3c4cc5c9ce43066a0735416d7a3c827a1083d096c" + } +} diff --git a/research/shrunk-birth-terminal/arithmetic/certificate.py b/research/shrunk-birth-terminal/arithmetic/certificate.py new file mode 100644 index 0000000000..b4c9977d9e --- /dev/null +++ b/research/shrunk-birth-terminal/arithmetic/certificate.py @@ -0,0 +1,111 @@ +#!/usr/bin/env python3 +"""Deterministic exact arithmetic for a supplied complete two-factor profile. + +All mathematics uses integers/Fraction; no producer or foreign baseline runs. +Prepared with OpenAI Codex assistance. Inherited notices are retained in references. +""" +import argparse,ast,importlib.util,json,math,sys +from copy import deepcopy +from fractions import Fraction as Q +from hashlib import sha256,sha1 +from pathlib import Path +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +import balanced_stopped as balanced +import interval_moment as intervals +HERE=Path(__file__).resolve().parent +read=lambda p:json.loads(p.read_text()) +sha=lambda p:sha256(p.read_bytes()).hexdigest() +def check(ok,message): + if not ok:raise ValueError(message) +def js(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):js(v) for k,v in x.items()} + if isinstance(x,(list,tuple)):return [js(v) for v in x] + return x +def exact(x): + if isinstance(x,dict):return {k:exact(v) for k,v in x.items()} + if isinstance(x,list):return [exact(v) for v in x] + if isinstance(x,str) and '/' in x and all(s.lstrip('-').isdigit() for s in x.split('/')):return Q(x) + return x +def no_floats(x,path=''): + if isinstance(x,float):raise ValueError('Float forbidden at '+(path or '/')) + if isinstance(x,dict): + for k,v in x.items(): + check(type(k) is str,'Certificate key must be a string at '+path) + no_floats(v,path+'/'+k) + elif isinstance(x,(list,tuple)): + for i,v in enumerate(x):no_floats(v,path+'/'+str(i)) + else:check(type(x) in (str,int,bool,type(None),Q),'Unsupported certificate value at '+path) +def profile(raw): + p={key:raw[key] for key in ('h','v','m','N','L','R','W','total_rank','deficit','maxchild')} + check(all(type(v) is int for v in p.values()),'Profile dimensions must be explicit integers') + H=raw['child_multiplicities'];check(type(H) is dict,'Histogram object required') + check(all(type(t) is str and t.isdigit() and t==str(int(t)) and type(n) is int for t,n in H.items()),'Canonical integer histogram required') + p['child_multiplicities']=dict(sorted(H.items(),key=lambda z:int(z[0]))) + h,v,m,N,L,R,W=(p[k] for k in ('h','v','m','N','L','R','W')) + check(h>=3 and R>0 and m==h*h and v==math.comb(h,3) and N==v*v and L==2*v*h*(h-1),'Two-factor dimensional identity') + check(W==2*N+2*v*R and p['deficit']==N-L>0,'Role width or deficit identity') + no_floats(p);intervals.prepare(p);return p +def module(path,name): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m +def secondary(): + source=HERE/'references/pr100';arithmetic=module(source/'binary_frame_math.py','pinned_secondary_arithmetic') + tree=ast.parse((source/'refine.py').read_text());wanted={'floor_scaled','ceiling_scaled','exact_moment'} + nodes=[n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name in wanted];check({n.name for n in nodes}==wanted,'Frozen enclosure functions missing') + env=dict(Q=Q,factorial=math.factorial,arithmetic=arithmetic) + exec(compile(ast.Module(body=nodes,type_ignores=[]),str(source/'refine.py'),'exec'),env) + return env['exact_moment'] +def axis(p): + m,W,r=(p[k] for k in ('m','W','maxchild')) + return dict(m=m,W=W,maxchild=r,halving_degree=balanced.halving_degree(m,r),wire_bits=W.bit_length()) +def bridge(bit,p,G,old): + coarse,c=axis(bit),axis(p);m,W,s=(p[k] for k in ('m','W','total_rank'));E=64*(W+m+G+1)**3;B=s+E + literal=2*G*W**2+8*s+4*W+4+32*m;c.update(s=s,scalar_group_upper=G) + coeff=sum(x['halving_degree']*x['wire_bits'] for x in (coarse,c,old));degree=1000*((51*coeff)//25000+1) + return dict(bit_coarse=coarse,complex=c,ordinary_leaf_row_degree=old['halving_degree']*old['wire_bits'],semantic=dict(E=E,B=B,C0=32*m*B**2,C1=1,literal_charge=literal,strict_literal_gap=E-literal,induction_gap=2*B*(m-p['maxchild'])-s-E,fixed_odd_divisor=21,exact_grid='Retain the common dyadic/21 grid and completed-child odd-denominator preservation.'),rows=dict(coefficient=coeff,degree=degree,degree_gap=Q(degree)-Q(51,25)*coeff,suffix_slope=4*degree,contract='W_complex^D_complex * W_coarse^D_coarse * W_old^D_old; all three simultaneous stocks retained.')) +def below(value,denominator): + x=value*denominator;return Q(-((-x.numerator)//x.denominator)-1,denominator) +def source_hashes(): + provenance=read(HERE/'REFERENCE_PINS.json');no_floats(provenance) + for name,record in provenance.items(): + data=(HERE/name).read_bytes();check(sha256(data).hexdigest()==record['sha256'],'Pinned source SHA changed: '+name) + if 'git_blob' in record:check(sha1(b'blob '+str(len(data)).encode()+b'\0'+data).hexdigest()==record['git_blob'],'Pinned Git blob changed: '+name) + names=['certificate.py','validate.py','balanced_stopped.py','interval_moment.py','REFERENCE_PINS.json','inputs/bit-profile.json','references/pr104/copied-centers-network.json','references/pr104/balanced_assembly.py','references/pr104/structured_bulk_assembly.py','references/pr100/refine.py','references/pr100/binary_frame_math.py'] + return {name:sha(HERE/name) for name in names} +def build(profile_path,bill_path): + pins=source_hashes();raw=read(profile_path);p=profile(raw);bill=read(bill_path);G=bill['global_scalar_group_upper'];check(type(G) is int and G>0,'Scalar bill must be a positive integer') + bit=profile(read(HERE/'inputs/bit-profile.json'));old_source=read(HERE/'references/pr104/copied-centers-network.json');old=old_source['finite_bridge']['bit'];old_saving=Q(old_source['bit']['saving']) + check(old_saving==Q(384599,10**10),'Ordinary leaf saving changed');coarse=Q(620523,5*10**9);theta=Q(1,1000);A=(1-theta)*coarse+theta*old_saving + check(0=1,'log interval domain') + base=Q(4,3);k=0 + while x>base:x/=base;k+=1 + def short(y): + z=(y-1)/(y+1);power=z;s=Q(0) + for j in range(LOG_TERMS):s+=power/Q(2*j+1);power*=z*z + lo=2*s;tail=2*power/(Q(2*LOG_TERMS+1)*(1-z*z)) + return lo,lo+tail + lo,hi=short(x);blo,bhi=short(base) + return lower(k*blo+lo),upper(k*bhi+hi) + +def exp_interval(lo,hi): + require(0<=lo<=hi1 and W>0,'profile dimensions') + raw=profile['child_multiplicities'];hist={int(t):n for t,n in raw.items()} + require(len(hist)==len(raw),'aliased histogram keys') + require(all(00 for t,n in hist.items()),'invalid child or multiplicity') + mass=sum(t*n for t,n in hist.items());require(mass==profile['total_rank']==W*m-profile['N']+profile['L'],'rank mass') + require(max(hist)==profile['maxchild'],'maximum child') + require(0=0,'nonnegative saving');lo=hi=Q(0);rows=[] + for t,n,L,U in prepare(profile): + E,F=exp_interval(a*L,a*U);w=Q(t*n,profile['m']*profile['W']);lo+=w*E;hi+=w*F + if details:rows.append(dict(child=t,multiplicity=n,log_lower=L,log_upper=U,exp_lower=E,exp_upper=F,contribution_lower=w*E,contribution_upper=w*F)) + result=dict(saving=a,lower=lo,upper=hi,strict_gap_lower=1-hi) + if details:result['terms']=rows + return result + +def saving_grid(profile,denominator=10**24): + require(type(denominator) is int and denominator>0,'positive saving grid') + prepare(profile);lo=0;hi=denominator//32;iterations=0 + require(moment(profile,Q(lo,denominator))['upper']<1,'initial contraction') + require(moment(profile,Q(hi,denominator))['lower']>1,'initial exclusion') + while hi-lo>1: + mid=(hi+lo)//2;m=moment(profile,Q(mid,denominator));iterations+=1 + if m['upper']<1:lo=mid + elif m['lower']>1:hi=mid + else:raise ValueError('Moment interval overlaps one; increase enclosure precision') + accepted=moment(profile,Q(lo,denominator),True);rejected=moment(profile,Q(hi,denominator),True) + require(accepted['upper']<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/research/shrunk-birth-terminal/arithmetic/references/pr100/refine.py b/research/shrunk-birth-terminal/arithmetic/references/pr100/refine.py new file mode 100644 index 0000000000..399299089e --- /dev/null +++ b/research/shrunk-birth-terminal/arithmetic/references/pr100/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/research/shrunk-birth-terminal/arithmetic/references/pr104/balanced_assembly.py b/research/shrunk-birth-terminal/arithmetic/references/pr104/balanced_assembly.py new file mode 100644 index 0000000000..c7fd42867d --- /dev/null +++ b/research/shrunk-birth-terminal/arithmetic/references/pr104/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/research/shrunk-birth-terminal/arithmetic/references/pr104/copied-centers-network.json b/research/shrunk-birth-terminal/arithmetic/references/pr104/copied-centers-network.json new file mode 100644 index 0000000000..20bbb6806c --- /dev/null +++ b/research/shrunk-birth-terminal/arithmetic/references/pr104/copied-centers-network.json @@ -0,0 +1,684 @@ +{ + "adopted_sources": { + "files": { + "PROVENANCE.json": "27df488b36b4fa599b6e6b92408a4b37169125f40918c6ff29bb035e4342a7d4", + "README.md": "add72b080a24707aeda0d7a9ab8147003e3dc972575954d597b078aa82fb9619", + "SOURCES.json": "fd12f8ce03a9f504cbf62351e8f5f09b6209e6f9929081f7ad24a8e55cf09d64", + "pr29/LICENSE": "c95bae1d1ce0235ecccd3560b772ec1efb97f348a79f0fbe0a634f0c2ccefe2c", + "pr29/NOTICE": "1b4512d2fe2063aca8e59529f5f1552641b41128872fefa1f3411c991097a49f", + "pr29/SOURCE.json": "b2b71c863ebdb37c4110a13136490b1ee573258a4bc5ec0f72e725513d3896f3", + "pr29/paureel-direct-transfer.tex": "573bbc0ca0799dc255febb4dd35fba1549f3771480a32aa8e181ff62bc7cb253", + "pr29/two-stage-16-note.tex": "e01fc480181fb00d90599e002126b06056e5e574f97fd1d5698cdedb9097b54d", + "pr33/LICENSE": "c95bae1d1ce0235ecccd3560b772ec1efb97f348a79f0fbe0a634f0c2ccefe2c", + "pr33/NOTICE": "6cdb4f22681c300d0cfaa1cc28b7dc0ac3a3295f8ad5d76f779ceebced592847", + "pr33/SOURCE.json": "bb8f77e7da502ae2d36c81e74a899c8356eb21964310c894f4d76c61c7a1ee7f", + "pr33/two-stage-corners-47-45-note.tex": "eba0e302370c0628bab27f675c8961b3005ef2edc2ccb5591465c7f7ef559e5a" + } + }, + "assembly": { + "absorption_gap": "20374595379574062554852831/500038459899423101496154010000000000", + "margins": { + "Gaussian_arithmetic": "2307743950002130057689850384599/40003076791953848119692320800000000", + "bulk_exposure": "384599/10000000000", + "compact_phase_layer": "1922994942310150384599/50003845989942310149615401", + "coordinate_movement": "384599/10000000000", + "dimension": "49999999500000000000000000/50003845989942310149615401", + "original_prefix": "192349498077004980770049615401/5000384598994231014961540100000000", + "scalar_work": "3077141950002129750010650384599/40003076791953848119692320800000000" + }, + "minimum_margin": "1922994942310150384599/50003845989942310149615401", + "parameters": { + "C0": 2358858462850846165593256368932965330169899180021667007021321420800, + "C1": 1, + "a_bit": "384599/10000000000", + "a_complex": "717/10000000", + "alpha_squared_power": "2884742442310150000000/50003845989942310149615401", + "beta": "1/4", + "c": "1922994980770049615401/50000000000000000000000000", + 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+ }, + "finite_bridge": { + "bit": { + "W": 188181929, + "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": 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Copied-stream scheduling, simultaneous basis existence, analytic and tape interfaces remain written proof dependencies.", + "source_sha256": { + "certificates/copied-centers-bit-axes.json": "ed307cef595091b11ba8f8e6ff11302ad8db190227a2fbf34c232fd680206254", + "certificates/copied-centers-complex-input.json": "91a9e54b455ecc36c3150abcf4a1c9138691c8faab464b5ce159ba8e376764e7", + "certificates/copied-centers-corner-25-23.json": "23b0540ddc1d98a775383bfc65c7cf512aad86b399bf71167220b2a8182f5610", + "certificates/copied-centers-input.json": "5f8a57b1a4dd3f271d4e859ad350db3674b74f744127e74a989e7790718cea24", + "notes/copied-centers-assembly.tex": "00117892971ae766188ace0af03030c44164fda105e42b70d84f52c3339a7dcb", + "notes/copied-centers-bit.tex": "ccc8191ddb51698251ed4461a4c26104501b9b2ee37ce3cbe82fa73e85ae40dd", + "notes/copied-centers-complex.tex": "18eac6d5c5755e53230c0c12a633f38b6ce9666ef0322c1aff79394f2952af72", + "notes/copied-centers-lemma.tex": "d0ce6d3d504996aadb098227885224e48df46101daec8893523a0a8b7364d8fe", + "notes/copied-centers-note.tex": "1099559bea3090399a2496bfb8fdf8966ac39d22fd413e35643af5ee0bb08556", + "references/copied-centers/MANIFEST.json": "5636f7beb34ae439f076d36e13d95d3057ce41ccbdba9da63d7727198b093ccb", + "scripts/copied_centers/README.md": "8d348a28fc11615fb686f7d47548db06a5000378b54e0e47438d17292b5942b9", + "scripts/copied_centers/__init__.py": "13db4f09038a2ff5335cbd4dbd93274b0fb16b3c7b51e4de67cbb2801a3f78e1", + "scripts/copied_centers/corners.py": "9eecdc39c67cc18c806a33f0be03986c28591d322881fd60c11f52c625c8067b", + "scripts/copied_centers/physical.py": "837345d1f8753eab0e70f105b1d1bb0db965b993da037b1825ddef3672609d7d", + "scripts/copied_centers_network.py": "409ebfbd8a41c4c4d089aa0949fcf5a949415dc26f57440ffd48b7bd8881e6a9", + "scripts/copied_centers_producer.py": "33afa6fe25677e13656fa8a200a25ed3510ef70c1ff9f1186612cbd9ee75d209", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + }, + "status": "Conditional copied-center multiplication witness" +} diff --git a/research/shrunk-birth-terminal/arithmetic/references/pr104/structured_bulk_assembly.py b/research/shrunk-birth-terminal/arithmetic/references/pr104/structured_bulk_assembly.py new file mode 100644 index 0000000000..b76f9cb5a4 --- /dev/null +++ b/research/shrunk-birth-terminal/arithmetic/references/pr104/structured_bulk_assembly.py @@ -0,0 +1,103 @@ +#!/usr/bin/env python3 +"""Copyright 2026 icekylinx. Apache-2.0. +Substantial OpenAI GPT-6 Astra and Codex assistance. + +Exact finite bridge and assembly for the round-three networks. + +Adapted parameter calculation and semantic/product-row proof from PR23, +Zhihao Chen (jacklightChen), which attributes routing, phase-cell inverse +and bulk resampling to the RaD project (hipotures), commit +45d9b60355872041f9275f77c057514def0d45bc. This file does not regenerate, +audit, or substitute for the finite-network or analytic source proofs. +""" +from fractions import Fraction as Q + +def js(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):js(v) for k,v in x.items()} + if isinstance(x,(tuple,list)):return [js(v) for v in x] + return x + +def halving(m,r): + assert 0=s+E and 2*B+18Q(coeff*51,25) + return dict(bit=dict(m=bit_m,W=bit_W,maxchild=bit_maxchild, + halving_degree=db,wire_bits=wb), + complex=dict(m=m,W=W,s=s,maxchild=r,halving_degree=dc, + wire_bits=wc,scalar_terms=scalar_terms,scalar_group_upper=G), + semantic=dict(E=E,literal_charge=charge,strict_literal_gap=E-charge, + B=B,C0=C0,C1=1,induction_gap=2*B*(m-r)-s-E), + rows=dict(coefficient=coeff,degree=degree,suffix_slope=4*degree, + degree_gap=Q(degree)-Q(coeff*51,25), + contract='W_complex^D_complex * W_bit^D_bit; preceding row prefix, single complete-row padding, nested bit stock restored')) + +def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)): + a,b=bit_saving,complex_saving + tau,sigma=1-a,1-b + q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2 + c=q*(1+eta); eps=(1-eta)/(1+c+q) + minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8 + internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma) + margins=dict(original_prefix=1-eps*(1+c),coordinate_movement=a, + compact_phase_layer=minimum,bulk_exposure=a, + Gaussian_arithmetic=min(1-eps-delta,r-delta), + scalar_work=1-eps-delta,dimension=eps) + slacks=dict(bit_positive=a,complex_above_bit=b-a, + complex_below_one_over32=Q(1,32)-b,beta_positive=beta, + beta_below_one=1-beta,leaf_saving_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,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-minimum, + artificial_boundary=8-eps+r-delta-minimum, + literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']), + row_product_gap=bridge['rows']['degree_gap']) + slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()}) + assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0} + assert min(margins.values())==minimum + assert margins['original_prefix']-minimum==eta + return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma, + eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam, + lambda_prime=lp,alpha_squared_power=r,delta=delta, + C0=bridge['semantic']['C0'],C1=1,kappa=kappa), + strict_constraints=slacks,margins=margins,minimum_margin=minimum, + absorption_gap=minimum-kappa, + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c)) diff --git a/research/shrunk-birth-terminal/arithmetic/validate.py b/research/shrunk-birth-terminal/arithmetic/validate.py new file mode 100644 index 0000000000..2ca657fc11 --- /dev/null +++ b/research/shrunk-birth-terminal/arithmetic/validate.py @@ -0,0 +1,77 @@ +#!/usr/bin/env python3 +"""Adversarial checks and exact upstream adaptation audit for the selected witness.""" +import argparse,json,sys +from pathlib import Path +from fractions import Fraction as Q +from copy import deepcopy +if sys.flags.optimize:raise ValueError('Assertions must remain enabled') +sys.dont_write_bytecode=True +import certificate as c +import balanced_stopped as balanced +import interval_moment as intervals +HERE=Path(__file__).resolve().parent + +def adaptation(): + s=(HERE/'balanced_stopped.py').read_text();s=s[s.index('"""Exact, import-safe balanced'):] + replacements=[ + ('def validate_bridge(finite_bridge, ordinary_leaf):','def validate_bridge(finite_bridge):'), + (" for name in ('bit_coarse', 'complex', 'ordinary_leaf'):\n data = ordinary_leaf if name == 'ordinary_leaf' else finite_bridge[name]", " for name in ('bit', 'complex'):\n data = finite_bridge[name]"), + (" leaf_degree = result['ordinary_leaf']['halving_degree']*result['ordinary_leaf']['wire_bits']\n require(integer(finite_bridge['ordinary_leaf_row_degree']) == leaf_degree,\n 'ordinary leaf stock missing or stale')\n coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits']\n for name in ('bit_coarse', 'complex', 'ordinary_leaf'))", " coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits']\n for name in ('bit', 'complex'))"), + ('def assembly(finite_bridge, ordinary_leaf, a_bit, kappa,','def assembly(finite_bridge, a_bit, kappa,'), + (' f = validate_bridge(finite_bridge, ordinary_leaf)',' f = validate_bridge(finite_bridge)'), + ('def cutoffs(finite_bridge, ordinary_leaf, result):','def cutoffs(finite_bridge, result):'), + (" largest = max(f[name]['m'] for name in ('bit_coarse','complex','ordinary_leaf'))", " largest = max(f['bit']['m'],f['complex']['m'])")] + for old,new in replacements:c.check(old in s,'Adapter normalization hook missing');s=s.replace(old,new) + c.check(s==(HERE/'references/pr104/balanced_assembly.py').read_text(),'Unreviewed adapter difference') + return True + +def validate(raw,reference=None): + c.no_floats(raw);j=c.exact(raw);f=j['finite_bridge'];old=j['ordinary_leaf_bridge'];p=j['profile'];k=Q(j['kappa']);a=Q(j['assembly_bit']);b=Q(j['complex_saving']);beta=Q(j['beta']);eta=Q(j['eta']) + c.check(j['source_sha256']==c.source_hashes(),'Arithmetic source pins changed') + c.profile(p);c.profile(j['bit_profile']);balanced.validate_bridge(f,old);adaptation() + controls=[] + def rejects(name,fn): + try:fn() + except (ValueError,balanced.InvalidAssembly,KeyError):controls.append(dict(name=name,rejected=True)) + else:raise ValueError('Adverse control accepted: '+name) + mutations=[('missing old stock',lambda x:x.pop('ordinary_leaf_row_degree')),('zero old stock',lambda x:x.update(ordinary_leaf_row_degree=0)),('two-stock coefficient',lambda x:x['rows'].update(coefficient=x['rows']['coefficient']-252,degree_gap=x['rows']['degree_gap']+Q(51*252,25))),('stale coarse child',lambda x:x['bit_coarse'].update(maxchild=527)),('stale scalar charge',lambda x:x['complex'].update(scalar_group_upper=x['complex']['scalar_group_upper']-1)),('zero scalar charge',lambda x:x['complex'].update(scalar_group_upper=0)),('stale C0',lambda x:x['semantic'].update(C0=x['semantic']['C0']-1)),('insufficient row stock',lambda x:x['rows'].update(degree=1,degree_gap=Q(1)-Q(51,25)*x['rows']['coefficient'],suffix_slope=4))] + for name,mut in mutations: + x=deepcopy(f);mut(x);rejects(name,lambda:balanced.validate_bridge(x,old)) + rejects('zero stopped leaf gap',lambda:balanced.assembly(f,old,(1-beta)*b,k,beta=beta,h=eta,a_complex=b)) + rejects('next kappa',lambda:balanced.assembly(f,old,a,k+Q(1,10**18),beta=beta,h=eta,a_complex=b)) + rejects('old prefix at selected parameters',lambda:balanced.assembly(f,old,a,k,beta=beta,h=eta,a_complex=b,original_prefix=True)) + x=deepcopy(p);x['child_multiplicities']['1']-=1;rejects('unpaid singleton deletion',lambda:intervals.prepare(x)) + for name,x in [('top float',0.125),('nested float',{'profile':{'seconds':0.125}}),('list float',{'items':[{'x':0.125}]})]:rejects(name,lambda:c.no_floats(x)) + x=deepcopy(p);x['W']=str(x['W']);rejects('noninteger width',lambda:c.profile(x)) + x=deepcopy(p);x['h']+=1;rejects('inconsistent two-factor dimensions',lambda:c.profile(x)) + x=deepcopy(p);x['child_multiplicities']['1']=1.5;rejects('floating child count',lambda:c.profile(x)) + x=deepcopy(p);x['discovery']={'seconds':0.125};c.check(c.profile(x)==p,'Discovery metadata leaked into canonical profile') + terms=[] + for x in (f['bit_coarse'],f['complex'],old): + m,r,d=x['m'],x['maxchild'],x['halving_degree'];c.check(m**d>2*r**d and (d==1 or m**(d-1)<=2*r**(d-1)),'Nonminimal halving degree');c.check(x['wire_bits']==x['W'].bit_length(),'Wire bitlength');terms.append(d*x['wire_bits']) + c.check(terms==[9909,5400,252] and sum(terms)==f['rows']['coefficient']==15561,'All three row factors') + q=a*(1-2*eta);eps=(1-eta)/(1+q);g=eps*q;cc=q+eta/4 + c.check(1-eps-g==eta and 1-eps*(1+cc)==eta-eps*eta/4>0,'Balanced identities') + c.check(k0,'Nonpositive promotion');hist[r]+=1;transitions+=1;current[role]=F + if role<2*v: + bank,t=divmod(role,v);bit=1<literal and 2*B*(h*h-574)>=mass+E and 32*h*h*B*B>2*B+18,'Finite guard') +stock=cert['assembly']['finite_bridge'];coeff=0 +for name in ('bit_coarse','complex','ordinary_leaf'): + x=stock[name];m0,d,child,bits,w0=(x[t]for t in ('m','halving_degree','maxchild','wire_bits','W'));require(m0**d>2*child**d and m0**(d-1)<=2*child**(d-1) and 2**(bits-1)<=w0<2**bits,'Stock inequalities');coeff+=d*bits +require(coeff==15561 and 32000-Q(51,25)*coeff==Q(6389,25),'All three stock contribution') +slacks={'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':cc,'c_below_one':1-cc,'q_below_reservations':cc-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-cc),'lambda_prime_below_one':q,'epsilon_positive':eps,'epsilon_below_one':1-eps,'guard_width':1-eps,'K_geometry':1-eps*(1+cc),'K_dominates_log':eps*cc,'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(E-literal),'row_product_gap':Q(6389,25)} +margins=[1-eps,a,g,a,min(1-eps-delta,r-delta),1-eps-delta,eps] +slacks.update({f'g{i}_above_kappa':x-k for i,x in enumerate(margins,1)}) +require(len(slacks)==47 and all(x>0 for x in slacks.values()) and slacks=={key:Q(value)for key,value in cert['assembly']['constraints'].items()},'Full independent 47 inequalities') +require(min(margins)==g and all(x>k for x in margins),'Seven controlling margins') +for label in ('accepted','rejected'): + record=cert['independent_moment'][label];saving=b+(Q(1,10**24)if label=='rejected'else 0);require(Q(record['saving'])==saving,'Moment adjacent saving') + require(set(map(int,record['terms']))==set(H),'Complete moment support');total=Q(0) + for ts,x in record['terms'].items(): + t=int(ts);lo,hi=saving*Q(x['log_lower']),saving*Q(x['log_upper']);require(0<=lo<=hi<1,'Taylor domain');weight=Q(t*H[t],h*h*W);require(weight==Q(x['weight']),'Derived physical moment weight') + if label=='accepted':val=Q(x['exp_upper']);require(sum((hi**j/factorial(j)for j in range(9)),Q())+hi**9/factorial(9)/(1-hi/10)<=val,'Accepted tail domination') + else:val=Q(x['exp_lower']);require(val<=sum((lo**j/factorial(j)for j in range(9)),Q()),'Rejected lower domination') + total+=weight*val + require(total==Q(record['upper'if label=='accepted'else'lower']),'Full moment sum') + require(total<1 if label=='accepted'else total>1,'Strict paid moment') +# Source has only scoped norm_num arithmetic, and every theorem appears in log. +s=source.read_text();clean=re.sub(r'/\-.*?\-/','',s,flags=re.S);clean=re.sub(r'--[^\n]*','',clean) +require(not re.search(r'\b(sorry|admit|axiom|native_decide|unsafe)\b',clean),'Unapproved proof construct') +require(re.findall(r'^import (.+)$',clean,re.M)==['Mathlib.Tactic.NormNum','Mathlib.Data.Nat.Choose.Basic'],'Import boundary') +names=re.findall(r'^theorem (\w+)\s*:',clean,re.M);prints=re.findall(r'^#print axioms KappaCheck\.ShrunkBirthTerminal\.(\w+)',clean,re.M) +require(len(names)==len(set(names))==240 and set(names)==set(prints),'Theorem/axiom print coverage') +for path,digest in receipt['compile_receipts'].items():require(sha(LEAN/path)==digest,'Compile receipt '+path) +log=(LEAN/'receipts/compile/output.log').read_text();entries=re.findall(r"'KappaCheck\.ShrunkBirthTerminal\.(\w+)' depends on axioms: \[([^]]*)\]",log) +require(len(entries)==240 and {name for name,_ in entries}==set(names),'Compiled theorem identity coverage') +allowed={'propext','Classical.choice','Quot.sound'} +for name,axioms in entries:require(set(x.strip()for x in axioms.split(',')if x.strip())<=allowed,'Extra axiom '+name) +require((LEAN/'receipts/compile/exit-code').read_text().strip()=='0' and receipt['exit_code']==0 and receipt['lean']=='4.21.0' and receipt['mathlib_commit']=='308445d7985027f538e281e18df29ca16ede2ba3','Compiler receipt identity') +require(not re.search(r'(^|\n).*error:',log),'Compiler error marker') +result=dict(status='PASS independent frozen formal-boundary and complete actual-word frame/count audit',audit_source_sha256=sha(Path(__file__)),lean_source_sha256=sha(source),generator_sha256=sha(gen),input_sha256=sha(inp),compile_verification_sha256=sha(LEAN/'verification.json'),source_regeneration_byte_exact=True,actual_word_sha256=sha(word_path),actual_forward_frame_transitions=transitions,distinct_nondegenerate_frames_checked=len(checked),distinct_nested_frame_pairs_checked=len(checked_pairs),copied_centers=copies,all_34_paid_histogram_bins_reconstructed=True,three_stocks=[9909,5400,252],exact_slacks=47,margins=7,independent_taylor_moments='accepted upper and adjacent rejected lower',theorems=240,all_axiom_entries_accounted=True,allowed_axioms=sorted(allowed),no_float_mathematical_input=True,kappa=str(k),remote_compile_repeated=False,external_limitations=['The Lean kernel proves rational inequalities on the supplied logarithm enclosures, not their analytic logarithm meaning or the real exponential enclosure theorem.','The stopped bit moment/ordinary leaf validity, all-size word/compiler and packed routing/phase interfaces, simultaneous basis, prime selection, exact recovery and fixed-tape transfer remain external.','This audit independently reconstructs exact forward binary frame containment, nonsingularity and every histogram bin from the literal word. Reflected/all-column Gaussian scalar identities remain separately bound construction evidence.','The frozen compile record is checked by hashes and all theorem/axiom entries; the remote compilation was performed by the parent and is not duplicated here.']) +no_float(result);(HERE/'receipt.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n');print('PASS formal audit',sha(HERE/'receipt.json')) diff --git a/research/shrunk-birth-terminal/audit/independent-lean/receipt.json b/research/shrunk-birth-terminal/audit/independent-lean/receipt.json new file mode 100644 index 0000000000..35e0007e28 --- /dev/null +++ b/research/shrunk-birth-terminal/audit/independent-lean/receipt.json @@ -0,0 +1,39 @@ +{ + "actual_forward_frame_transitions": 233458, + "actual_word_sha256": "11dfe85123d23c17b4e1f4309b7c5fdfdac55faef7563881f2f3db5b2dfae82e", + "all_34_paid_histogram_bins_reconstructed": true, + "all_axiom_entries_accounted": true, + "allowed_axioms": [ + "Classical.choice", + "Quot.sound", + "propext" + ], + "audit_source_sha256": "deb66e18fd5ef8bd1f7efd28090fd7f96c716499f2b29db386ee905d3deef7ed", + "compile_verification_sha256": "47249c2da5d725b288a4277bae3873a4bd2265a44db836406461d30632329663", + "copied_centers": 24, + "distinct_nested_frame_pairs_checked": 188744, + "distinct_nondegenerate_frames_checked": 71928, + "exact_slacks": 47, + "external_limitations": [ + "The Lean kernel proves rational inequalities on the supplied logarithm enclosures, not their analytic logarithm meaning or the real exponential enclosure theorem.", + "The stopped bit moment/ordinary leaf validity, all-size word/compiler and packed routing/phase interfaces, simultaneous basis, prime selection, exact recovery and fixed-tape transfer remain external.", + "This audit independently reconstructs exact forward binary frame containment, nonsingularity and every histogram bin from the literal word. Reflected/all-column Gaussian scalar identities remain separately bound construction evidence.", + "The frozen compile record is checked by hashes and all theorem/axiom entries; the remote compilation was performed by the parent and is not duplicated here." + ], + "generator_sha256": "e9d34fb5179c7d4fd7f4c12da813b7e3779a7e88286aee751fa9adb5b888bc95", + "independent_taylor_moments": "accepted upper and adjacent rejected lower", + "input_sha256": "ecd604ec8f7185e7d23f2f2671f11b8aa9c1e3420e89e597d3a958fe613e9abf", + "kappa": "28200546274389/250000000000000000", + "lean_source_sha256": "8c69d10ece16816edaef9df72182c9eecef3b464f88c82e0b8435f09c94ad095", + "margins": 7, + "no_float_mathematical_input": true, + "remote_compile_repeated": false, + "source_regeneration_byte_exact": true, + "status": "PASS independent frozen formal-boundary and complete actual-word frame/count audit", + "theorems": 240, + "three_stocks": [ + 9909, + 5400, + 252 + ] +} diff --git a/research/shrunk-birth-terminal/audit/independent-lean/regeneration/ShrunkBirthTerminal.lean b/research/shrunk-birth-terminal/audit/independent-lean/regeneration/ShrunkBirthTerminal.lean new file mode 100644 index 0000000000..985b71d41e --- /dev/null +++ b/research/shrunk-birth-terminal/audit/independent-lean/regeneration/ShrunkBirthTerminal.lean @@ -0,0 +1,1248 @@ +import Mathlib.Tactic.NormNum +import Mathlib.Data.Nat.Choose.Basic + +/-! +Exact arithmetic companion for the shrunk-frame / birth-reuse / terminal-elision +composition. Prepared with OpenAI assistance. Upstream construction and analytic +credits are retained in the accompanying proof and source provenance. + +Scope: supplied physical-count arrays, all 47 parameter slacks, seven margins, +three row stocks, scalar guards and independent degree-eight moment arithmetic. +The physical-array derivation, real logarithm / exponential enclosure validity, +and all-size framed-word, stopped-product, tape, prime and recovery hypotheses +remain external. This is not an unconditional integer-multiplication theorem. +No sorry, native_decide or additional axioms are introduced. +-/ +namespace KappaCheck.ShrunkBirthTerminal +set_option maxRecDepth 20000 +set_option maxHeartbeats 8000000 + +-- Source SHA256 89b115978ab95d8e69e58472cde14a588157a3b3a8c577034c39ca0309eab34d: work/r12-audit/canonical-joint-expansion/joint-expansion/certificate.json +-- Source SHA256 3203dcb2709c3c8f1513c9ff31faafe9903f7ba14cdd7bbe1aaa38c9edbfcf43: work/r12-terminal/joint-expansion/READOUT_COST.json +-- Source SHA256 457287cf9986574cef50235644af77c893b3513e7a0872827b1cce352f4b62d5: work/r12-terminal/joint-expansion/physical-audit.json +-- Source SHA256 11dfe85123d23c17b4e1f4309b7c5fdfdac55faef7563881f2f3db5b2dfae82e: work/r12-terminal/joint-expansion/word.json.gz +def h : ℕ := 24 +def m : ℕ := h*h +def v : ℕ := Nat.choose h 3 +def n : ℕ := v*v +def virtualRoles : ℕ := 28705 +def births : ℕ := 2108 +def terminals : ℕ := 381 +def roles : ℕ := virtualRoles-births-terminals +def width : ℕ := 2*n+2*v*roles +def forwardHistogram : List (ℕ × ℕ) := [(1, 106459), (2, 65902), (3, 7179), (4, 14980), (5, 6582), (6, 3788), (7, 2901), (8, 5452), (9, 973), (10, 1911), (11, 1645), (12, 8295), (13, 3257), (14, 450), (15, 800), (16, 156), (17, 100), (18, 50), (19, 77), (20, 136), (21, 302), (22, 16), (23, 2071)] +def initialDimensionHistogram : List (ℕ × ℕ) := [(0, 23980), (2, 854), (4, 366), (6, 589), (8, 110), (10, 12), (19, 183), (20, 25), (21, 7), (22, 90)] +def counts : List (ℕ × ℕ) := + (forwardHistogram.map fun p => (p.1, 2*v*p.2)) ++ + (initialDimensionHistogram.map fun p => (m-h+p.1, 2*v*p.2)) ++ + [((h-1)^2, 2*n), (1, n)] +def count (t : ℕ) : ℕ := (counts.map fun p => if p.1=t then p.2 else 0).sum +def mass : ℕ := (counts.map fun p => p.1*p.2).sum + +theorem network_counts : h = 24 ∧ m = 576 ∧ v = 2024 ∧ n = 4096576 ∧ roles = 26216 ∧ width = 114315520 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose] + +theorem initial_dimension_count : (initialDimensionHistogram.map Prod.snd).sum = roles := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem rank_mass : mass = 65843877440 ∧ m*width-mass = 1862080 ∧ n-2*v*h*(h-1) = 1862080 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_1 : count 1 = 435042608 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_2 : count 2 = 266771296 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_3 : count 3 = 29060592 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_4 : count 4 = 60639040 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_5 : count 5 = 26643936 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_6 : count 6 = 15333824 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_7 : count 7 = 11743248 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_8 : count 8 = 22069696 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_9 : count 9 = 3938704 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_10 : count 10 = 7735728 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_11 : count 11 = 6658960 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_12 : count 12 = 33578160 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_13 : count 13 = 13184336 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_14 : count 14 = 1821600 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_15 : count 15 = 3238400 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_16 : count 16 = 631488 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_17 : count 17 = 404800 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_18 : count 18 = 202400 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_19 : count 19 = 311696 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_20 : count 20 = 550528 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_21 : count 21 = 1222496 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_22 : count 22 = 64768 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_23 : count 23 = 8383408 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_529 : count 529 = 8193152 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_552 : count 552 = 97071040 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_554 : count 554 = 3456992 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_556 : count 556 = 1481568 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_558 : count 558 = 2384272 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_560 : count 560 = 445280 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_562 : count 562 = 48576 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_571 : count 571 = 740784 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_572 : count 572 = 101200 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_573 : count 573 = 28336 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_574 : count 574 = 364320 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +def childSizes : List ℕ := [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 529, 552, 554, 556, 558, 560, 562, 571, 572, 573, 574] +theorem complete_child_support : ∀ p ∈ counts, p.2 ≠ 0 → p.1 ∈ childSizes := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram, childSizes] + +theorem strict_child_contraction : ∀ t ∈ childSizes, 0 < t ∧ t < m := by + norm_num [childSizes, h, m] + +def a : ℚ := (56407455433006738868999943092544566993261131 / 500000000000000000000000000000000000000000000000) +def b : ℚ := (56407455433006738869 / 500000000000000000000000) +def kappa : ℚ := (28200546274389 / 250000000000000000) +def eta : ℚ := (1 / 1000000000000000000000000) +def beta : ℚ := (1 / 1000000000000000000000000) +def backoff : ℚ := (1 / 1000000000000000000000000000000) +def actualBitSaving : ℚ := (1240189553 / 10000000000000) +def tau : ℚ := 1-a +def sigma : ℚ := 1-b +def qParam : ℚ := a*(1-2*eta) +def lp : ℚ := 1-qParam +def c : ℚ := qParam+eta/4 +def epsilon : ℚ := (1-eta)/(1+qParam) +def lam : ℚ := (tau+lp)/2 +def g : ℚ := epsilon*qParam +def r : ℚ := (g+1-epsilon)/2 +def delta : ℚ := eta/8 +def internal : ℚ := tau+(1-beta)*max (sigma-tau) 0 +def leaf : ℚ := sigma+beta*(1-sigma) + +def scalar : ℕ := 3116113870848 +def guardE : ℕ := 64*(width+m+scalar+1)^3 +def guardB : ℕ := mass+guardE +def literal : ℕ := 2*scalar*width^2+8*mass+4*width+4+32*m +def guardC : ℕ := 32*m*guardB^2 +def literalGap : ℚ := (guardE : ℚ)-literal +def rowCoefficient : ℕ := 367*27+200*27+9*28 +def rowGap : ℚ := 32000-(51/25)*rowCoefficient +def margins : List ℚ := [1-epsilon,a,g,a,min (1-epsilon-delta) (r-delta),1-epsilon-delta,epsilon] + +theorem slack_a_positive : (a) = ((56407455433006738868999943092544566993261131 / 500000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (a) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_a_below_b : (b-a) = ((56907455433006738869 / 500000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (b-a) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_b_below_one_over32 : (1/32-b) = ((15568592544566993261131 / 500000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1/32-b) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_beta_positive : (beta) = ((1 / 1000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (beta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_beta_below_one : (1-beta) = ((999999999999999999999999 / 1000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-beta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_phase_leaf_above_bit : ((1-beta)*b-a) = ((1 / 1000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((1-beta)*b-a) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_q_positive : (qParam) = ((28203727716503369434499915138816850489891696500056907455433006738869 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (qParam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_q_below_internal : (1-internal-qParam) = ((56407455433006738868999943092544566993261131 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-internal-qParam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_q_below_leaf : (1-leaf-qParam) = ((56657455433006738868999943092544566993261131 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-leaf-qParam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_c_positive : (c) = ((28203727716503369434562415138816850489891696500056907455433006738869 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (c) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_c_below_one : (1-c) = ((249971796272283496630565437584861183149510108303499943092544566993261131 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-c) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_q_below_reservations : (c-qParam) = ((1 / 4000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (c-qParam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_lambda_above_tau : (lam-tau) = ((56407455433006738868999943092544566993261131 / 500000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lam-tau) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_lambda_above_sigma : (lam-sigma) = ((113314910866013477737999943092544566993261131 / 500000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lam-sigma) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_lambda_above_internal : (lam-internal) = ((56407455433006738868999943092544566993261131 / 500000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lam-internal) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_lambda_prime_above_lambda : (lp-lam) = ((56407455433006738868999943092544566993261131 / 500000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lp-lam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_compact_leaf : (lp-leaf) = ((56657455433006738868999943092544566993261131 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lp-leaf) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_compact_reservations : (lp-(1-c)) = ((1 / 4000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lp-(1-c)) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_lambda_prime_below_one : (qParam) = ((28203727716503369434499915138816850489891696500056907455433006738869 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (qParam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_epsilon_positive : (epsilon) = ((249999750000249999750000000000000000000000000000000000000000000000 / 250027953699762803606630893284245532604957286739213317694137738869) : ℚ) ∧ (0 : ℚ) < (epsilon) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_epsilon_below_one : (1-epsilon) = ((28203699512803856630893284245532604957286739213317694137738869 / 250027953699762803606630893284245532604957286739213317694137738869) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_guard_width : (1-epsilon) = ((28203699512803856630893284245532604957286739213317694137738869 / 250027953699762803606630893284245532604957286739213317694137738869) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_K_geometry : (1-epsilon*(1+c)) = ((187528016199700303669130893284245532604957286739213317694137738869 / 250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon*(1+c)) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_K_dominates_log : (epsilon*c) = ((28203699512803856630705756229332904653617608320033448605133911713260786682305862261131 / 250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (epsilon*c) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_record_suffix : (1-epsilon) = ((28203699512803856630893284245532604957286739213317694137738869 / 250027953699762803606630893284245532604957286739213317694137738869) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_phase_local : (1-epsilon-delta) = ((225629596102430853046896246010561076854687282813257307569305994713260786682305862261131 / 2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon-delta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_phase_boundary : (r-delta) = ((45125919220486170609179226839152405128052151848024065087777233113260786682305862261131 / 400044725919620485770609429254792852167931658782741308310620382190400000000000000000000000) : ℚ) ∧ (0 : ℚ) < (r-delta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_gamma_sublinear : (1-epsilon-r) = ((1 / 2000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon-r) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_cell_above_band : (epsilon-(1-r)/2) = ((499999500000499999499999749972046300237196393369106715754467395042713260786682305862261131 / 1000111814799051214426523573136982130419829146956853270776550955476000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (epsilon-(1-r)/2) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_prime_interval_packing : (1-epsilon) = ((28203699512803856630893284245532604957286739213317694137738869 / 250027953699762803606630893284245532604957286739213317694137738869) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_alpha_positive : (r) = ((56407399025607713261536540537365447110966847533351142742872780713260786682305862261131 / 500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (r) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_alpha_below_one : (1-r) = ((499999500000499999500000250027953699762803606630893284245532604957286739213317694137738869 / 500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-r) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_alpha_below_one_fourth : (1/4-r) = ((124957569450855794090053910101585400855367676522073307704325996653786739213317694137738869 / 500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1/4-r) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_delta_positive : (delta) = ((1 / 8000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (delta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_delta_below_one_eighth : (1/8-delta) = ((999999999999999999999999 / 8000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1/8-delta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_short_record_fallback : (epsilon-a) = ((124985771559469674632287261529685377995480559442484781152571541385040823194886876611665983695762005501567194399161 / 125013976849881401803315446642122766302478643369606658847068869434500000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (epsilon-a) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_small_field_exposure : (1-epsilon-g) = ((1 / 1000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon-g) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_artificial_boundary : (8-epsilon+r-delta-g) = ((14001791036782819432824377920275575186005677171202332185161413102487860217639953082413216607 / 2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (8-epsilon+r-delta-g) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_literal_scalar_guard : (literalGap) = (1936723974066543198917496885658826453564 : ℚ) ∧ (0 : ℚ) < (literalGap) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_row_product_gap : (rowGap) = ((6389 / 25) : ℚ) ∧ (0 : ℚ) < (rowGap) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g1_above_kappa : ((1-epsilon)-kappa) = ((12837801344731479849844430239564663423413902568985912017495473959 / 62506988424940700901657723321061383151239321684803329423534434717250000000000000000) : ℚ) ∧ (0 : ℚ) < ((1-epsilon)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g2_above_kappa : ((a)-kappa) = ((6362884228738868999943092544566993261131 / 500000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((a)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g3_above_kappa : ((g)-kappa) = ((51350955350972219636574114327365369448123005318656908856664201698261131 / 250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((g)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g4_above_kappa : ((a)-kappa) = ((6362884228738868999943092544566993261131 / 500000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((a)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g5_above_kappa : ((min (1-epsilon-delta) (r-delta))-kappa) = ((82161678578327771276200746902320561664316371484223097698653339199861131 / 400044725919620485770609429254792852167931658782741308310620382190400000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((min (1-epsilon-delta) (r-delta))-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g6_above_kappa : ((1-epsilon-delta)-kappa) = ((410809393003453655432218161035175945303712277250262445346537472550261131 / 2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((1-epsilon-delta)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g7_above_kappa : ((epsilon)-kappa) = ((62492886575184298986180078023670096698605108554761333999879467851735912017495473959 / 62506988424940700901657723321061383151239321684803329423534434717250000000000000000) : ℚ) ∧ (0 : ℚ) < ((epsilon)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem margins_strict : ∀ x ∈ margins, kappa < x := by + norm_num [margins, a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem balanced_identities : 1-epsilon-g = eta ∧ 1-epsilon-r = eta/2 ∧ 1-epsilon*(1+c) = eta-epsilon*eta/4 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem stopped_parameter_choice : a = min actualBitSaving ((1-beta)*b-backoff) ∧ 0 < eta ∧ eta < 1/2 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem controlling_margin : kappa < g ∧ g < kappa+1/1000000000000000000 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem fixed_profile_grid_exclusion : (b+1/1000000000000000000000000)/(1+b+1/1000000000000000000000000) < kappa+1/1000000000000000000 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem gain_over_pinned_bounds : kappa > (384569/10000000000 : ℚ) ∧ kappa > (52789616935221/1000000000000000000 : ℚ) ∧ kappa > (111192082577/1000000000000000 : ℚ) ∧ (1/2^14 : ℚ) < kappa ∧ kappa < (1/2^13 : ℚ) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem stock_bit_coarse : (529:ℕ)^367 > 2*528^367 ∧ (529:ℕ)^366 ≤ 2*528^366 ∧ (2:ℕ)^26 ≤ 108516254 ∧ 108516254 < (2:ℕ)^27 := by + norm_num [] + +theorem stock_complex : (576:ℕ)^200 > 2*574^200 ∧ (576:ℕ)^199 ≤ 2*574^199 ∧ (2:ℕ)^26 ≤ 114315520 ∧ 114315520 < (2:ℕ)^27 := by + norm_num [] + +theorem stock_ordinary_leaf : (575:ℕ)^9 > 2*529^9 ∧ (575:ℕ)^8 ≤ 2*529^8 ∧ (2:ℕ)^27 ≤ 188181929 ∧ 188181929 < (2:ℕ)^28 := by + norm_num [] + +theorem row_stock : rowCoefficient = 15561 ∧ rowGap = (6389/25 : ℚ) ∧ 4*(32000:ℕ) = 128000 := by + norm_num [rowCoefficient, rowGap] + +theorem semantic_constants : guardE = 1936723974147986188574068436730358952000 ∧ guardB = 1936723974147986188574068436796202829440 ∧ guardC = 69136584229593344553734547662349298866110568132764137982571664415937240220513075200 ∧ literal = 81442989656571551071532498436 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem finite_bridge : guardE > literal ∧ 2*guardB*(m-574) ≥ mass+guardE ∧ guardC > 2*guardB+18 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +-- The analytic meaning of supplied log intervals is external. These +-- statements prove exact rational Taylor inequalities and complete paid sums. +def taylor8 (x : ℚ) : ℚ := 1+x+x^2/2+x^3/6+x^4/24+x^5/120+x^6/720+x^7/5040+x^8/40320 +def expUpper (x : ℚ) : ℚ := taylor8 x+x^9/362880/(1-x/10) + +def accepted_1 : ℚ := (10007173208708459192443081796658477476273 / 10000000000000000000000000000000000000000) +theorem accepted_interval_1 : (0 : ℚ) ≤ b*(3178053830347945619646941601297 / 500000000000000000000000000000) ∧ b*(3178053830347945619646941601297 / 500000000000000000000000000000) ≤ b*(1271221532139178247858776640519 / 200000000000000000000000000000) ∧ b*(1271221532139178247858776640519 / 200000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_1 : expUpper (b*(1271221532139178247858776640519 / 200000000000000000000000000000)) ≤ accepted_1 := by + norm_num [expUpper, taylor8, b, accepted_1] + +def accepted_2 : ℚ := (2001278141000794096250171811675050044519 / 2000000000000000000000000000000000000000) +theorem accepted_interval_2 : (0 : ℚ) ≤ b*(1132592096027189185975330216227 / 200000000000000000000000000000) ∧ b*(1132592096027189185975330216227 / 200000000000000000000000000000) ≤ b*(353935030008496620617290692571 / 62500000000000000000000000000) ∧ b*(353935030008496620617290692571 / 62500000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_2 : expUpper (b*(353935030008496620617290692571 / 62500000000000000000000000000)) ≤ accepted_2 := by + norm_num [expUpper, taylor8, b, accepted_2] + +def accepted_3 : ℚ := (5002966499022595054406188132806194434321 / 5000000000000000000000000000000000000000) +theorem accepted_interval_3 : (0 : ℚ) ≤ b*(5257495372027781547898637965671 / 1000000000000000000000000000000) ∧ b*(5257495372027781547898637965671 / 1000000000000000000000000000000) ≤ b*(657186921503472693487329745709 / 125000000000000000000000000000) ∧ b*(657186921503472693487329745709 / 125000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_3 : expUpper (b*(657186921503472693487329745709 / 125000000000000000000000000000)) ≤ accepted_3 := by + norm_num [expUpper, taylor8, b, accepted_3] + +def accepted_4 : ℚ := (10005608262486795586682598316938196351633 / 10000000000000000000000000000000000000000) +theorem accepted_interval_4 : (0 : ℚ) ≤ b*(4969813299576000620459418959677 / 1000000000000000000000000000000) ∧ b*(4969813299576000620459418959677 / 1000000000000000000000000000000) ≤ b*(2484906649788000310229709479839 / 500000000000000000000000000000) ∧ b*(2484906649788000310229709479839 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_4 : expUpper (b*(2484906649788000310229709479839 / 500000000000000000000000000000)) ≤ accepted_4 := by + norm_num [expUpper, taylor8, b, accepted_4] + +def accepted_5 : ℚ := (5002678192638354252310939591491486682637 / 5000000000000000000000000000000000000000) +theorem accepted_interval_5 : (0 : ℚ) ≤ b*(4746669748261790864693123869367 / 1000000000000000000000000000000) ∧ b*(4746669748261790864693123869367 / 1000000000000000000000000000000) ≤ b*(593333718532723858086640483671 / 125000000000000000000000000000) ∧ b*(593333718532723858086640483671 / 125000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_5 : expUpper (b*(593333718532723858086640483671 / 125000000000000000000000000000)) ≤ accepted_5 := by + norm_num [expUpper, taylor8, b, accepted_5] + +def accepted_6 : ℚ := (10005150591318081334437472307882593960501 / 10000000000000000000000000000000000000000) +theorem accepted_interval_6 : (0 : ℚ) ≤ b*(4564348191467836238481405844213 / 1000000000000000000000000000000) ∧ b*(4564348191467836238481405844213 / 1000000000000000000000000000000) ≤ b*(2282174095733918119240702922107 / 500000000000000000000000000000) ∧ b*(2282174095733918119240702922107 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_6 : expUpper (b*(2282174095733918119240702922107 / 500000000000000000000000000000)) ≤ accepted_6 := by + norm_num [expUpper, taylor8, b, accepted_6] + +def accepted_7 : ℚ := (10004976598307617933072074586029358175999 / 10000000000000000000000000000000000000000) +theorem accepted_interval_7 : (0 : ℚ) ≤ b*(88203950232811558683770609183 / 20000000000000000000000000000) ∧ b*(88203950232811558683770609183 / 20000000000000000000000000000) ≤ b*(4410197511640577934188530459151 / 1000000000000000000000000000000) ∧ b*(4410197511640577934188530459151 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_7 : expUpper (b*(4410197511640577934188530459151 / 1000000000000000000000000000000)) ≤ accepted_7 := by + norm_num [expUpper, taylor8, b, accepted_7] + +def accepted_8 : ℚ := (1250603235144018751348201924633183002973 / 1250000000000000000000000000000000000000) +theorem accepted_interval_8 : (0 : ℚ) ≤ b*(4276666119016055311042186838219 / 1000000000000000000000000000000) ∧ b*(4276666119016055311042186838219 / 1000000000000000000000000000000) ≤ b*(213833305950802765552109341911 / 50000000000000000000000000000) ∧ b*(213833305950802765552109341911 / 50000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_8 : expUpper (b*(213833305950802765552109341911 / 50000000000000000000000000000)) ≤ accepted_8 := by + norm_num [expUpper, taylor8, b, accepted_8] + +def accepted_9 : ℚ := (10004692941083916304711037875234252480853 / 10000000000000000000000000000000000000000) +theorem accepted_interval_9 : (0 : ℚ) ≤ b*(4158883083359671856503392728749 / 1000000000000000000000000000000) ∧ b*(4158883083359671856503392728749 / 1000000000000000000000000000000) ≤ b*(3327106466687737485202714183 / 800000000000000000000000000) ∧ b*(3327106466687737485202714183 / 800000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_9 : expUpper (b*(3327106466687737485202714183 / 800000000000000000000000000)) ≤ accepted_9 := by + norm_num [expUpper, taylor8, b, accepted_9] + +def accepted_10 : ℚ := (2000914804727484006991228354413582185253 / 2000000000000000000000000000000000000000) +theorem accepted_interval_10 : (0 : ℚ) ≤ b*(4053522567701845555275891747909 / 1000000000000000000000000000000) ∧ b*(4053522567701845555275891747909 / 1000000000000000000000000000000) ≤ b*(405352256770184555527589174791 / 100000000000000000000000000000) ∧ b*(405352256770184555527589174791 / 100000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_10 : expUpper (b*(405352256770184555527589174791 / 100000000000000000000000000000)) ≤ accepted_10 := by + norm_num [expUpper, taylor8, b, accepted_10] + +def accepted_11 : ℚ := (10004466450939586496552205020318496489341 / 10000000000000000000000000000000000000000) +theorem accepted_interval_11 : (0 : ℚ) ≤ b*(989553096974380173807984906157 / 250000000000000000000000000000) ∧ b*(989553096974380173807984906157 / 250000000000000000000000000000) ≤ b*(3958212387897520695231939624629 / 1000000000000000000000000000000) ∧ b*(3958212387897520695231939624629 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_11 : expUpper (b*(3958212387897520695231939624629 / 1000000000000000000000000000000)) ≤ accepted_11 := by + norm_num [expUpper, taylor8, b, accepted_11] + +def accepted_12 : ℚ := (2501092061442675825070071222311488555861 / 2500000000000000000000000000000000000000) +theorem accepted_interval_12 : (0 : ℚ) ≤ b*(774240202181578185812834744551 / 200000000000000000000000000000) ∧ b*(774240202181578185812834744551 / 200000000000000000000000000000) ≤ b*(967800252726972732266043430689 / 250000000000000000000000000000) ∧ b*(967800252726972732266043430689 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_12 : expUpper (b*(967800252726972732266043430689 / 250000000000000000000000000000)) ≤ accepted_12 := by + norm_num [expUpper, taylor8, b, accepted_12] + +def accepted_13 : ℚ := (1000427790662396194996233470122394286203 / 1000000000000000000000000000000000000000) +theorem accepted_interval_13 : (0 : ℚ) ≤ b*(947789575808588625810098940257 / 250000000000000000000000000000) ∧ b*(947789575808588625810098940257 / 250000000000000000000000000000) ≤ b*(3791158303234354503240395761029 / 1000000000000000000000000000000) ∧ b*(3791158303234354503240395761029 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_13 : expUpper (b*(3791158303234354503240395761029 / 1000000000000000000000000000000)) ≤ accepted_13 := by + norm_num [expUpper, taylor8, b, accepted_13] + +def accepted_14 : ℚ := (1250524283295687260942300726950585983367 / 1250000000000000000000000000000000000000) +theorem accepted_interval_14 : (0 : ℚ) ≤ b*(929262582770158156192824584423 / 250000000000000000000000000000) ∧ b*(929262582770158156192824584423 / 250000000000000000000000000000) ≤ b*(3717050331080632624771298337693 / 1000000000000000000000000000000) ∧ b*(3717050331080632624771298337693 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_14 : expUpper (b*(3717050331080632624771298337693 / 1000000000000000000000000000000)) ≤ accepted_14 := by + norm_num [expUpper, taylor8, b, accepted_14] + +def accepted_15 : ℚ := (10004116399776304731797587454524115614907 / 10000000000000000000000000000000000000000) +theorem accepted_interval_15 : (0 : ℚ) ≤ b*(729611491918736234659575726489 / 200000000000000000000000000000) ∧ b*(729611491918736234659575726489 / 200000000000000000000000000000) ≤ b*(1824028729796840586648939316223 / 500000000000000000000000000000) ∧ b*(1824028729796840586648939316223 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_15 : expUpper (b*(1824028729796840586648939316223 / 500000000000000000000000000000)) ≤ accepted_15 := by + norm_num [expUpper, taylor8, b, accepted_15] + +def accepted_16 : ℚ := (5002021780497624814863799490608923226717 / 5000000000000000000000000000000000000000) +theorem accepted_interval_16 : (0 : ℚ) ≤ b*(3583518938456110001624954716761 / 1000000000000000000000000000000) ∧ b*(3583518938456110001624954716761 / 1000000000000000000000000000000) ≤ b*(1791759469228055000812477358381 / 500000000000000000000000000000) ∧ b*(1791759469228055000812477358381 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_16 : expUpper (b*(1791759469228055000812477358381 / 500000000000000000000000000000)) ≤ accepted_16 := by + norm_num [expUpper, taylor8, b, accepted_16] + +def accepted_17 : ℚ := (1000397513996078830412133154494488397217 / 1000000000000000000000000000000000000000) +theorem accepted_interval_17 : (0 : ℚ) ≤ b*(44036178957995939488054357309 / 12500000000000000000000000000) ∧ b*(44036178957995939488054357309 / 12500000000000000000000000000) ≤ b*(3522894316639675159044348584721 / 1000000000000000000000000000000) ∧ b*(3522894316639675159044348584721 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_17 : expUpper (b*(3522894316639675159044348584721 / 1000000000000000000000000000000)) ≤ accepted_17 := by + norm_num [expUpper, taylor8, b, accepted_17] + +def accepted_18 : ℚ := (2500977657830542212572203647666043033353 / 2500000000000000000000000000000000000000) +theorem accepted_interval_18 : (0 : ℚ) ≤ b*(346573590279972654708616060729 / 100000000000000000000000000000) ∧ b*(346573590279972654708616060729 / 100000000000000000000000000000) ≤ b*(3465735902799726547086160607291 / 1000000000000000000000000000000) ∧ b*(3465735902799726547086160607291 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_18 : expUpper (b*(3465735902799726547086160607291 / 1000000000000000000000000000000)) ≤ accepted_18 := by + norm_num [expUpper, taylor8, b, accepted_18] + +def accepted_19 : ℚ := (10003849611767539530251041249190273494001 / 10000000000000000000000000000000000000000) +theorem accepted_interval_19 : (0 : ℚ) ≤ b*(1705834340764725389642427885353 / 500000000000000000000000000000) ∧ b*(1705834340764725389642427885353 / 500000000000000000000000000000) ≤ b*(3411668681529450779284855770707 / 1000000000000000000000000000000) ∧ b*(3411668681529450779284855770707 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_19 : expUpper (b*(3411668681529450779284855770707 / 1000000000000000000000000000000)) ≤ accepted_19 := by + norm_num [expUpper, taylor8, b, accepted_19] + +def accepted_20 : ℚ := (10003791723174336695859928379092107147311 / 10000000000000000000000000000000000000000) +theorem accepted_interval_20 : (0 : ℚ) ≤ b*(3360375387141900245858659626451 / 1000000000000000000000000000000) ∧ b*(3360375387141900245858659626451 / 1000000000000000000000000000000) ≤ b*(840093846785475061464664906613 / 250000000000000000000000000000) ∧ b*(840093846785475061464664906613 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_20 : expUpper (b*(840093846785475061464664906613 / 250000000000000000000000000000)) ≤ accepted_20 := by + norm_num [expUpper, taylor8, b, accepted_20] + +def accepted_21 : ℚ := (10003736659875036312749799798518888013029 / 10000000000000000000000000000000000000000) +theorem accepted_interval_21 : (0 : ℚ) ≤ b*(827896305743117060698321305557 / 250000000000000000000000000000) ∧ b*(827896305743117060698321305557 / 250000000000000000000000000000) ≤ b*(3311585222972468242793285222229 / 1000000000000000000000000000000) ∧ b*(3311585222972468242793285222229 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_21 : expUpper (b*(3311585222972468242793285222229 / 1000000000000000000000000000000)) ≤ accepted_21 := by + norm_num [expUpper, taylor8, b, accepted_21] + +def accepted_22 : ℚ := (5001842079444036409320152786470891628601 / 5000000000000000000000000000000000000000) +theorem accepted_interval_22 : (0 : ℚ) ≤ b*(326506520733757538581470750317 / 100000000000000000000000000000) ∧ b*(326506520733757538581470750317 / 100000000000000000000000000000) ≤ b*(3265065207337575385814707503171 / 1000000000000000000000000000000) ∧ b*(3265065207337575385814707503171 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_22 : expUpper (b*(3265065207337575385814707503171 / 1000000000000000000000000000000)) ≤ accepted_22 := by + norm_num [expUpper, taylor8, b, accepted_22] + +def accepted_23 : ℚ := (10003633992322138767059090899422809010713 / 10000000000000000000000000000000000000000) +theorem accepted_interval_23 : (0 : ℚ) ≤ b*(3220613444766741548487130370783 / 1000000000000000000000000000000) ∧ b*(3220613444766741548487130370783 / 1000000000000000000000000000000) ≤ b*(100644170148960673390222824087 / 31250000000000000000000000000) ∧ b*(100644170148960673390222824087 / 31250000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_23 : expUpper (b*(100644170148960673390222824087 / 31250000000000000000000000000)) ≤ accepted_23 := by + norm_num [expUpper, taylor8, b, accepted_23] + +def accepted_529 : ℚ := (2500024006910801357156667820225605837451 / 2500000000000000000000000000000000000000) +theorem accepted_interval_529 : (0 : ℚ) ≤ b*(85119228837591857680377538973 / 1000000000000000000000000000000) ∧ b*(85119228837591857680377538973 / 1000000000000000000000000000000) ≤ b*(42559614418795928840188769487 / 500000000000000000000000000000) ∧ b*(42559614418795928840188769487 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_529 : expUpper (b*(42559614418795928840188769487 / 500000000000000000000000000000)) ≤ accepted_529 := by + norm_num [expUpper, taylor8, b, accepted_529] + +def accepted_552 : ℚ := (10000048013706336914502962445538143648637 / 10000000000000000000000000000000000000000) +theorem accepted_interval_552 : (0 : ℚ) ≤ b*(21279807209397964420094384743 / 500000000000000000000000000000) ∧ b*(21279807209397964420094384743 / 500000000000000000000000000000) ≤ b*(42559614418795928840188769487 / 1000000000000000000000000000000) ∧ b*(42559614418795928840188769487 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_552 : expUpper (b*(42559614418795928840188769487 / 1000000000000000000000000000000)) ≤ accepted_552 := by + norm_num [expUpper, taylor8, b, accepted_552] + +def accepted_554 : ℚ := (400001757343114255072912651180621264047 / 400000000000000000000000000000000000000) +theorem accepted_interval_554 : (0 : ℚ) ≤ b*(38942973948607430007253531611 / 1000000000000000000000000000000) ∧ b*(38942973948607430007253531611 / 1000000000000000000000000000000) ≤ b*(9735743487151857501813382903 / 250000000000000000000000000000) ∧ b*(9735743487151857501813382903 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_554 : expUpper (b*(9735743487151857501813382903 / 250000000000000000000000000000)) ≤ accepted_554 := by + norm_num [expUpper, taylor8, b, accepted_554] + +def accepted_556 : ℚ := (5000019934077114581960794678319392907493 / 5000000000000000000000000000000000000000) +theorem accepted_interval_556 : (0 : ℚ) ≤ b*(17669683222654431635317020401 / 500000000000000000000000000000) ∧ b*(17669683222654431635317020401 / 500000000000000000000000000000) ≤ b*(35339366445308863270634040803 / 1000000000000000000000000000000) ∧ b*(35339366445308863270634040803 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_556 : expUpper (b*(35339366445308863270634040803 / 1000000000000000000000000000000)) ≤ accepted_556 := by + norm_num [expUpper, taylor8, b, accepted_556] + +def accepted_558 : ℚ := (10000035817329848616000090876431682424381 / 10000000000000000000000000000000000000000) +theorem accepted_interval_558 : (0 : ℚ) ≤ b*(7937174578645075289249070687 / 250000000000000000000000000000) ∧ b*(7937174578645075289249070687 / 250000000000000000000000000000) ≤ b*(31748698314580301156996282749 / 1000000000000000000000000000000) ∧ b*(31748698314580301156996282749 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_558 : expUpper (b*(31748698314580301156996282749 / 1000000000000000000000000000000)) ≤ accepted_558 := by + norm_num [expUpper, taylor8, b, accepted_558] + +def accepted_560 : ℚ := (2000006356200048328919135749948149107147 / 2000000000000000000000000000000000000000) +theorem accepted_interval_560 : (0 : ℚ) ≤ b*(7042719241674080479710660023 / 250000000000000000000000000000) ∧ b*(7042719241674080479710660023 / 250000000000000000000000000000) ≤ b*(28170876966696321918842640093 / 1000000000000000000000000000000) ∧ b*(28170876966696321918842640093 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_560 : expUpper (b*(28170876966696321918842640093 / 1000000000000000000000000000000)) ≤ accepted_560 := by + norm_num [expUpper, taylor8, b, accepted_560] + +def accepted_562 : ℚ := (5000013879531026283516616597127113348633 / 5000000000000000000000000000000000000000) +theorem accepted_interval_562 : (0 : ℚ) ≤ b*(12302905401100082385006378221 / 500000000000000000000000000000) ∧ b*(12302905401100082385006378221 / 500000000000000000000000000000) ≤ b*(24605810802200164770012756443 / 1000000000000000000000000000000) ∧ b*(24605810802200164770012756443 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_562 : expUpper (b*(24605810802200164770012756443 / 1000000000000000000000000000000)) ≤ accepted_562 := by + norm_num [expUpper, taylor8, b, accepted_562] + +def accepted_571 : ℚ := (2500002458929401650667719229571399047519 / 2500000000000000000000000000000000000000) +theorem accepted_interval_571 : (0 : ℚ) ≤ b*(4359225519940511281958503327 / 500000000000000000000000000000) ∧ b*(4359225519940511281958503327 / 500000000000000000000000000000) ≤ b*(1743690207976204512783401331 / 200000000000000000000000000000) ∧ b*(1743690207976204512783401331 / 200000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_571 : expUpper (b*(1743690207976204512783401331 / 200000000000000000000000000000)) ≤ accepted_571 := by + norm_num [expUpper, taylor8, b, accepted_571] + +def accepted_572 : ℚ := (2500001965425291953393961431121574574217 / 2500000000000000000000000000000000000000) +theorem accepted_interval_572 : (0 : ℚ) ≤ b*(6968669316093340343987940147 / 1000000000000000000000000000000) ∧ b*(6968669316093340343987940147 / 1000000000000000000000000000000) ≤ b*(1742167329023335085996985037 / 250000000000000000000000000000) ∧ b*(1742167329023335085996985037 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_572 : expUpper (b*(1742167329023335085996985037 / 250000000000000000000000000000)) ≤ accepted_572 := by + norm_num [expUpper, taylor8, b, accepted_572] + +def accepted_573 : ℚ := (5000002945566591540622685978536652726911 / 5000000000000000000000000000000000000000) +theorem accepted_interval_573 : (0 : ℚ) ≤ b*(5221943981151675048688013469 / 1000000000000000000000000000000) ∧ b*(5221943981151675048688013469 / 1000000000000000000000000000000) ≤ b*(522194398115167504868801347 / 100000000000000000000000000000) ∧ b*(522194398115167504868801347 / 100000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_573 : expUpper (b*(522194398115167504868801347 / 100000000000000000000000000000)) ≤ accepted_573 := by + norm_num [expUpper, taylor8, b, accepted_573] + +def accepted_574 : ℚ := (5000001962000812862191416361841862291317 / 5000000000000000000000000000000000000000) +theorem accepted_interval_574 : (0 : ℚ) ≤ b*(695652875264964180906992931 / 200000000000000000000000000000) ∧ b*(695652875264964180906992931 / 200000000000000000000000000000) ≤ b*(217391523520301306533435291 / 62500000000000000000000000000) ∧ b*(217391523520301306533435291 / 62500000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_574 : expUpper (b*(217391523520301306533435291 / 62500000000000000000000000000)) ≤ accepted_574 := by + norm_num [expUpper, taylor8, b, accepted_574] + +def acceptedMoment : ℚ := + ((1*435042608 : ℚ)/(576*114315520))*accepted_1 + + ((2*266771296 : ℚ)/(576*114315520))*accepted_2 + + ((3*29060592 : ℚ)/(576*114315520))*accepted_3 + + ((4*60639040 : ℚ)/(576*114315520))*accepted_4 + + ((5*26643936 : ℚ)/(576*114315520))*accepted_5 + + ((6*15333824 : ℚ)/(576*114315520))*accepted_6 + + ((7*11743248 : ℚ)/(576*114315520))*accepted_7 + + ((8*22069696 : ℚ)/(576*114315520))*accepted_8 + + ((9*3938704 : ℚ)/(576*114315520))*accepted_9 + + ((10*7735728 : ℚ)/(576*114315520))*accepted_10 + + ((11*6658960 : ℚ)/(576*114315520))*accepted_11 + + ((12*33578160 : ℚ)/(576*114315520))*accepted_12 + + ((13*13184336 : ℚ)/(576*114315520))*accepted_13 + + ((14*1821600 : ℚ)/(576*114315520))*accepted_14 + + ((15*3238400 : ℚ)/(576*114315520))*accepted_15 + + ((16*631488 : ℚ)/(576*114315520))*accepted_16 + + ((17*404800 : ℚ)/(576*114315520))*accepted_17 + + ((18*202400 : ℚ)/(576*114315520))*accepted_18 + + ((19*311696 : ℚ)/(576*114315520))*accepted_19 + + ((20*550528 : ℚ)/(576*114315520))*accepted_20 + + ((21*1222496 : ℚ)/(576*114315520))*accepted_21 + + ((22*64768 : ℚ)/(576*114315520))*accepted_22 + + ((23*8383408 : ℚ)/(576*114315520))*accepted_23 + + ((529*8193152 : ℚ)/(576*114315520))*accepted_529 + + ((552*97071040 : ℚ)/(576*114315520))*accepted_552 + + ((554*3456992 : ℚ)/(576*114315520))*accepted_554 + + ((556*1481568 : ℚ)/(576*114315520))*accepted_556 + + ((558*2384272 : ℚ)/(576*114315520))*accepted_558 + + ((560*445280 : ℚ)/(576*114315520))*accepted_560 + + ((562*48576 : ℚ)/(576*114315520))*accepted_562 + + ((571*740784 : ℚ)/(576*114315520))*accepted_571 + + ((572*101200 : ℚ)/(576*114315520))*accepted_572 + + ((573*28336 : ℚ)/(576*114315520))*accepted_573 + + ((574*364320 : ℚ)/(576*114315520))*accepted_574 +def acceptedFromCounts : ℚ := + ((1*(count 1 : ℚ))/(m*width))*accepted_1 + + ((2*(count 2 : ℚ))/(m*width))*accepted_2 + + ((3*(count 3 : ℚ))/(m*width))*accepted_3 + + ((4*(count 4 : ℚ))/(m*width))*accepted_4 + + ((5*(count 5 : ℚ))/(m*width))*accepted_5 + + ((6*(count 6 : ℚ))/(m*width))*accepted_6 + + ((7*(count 7 : ℚ))/(m*width))*accepted_7 + + ((8*(count 8 : ℚ))/(m*width))*accepted_8 + + ((9*(count 9 : ℚ))/(m*width))*accepted_9 + + ((10*(count 10 : ℚ))/(m*width))*accepted_10 + + ((11*(count 11 : ℚ))/(m*width))*accepted_11 + + ((12*(count 12 : ℚ))/(m*width))*accepted_12 + + ((13*(count 13 : ℚ))/(m*width))*accepted_13 + + ((14*(count 14 : ℚ))/(m*width))*accepted_14 + + ((15*(count 15 : ℚ))/(m*width))*accepted_15 + + ((16*(count 16 : ℚ))/(m*width))*accepted_16 + + ((17*(count 17 : ℚ))/(m*width))*accepted_17 + + ((18*(count 18 : ℚ))/(m*width))*accepted_18 + + ((19*(count 19 : ℚ))/(m*width))*accepted_19 + + ((20*(count 20 : ℚ))/(m*width))*accepted_20 + + ((21*(count 21 : ℚ))/(m*width))*accepted_21 + + ((22*(count 22 : ℚ))/(m*width))*accepted_22 + + ((23*(count 23 : ℚ))/(m*width))*accepted_23 + + ((529*(count 529 : ℚ))/(m*width))*accepted_529 + + ((552*(count 552 : ℚ))/(m*width))*accepted_552 + + ((554*(count 554 : ℚ))/(m*width))*accepted_554 + + ((556*(count 556 : ℚ))/(m*width))*accepted_556 + + ((558*(count 558 : ℚ))/(m*width))*accepted_558 + + ((560*(count 560 : ℚ))/(m*width))*accepted_560 + + ((562*(count 562 : ℚ))/(m*width))*accepted_562 + + ((571*(count 571 : ℚ))/(m*width))*accepted_571 + + ((572*(count 572 : ℚ))/(m*width))*accepted_572 + + ((573*(count 573 : ℚ))/(m*width))*accepted_573 + + ((574*(count 574 : ℚ))/(m*width))*accepted_574 +theorem accepted_profile_link : acceptedFromCounts = acceptedMoment := by + norm_num [acceptedFromCounts, acceptedMoment, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, count_1, count_10, count_11, count_12, count_13, count_14, count_15, count_16, count_17, count_18, count_19, count_2, count_20, count_21, count_22, count_23, count_3, count_4, count_5, count_529, count_552, count_554, count_556, count_558, count_560, count_562, count_571, count_572, count_573, count_574, count_6, count_7, count_8, count_9] + +theorem accepted_moment : acceptedMoment < 1 ∧ acceptedMoment = (40665599999999999999999992105609200772387856393 / 40665600000000000000000000000000000000000000000) := by + norm_num [acceptedMoment, accepted_1, accepted_10, accepted_11, accepted_12, accepted_13, accepted_14, accepted_15, accepted_16, accepted_17, accepted_18, accepted_19, accepted_2, accepted_20, accepted_21, accepted_22, accepted_23, accepted_3, accepted_4, accepted_5, accepted_529, accepted_552, accepted_554, accepted_556, accepted_558, accepted_560, accepted_562, accepted_571, accepted_572, accepted_573, accepted_574, accepted_6, accepted_7, accepted_8, accepted_9] + +theorem accepted_paid_moment : acceptedFromCounts < 1 := by + rw [accepted_profile_link] + exact accepted_moment.1 + +def rejected_1 : ℚ := (5003586604354229596221572701664384374267 / 5000000000000000000000000000000000000000) +theorem rejected_interval_1 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(3178053830347945619646941601297 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3178053830347945619646941601297 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(1271221532139178247858776640519 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1271221532139178247858776640519 / 200000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_1 : rejected_1 ≤ taylor8 ((b+1/1000000000000000000000000)*(3178053830347945619646941601297 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_1] + +def rejected_2 : ℚ := (10006390705003970481250915724170359842273 / 10000000000000000000000000000000000000000) +theorem rejected_interval_2 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(1132592096027189185975330216227 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1132592096027189185975330216227 / 200000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(353935030008496620617290692571 / 62500000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(353935030008496620617290692571 / 62500000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_2 : rejected_2 ≤ taylor8 ((b+1/1000000000000000000000000)*(1132592096027189185975330216227 / 200000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_2] + +def rejected_3 : ℚ := (10005932998045190108812428871758817532111 / 10000000000000000000000000000000000000000) +theorem rejected_interval_3 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(5257495372027781547898637965671 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(5257495372027781547898637965671 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(657186921503472693487329745709 / 125000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(657186921503472693487329745709 / 125000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_3 : rejected_3 ≤ taylor8 ((b+1/1000000000000000000000000)*(5257495372027781547898637965671 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_3] + +def rejected_4 : ℚ := (1000560826248679558668264804294320832637 / 1000000000000000000000000000000000000000) +theorem rejected_interval_4 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4969813299576000620459418959677 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4969813299576000620459418959677 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(2484906649788000310229709479839 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(2484906649788000310229709479839 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_4 : rejected_4 ≤ taylor8 ((b+1/1000000000000000000000000)*(4969813299576000620459418959677 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_4] + +def rejected_5 : ℚ := (10005356385276708504621926675105446707631 / 10000000000000000000000000000000000000000) +theorem rejected_interval_5 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4746669748261790864693123869367 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4746669748261790864693123869367 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(593333718532723858086640483671 / 125000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(593333718532723858086640483671 / 125000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_5 : rejected_5 ≤ taylor8 ((b+1/1000000000000000000000000)*(4746669748261790864693123869367 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_5] + +def rejected_6 : ℚ := (5002575295659040667218758987436799803833 / 5000000000000000000000000000000000000000) +theorem rejected_interval_6 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4564348191467836238481405844213 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4564348191467836238481405844213 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(2282174095733918119240702922107 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(2282174095733918119240702922107 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_6 : rejected_6 ≤ taylor8 ((b+1/1000000000000000000000000)*(4564348191467836238481405844213 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_6] + +def rejected_7 : ℚ := (5002488299153808966536059354976127437137 / 5000000000000000000000000000000000000000) +theorem rejected_interval_7 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(88203950232811558683770609183 / 20000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(88203950232811558683770609183 / 20000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(4410197511640577934188530459151 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4410197511640577934188530459151 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_7 : rejected_7 ≤ taylor8 ((b+1/1000000000000000000000000)*(88203950232811558683770609183 / 20000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_7] + +def rejected_8 : ℚ := (10004825881152150010785658184365335434401 / 10000000000000000000000000000000000000000) +theorem rejected_interval_8 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4276666119016055311042186838219 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4276666119016055311042186838219 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(213833305950802765552109341911 / 50000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(213833305950802765552109341911 / 50000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_8 : rejected_8 ≤ taylor8 ((b+1/1000000000000000000000000)*(4276666119016055311042186838219 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_8] + +def rejected_9 : ℚ := (625293308817744769044442467723904887727 / 625000000000000000000000000000000000000) +theorem rejected_interval_9 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4158883083359671856503392728749 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4158883083359671856503392728749 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3327106466687737485202714183 / 800000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3327106466687737485202714183 / 800000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_9 : rejected_9 ≤ taylor8 ((b+1/1000000000000000000000000)*(4158883083359671856503392728749 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_9] + +def rejected_10 : ℚ := (10004574023637420034956182325834494831437 / 10000000000000000000000000000000000000000) +theorem rejected_interval_10 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4053522567701845555275891747909 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4053522567701845555275891747909 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(405352256770184555527589174791 / 100000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(405352256770184555527589174791 / 100000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_10 : rejected_10 ≤ taylor8 ((b+1/1000000000000000000000000)*(4053522567701845555275891747909 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_10] + +def rejected_11 : ℚ := (5002233225469793248276122310060767877723 / 5000000000000000000000000000000000000000) +theorem rejected_interval_11 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(989553096974380173807984906157 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(989553096974380173807984906157 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3958212387897520695231939624629 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3958212387897520695231939624629 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_11 : rejected_11 ≤ taylor8 ((b+1/1000000000000000000000000)*(989553096974380173807984906157 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_11] + +def rejected_12 : ℚ := (10004368245770703300280323618166419601223 / 10000000000000000000000000000000000000000) +theorem rejected_interval_12 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(774240202181578185812834744551 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(774240202181578185812834744551 / 200000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(967800252726972732266043430689 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(967800252726972732266043430689 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_12 : rejected_12 ≤ taylor8 ((b+1/1000000000000000000000000)*(774240202181578185812834744551 / 200000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_12] + +def rejected_13 : ℚ := (10004277906623961949962372629025195281639 / 10000000000000000000000000000000000000000) +theorem rejected_interval_13 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(947789575808588625810098940257 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(947789575808588625810098940257 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3791158303234354503240395761029 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3791158303234354503240395761029 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_13 : rejected_13 ≤ taylor8 ((b+1/1000000000000000000000000)*(947789575808588625810098940257 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_13] + +def rejected_14 : ℚ := (2000838853273099617507688600339659343221 / 2000000000000000000000000000000000000000) +theorem rejected_interval_14 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(929262582770158156192824584423 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(929262582770158156192824584423 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3717050331080632624771298337693 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3717050331080632624771298337693 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_14 : rejected_14 ≤ taylor8 ((b+1/1000000000000000000000000)*(929262582770158156192824584423 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_14] + +def rejected_15 : ℚ := (10004116399776304731797623950115573324387 / 10000000000000000000000000000000000000000) +theorem rejected_interval_15 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(729611491918736234659575726489 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(729611491918736234659575726489 / 200000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(1824028729796840586648939316223 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1824028729796840586648939316223 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_15 : rejected_15 ≤ taylor8 ((b+1/1000000000000000000000000)*(729611491918736234659575726489 / 200000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_15] + +def rejected_16 : ℚ := (5002021780497624814863817415448703641629 / 5000000000000000000000000000000000000000) +theorem rejected_interval_16 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(3583518938456110001624954716761 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3583518938456110001624954716761 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(1791759469228055000812477358381 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1791759469228055000812477358381 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_16 : rejected_16 ≤ taylor8 ((b+1/1000000000000000000000000)*(3583518938456110001624954716761 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_16] + +def rejected_17 : ℚ := (10003975139960788304121366787892047209213 / 10000000000000000000000000000000000000000) +theorem rejected_interval_17 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(44036178957995939488054357309 / 12500000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(44036178957995939488054357309 / 12500000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3522894316639675159044348584721 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3522894316639675159044348584721 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_17 : rejected_17 ≤ taylor8 ((b+1/1000000000000000000000000)*(44036178957995939488054357309 / 12500000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_17] + +def rejected_18 : ℚ := (1250488828915271106286106157697051796507 / 1250000000000000000000000000000000000000) +theorem rejected_interval_18 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(346573590279972654708616060729 / 100000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(346573590279972654708616060729 / 100000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3465735902799726547086160607291 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3465735902799726547086160607291 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_18 : rejected_18 ≤ taylor8 ((b+1/1000000000000000000000000)*(346573590279972654708616060729 / 100000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_18] + +def rejected_19 : ℚ := (5001924805883769765125537689505343779089 / 5000000000000000000000000000000000000000) +theorem rejected_interval_19 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(1705834340764725389642427885353 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1705834340764725389642427885353 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3411668681529450779284855770707 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3411668681529450779284855770707 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_19 : rejected_19 ≤ taylor8 ((b+1/1000000000000000000000000)*(1705834340764725389642427885353 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_19] + +def rejected_20 : ℚ := (400151668926973467834398479823503626527 / 400000000000000000000000000000000000000) +theorem rejected_interval_20 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(3360375387141900245858659626451 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3360375387141900245858659626451 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(840093846785475061464664906613 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(840093846785475061464664906613 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_20 : rejected_20 ≤ taylor8 ((b+1/1000000000000000000000000)*(3360375387141900245858659626451 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_20] + +def rejected_21 : ℚ := (10003736659875036312749832926745384230677 / 10000000000000000000000000000000000000000) +theorem rejected_interval_21 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(827896305743117060698321305557 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(827896305743117060698321305557 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3311585222972468242793285222229 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3311585222972468242793285222229 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_21 : rejected_21 ≤ taylor8 ((b+1/1000000000000000000000000)*(827896305743117060698321305557 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_21] + +def rejected_22 : ℚ := (100036841588880728186403382356228745047 / 100000000000000000000000000000000000000) +theorem rejected_interval_22 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(326506520733757538581470750317 / 100000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(326506520733757538581470750317 / 100000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3265065207337575385814707503171 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3265065207337575385814707503171 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_22 : rejected_22 ≤ taylor8 ((b+1/1000000000000000000000000)*(326506520733757538581470750317 / 100000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_22] + +def rejected_23 : ℚ := (5001816996161069383529561558630470038693 / 5000000000000000000000000000000000000000) +theorem rejected_interval_23 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(3220613444766741548487130370783 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3220613444766741548487130370783 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(100644170148960673390222824087 / 31250000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(100644170148960673390222824087 / 31250000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_23 : rejected_23 ≤ taylor8 ((b+1/1000000000000000000000000)*(3220613444766741548487130370783 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_23] + +def rejected_529 : ℚ := (10000096027643205428626672132102884396499 / 10000000000000000000000000000000000000000) +theorem rejected_interval_529 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(85119228837591857680377538973 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(85119228837591857680377538973 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(42559614418795928840188769487 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(42559614418795928840188769487 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_529 : rejected_529 ≤ taylor8 ((b+1/1000000000000000000000000)*(85119228837591857680377538973 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_529] + +def rejected_552 : ℚ := (10000048013706336914502962871136330153269 / 10000000000000000000000000000000000000000) +theorem rejected_interval_552 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(21279807209397964420094384743 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(21279807209397964420094384743 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(42559614418795928840188769487 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(42559614418795928840188769487 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_552 : rejected_552 ≤ taylor8 ((b+1/1000000000000000000000000)*(21279807209397964420094384743 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_552] + +def rejected_554 : ℚ := (1250005491697232047102852083618372607909 / 1250000000000000000000000000000000000000) +theorem rejected_interval_554 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(38942973948607430007253531611 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(38942973948607430007253531611 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(9735743487151857501813382903 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(9735743487151857501813382903 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_554 : rejected_554 ≤ taylor8 ((b+1/1000000000000000000000000)*(38942973948607430007253531611 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_554] + +def rejected_556 : ℚ := (156250622939909830686274839219279032113 / 156250000000000000000000000000000000000) +theorem rejected_interval_556 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(17669683222654431635317020401 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(17669683222654431635317020401 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(35339366445308863270634040803 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(35339366445308863270634040803 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_556 : rejected_556 ≤ taylor8 ((b+1/1000000000000000000000000)*(17669683222654431635317020401 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_556] + +def rejected_558 : ℚ := (1000003581732984861600009119391980159563 / 1000000000000000000000000000000000000000) +theorem rejected_interval_558 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(7937174578645075289249070687 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(7937174578645075289249070687 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(31748698314580301156996282749 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(31748698314580301156996282749 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_558 : rejected_558 ≤ taylor8 ((b+1/1000000000000000000000000)*(7937174578645075289249070687 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_558] + +def rejected_560 : ℚ := (10000031781000241644595679031450409373193 / 10000000000000000000000000000000000000000) +theorem rejected_interval_560 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(7042719241674080479710660023 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(7042719241674080479710660023 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(28170876966696321918842640093 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(28170876966696321918842640093 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_560 : rejected_560 ≤ taylor8 ((b+1/1000000000000000000000000)*(7042719241674080479710660023 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_560] + +def rejected_562 : ℚ := (10000027759062052567033233440313016625343 / 10000000000000000000000000000000000000000) +theorem rejected_interval_562 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(12302905401100082385006378221 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(12302905401100082385006378221 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(24605810802200164770012756443 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(24605810802200164770012756443 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_562 : rejected_562 ≤ taylor8 ((b+1/1000000000000000000000000)*(12302905401100082385006378221 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_562] + +def rejected_571 : ℚ := (10000009835717606602670877005470191212957 / 10000000000000000000000000000000000000000) +theorem rejected_interval_571 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4359225519940511281958503327 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4359225519940511281958503327 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(1743690207976204512783401331 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1743690207976204512783401331 / 200000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_571 : rejected_571 ≤ taylor8 ((b+1/1000000000000000000000000)*(4359225519940511281958503327 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_571] + +def rejected_572 : ℚ := (5000003930850583906787922897086522557623 / 5000000000000000000000000000000000000000) +theorem rejected_interval_572 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(6968669316093340343987940147 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(6968669316093340343987940147 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(1742167329023335085996985037 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1742167329023335085996985037 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_572 : rejected_572 ≤ taylor8 ((b+1/1000000000000000000000000)*(6968669316093340343987940147 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_572] + +def rejected_573 : ℚ := (2000001178226636616249074401858554980071 / 2000000000000000000000000000000000000000) +theorem rejected_interval_573 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(5221943981151675048688013469 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(5221943981151675048688013469 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(522194398115167504868801347 / 100000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(522194398115167504868801347 / 100000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_573 : rejected_573 ≤ taylor8 ((b+1/1000000000000000000000000)*(5221943981151675048688013469 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_573] + +def rejected_574 : ℚ := (10000003924001625724382832758466380866447 / 10000000000000000000000000000000000000000) +theorem rejected_interval_574 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(695652875264964180906992931 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(695652875264964180906992931 / 200000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(217391523520301306533435291 / 62500000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(217391523520301306533435291 / 62500000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_574 : rejected_574 ≤ taylor8 ((b+1/1000000000000000000000000)*(695652875264964180906992931 / 200000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_574] + +def rejectedMoment : ℚ := + ((1*435042608 : ℚ)/(576*114315520))*rejected_1 + + ((2*266771296 : ℚ)/(576*114315520))*rejected_2 + + ((3*29060592 : ℚ)/(576*114315520))*rejected_3 + + ((4*60639040 : ℚ)/(576*114315520))*rejected_4 + + ((5*26643936 : ℚ)/(576*114315520))*rejected_5 + + ((6*15333824 : ℚ)/(576*114315520))*rejected_6 + + ((7*11743248 : ℚ)/(576*114315520))*rejected_7 + + ((8*22069696 : ℚ)/(576*114315520))*rejected_8 + + ((9*3938704 : ℚ)/(576*114315520))*rejected_9 + + ((10*7735728 : ℚ)/(576*114315520))*rejected_10 + + ((11*6658960 : ℚ)/(576*114315520))*rejected_11 + + ((12*33578160 : ℚ)/(576*114315520))*rejected_12 + + ((13*13184336 : ℚ)/(576*114315520))*rejected_13 + + ((14*1821600 : ℚ)/(576*114315520))*rejected_14 + + ((15*3238400 : ℚ)/(576*114315520))*rejected_15 + + ((16*631488 : ℚ)/(576*114315520))*rejected_16 + + ((17*404800 : ℚ)/(576*114315520))*rejected_17 + + ((18*202400 : ℚ)/(576*114315520))*rejected_18 + + ((19*311696 : ℚ)/(576*114315520))*rejected_19 + + ((20*550528 : ℚ)/(576*114315520))*rejected_20 + + ((21*1222496 : ℚ)/(576*114315520))*rejected_21 + + ((22*64768 : ℚ)/(576*114315520))*rejected_22 + + ((23*8383408 : ℚ)/(576*114315520))*rejected_23 + + ((529*8193152 : ℚ)/(576*114315520))*rejected_529 + + ((552*97071040 : ℚ)/(576*114315520))*rejected_552 + + ((554*3456992 : ℚ)/(576*114315520))*rejected_554 + + ((556*1481568 : ℚ)/(576*114315520))*rejected_556 + + ((558*2384272 : ℚ)/(576*114315520))*rejected_558 + + ((560*445280 : ℚ)/(576*114315520))*rejected_560 + + ((562*48576 : ℚ)/(576*114315520))*rejected_562 + + ((571*740784 : ℚ)/(576*114315520))*rejected_571 + + ((572*101200 : ℚ)/(576*114315520))*rejected_572 + + ((573*28336 : ℚ)/(576*114315520))*rejected_573 + + ((574*364320 : ℚ)/(576*114315520))*rejected_574 +def rejectedFromCounts : ℚ := + ((1*(count 1 : ℚ))/(m*width))*rejected_1 + + ((2*(count 2 : ℚ))/(m*width))*rejected_2 + + ((3*(count 3 : ℚ))/(m*width))*rejected_3 + + ((4*(count 4 : ℚ))/(m*width))*rejected_4 + + ((5*(count 5 : ℚ))/(m*width))*rejected_5 + + ((6*(count 6 : ℚ))/(m*width))*rejected_6 + + ((7*(count 7 : ℚ))/(m*width))*rejected_7 + + ((8*(count 8 : ℚ))/(m*width))*rejected_8 + + ((9*(count 9 : ℚ))/(m*width))*rejected_9 + + ((10*(count 10 : ℚ))/(m*width))*rejected_10 + + ((11*(count 11 : ℚ))/(m*width))*rejected_11 + + ((12*(count 12 : ℚ))/(m*width))*rejected_12 + + ((13*(count 13 : ℚ))/(m*width))*rejected_13 + + ((14*(count 14 : ℚ))/(m*width))*rejected_14 + + ((15*(count 15 : ℚ))/(m*width))*rejected_15 + + ((16*(count 16 : ℚ))/(m*width))*rejected_16 + + ((17*(count 17 : ℚ))/(m*width))*rejected_17 + + ((18*(count 18 : ℚ))/(m*width))*rejected_18 + + ((19*(count 19 : ℚ))/(m*width))*rejected_19 + + ((20*(count 20 : ℚ))/(m*width))*rejected_20 + + ((21*(count 21 : ℚ))/(m*width))*rejected_21 + + ((22*(count 22 : ℚ))/(m*width))*rejected_22 + + ((23*(count 23 : ℚ))/(m*width))*rejected_23 + + ((529*(count 529 : ℚ))/(m*width))*rejected_529 + + ((552*(count 552 : ℚ))/(m*width))*rejected_552 + + ((554*(count 554 : ℚ))/(m*width))*rejected_554 + + ((556*(count 556 : ℚ))/(m*width))*rejected_556 + + ((558*(count 558 : ℚ))/(m*width))*rejected_558 + + ((560*(count 560 : ℚ))/(m*width))*rejected_560 + + ((562*(count 562 : ℚ))/(m*width))*rejected_562 + + ((571*(count 571 : ℚ))/(m*width))*rejected_571 + + ((572*(count 572 : ℚ))/(m*width))*rejected_572 + + ((573*(count 573 : ℚ))/(m*width))*rejected_573 + + ((574*(count 574 : ℚ))/(m*width))*rejected_574 +theorem rejected_profile_link : rejectedFromCounts = rejectedMoment := by + norm_num [rejectedFromCounts, rejectedMoment, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, count_1, count_10, count_11, count_12, count_13, count_14, count_15, count_16, count_17, count_18, count_19, count_2, count_20, count_21, count_22, count_23, count_3, count_4, count_5, count_529, count_552, count_554, count_556, count_558, count_560, count_562, count_571, count_572, count_573, count_574, count_6, count_7, count_8, count_9] + +theorem rejected_moment : 1 < rejectedMoment ∧ rejectedMoment = (40665600000000000000000002301675639985445787697 / 40665600000000000000000000000000000000000000000) := by + norm_num [rejectedMoment, rejected_1, rejected_10, rejected_11, rejected_12, rejected_13, rejected_14, rejected_15, rejected_16, rejected_17, rejected_18, rejected_19, rejected_2, rejected_20, rejected_21, rejected_22, rejected_23, rejected_3, rejected_4, rejected_5, rejected_529, rejected_552, rejected_554, rejected_556, rejected_558, rejected_560, rejected_562, rejected_571, rejected_572, rejected_573, rejected_574, rejected_6, rejected_7, rejected_8, rejected_9] + +theorem rejected_paid_moment : 1 < rejectedFromCounts := by + rw [rejected_profile_link] + exact rejected_moment.1 + +end KappaCheck.ShrunkBirthTerminal +#print axioms KappaCheck.ShrunkBirthTerminal.network_counts +#print axioms KappaCheck.ShrunkBirthTerminal.initial_dimension_count +#print axioms KappaCheck.ShrunkBirthTerminal.rank_mass +#print axioms KappaCheck.ShrunkBirthTerminal.count_1 +#print axioms KappaCheck.ShrunkBirthTerminal.count_2 +#print axioms KappaCheck.ShrunkBirthTerminal.count_3 +#print axioms KappaCheck.ShrunkBirthTerminal.count_4 +#print axioms KappaCheck.ShrunkBirthTerminal.count_5 +#print axioms KappaCheck.ShrunkBirthTerminal.count_6 +#print axioms KappaCheck.ShrunkBirthTerminal.count_7 +#print axioms KappaCheck.ShrunkBirthTerminal.count_8 +#print axioms KappaCheck.ShrunkBirthTerminal.count_9 +#print axioms KappaCheck.ShrunkBirthTerminal.count_10 +#print axioms KappaCheck.ShrunkBirthTerminal.count_11 +#print axioms KappaCheck.ShrunkBirthTerminal.count_12 +#print axioms KappaCheck.ShrunkBirthTerminal.count_13 +#print axioms KappaCheck.ShrunkBirthTerminal.count_14 +#print axioms KappaCheck.ShrunkBirthTerminal.count_15 +#print axioms KappaCheck.ShrunkBirthTerminal.count_16 +#print axioms KappaCheck.ShrunkBirthTerminal.count_17 +#print axioms KappaCheck.ShrunkBirthTerminal.count_18 +#print axioms KappaCheck.ShrunkBirthTerminal.count_19 +#print axioms KappaCheck.ShrunkBirthTerminal.count_20 +#print axioms KappaCheck.ShrunkBirthTerminal.count_21 +#print axioms KappaCheck.ShrunkBirthTerminal.count_22 +#print axioms KappaCheck.ShrunkBirthTerminal.count_23 +#print axioms KappaCheck.ShrunkBirthTerminal.count_529 +#print axioms KappaCheck.ShrunkBirthTerminal.count_552 +#print axioms KappaCheck.ShrunkBirthTerminal.count_554 +#print axioms KappaCheck.ShrunkBirthTerminal.count_556 +#print axioms KappaCheck.ShrunkBirthTerminal.count_558 +#print axioms KappaCheck.ShrunkBirthTerminal.count_560 +#print axioms KappaCheck.ShrunkBirthTerminal.count_562 +#print axioms KappaCheck.ShrunkBirthTerminal.count_571 +#print axioms KappaCheck.ShrunkBirthTerminal.count_572 +#print axioms KappaCheck.ShrunkBirthTerminal.count_573 +#print axioms KappaCheck.ShrunkBirthTerminal.count_574 +#print axioms KappaCheck.ShrunkBirthTerminal.complete_child_support +#print axioms KappaCheck.ShrunkBirthTerminal.strict_child_contraction +#print axioms KappaCheck.ShrunkBirthTerminal.slack_a_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_a_below_b +#print axioms KappaCheck.ShrunkBirthTerminal.slack_b_below_one_over32 +#print axioms KappaCheck.ShrunkBirthTerminal.slack_beta_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_beta_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_phase_leaf_above_bit +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_below_internal +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_below_leaf +#print axioms KappaCheck.ShrunkBirthTerminal.slack_c_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_c_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_below_reservations +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_above_tau +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_above_sigma +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_above_internal +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_prime_above_lambda +#print axioms KappaCheck.ShrunkBirthTerminal.slack_compact_leaf +#print axioms KappaCheck.ShrunkBirthTerminal.slack_compact_reservations +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_prime_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_epsilon_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_epsilon_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_guard_width +#print axioms KappaCheck.ShrunkBirthTerminal.slack_K_geometry +#print axioms KappaCheck.ShrunkBirthTerminal.slack_K_dominates_log +#print axioms KappaCheck.ShrunkBirthTerminal.slack_record_suffix +#print axioms KappaCheck.ShrunkBirthTerminal.slack_phase_local +#print axioms KappaCheck.ShrunkBirthTerminal.slack_phase_boundary +#print axioms KappaCheck.ShrunkBirthTerminal.slack_gamma_sublinear +#print axioms KappaCheck.ShrunkBirthTerminal.slack_cell_above_band +#print axioms KappaCheck.ShrunkBirthTerminal.slack_prime_interval_packing +#print axioms KappaCheck.ShrunkBirthTerminal.slack_alpha_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_alpha_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_alpha_below_one_fourth +#print axioms KappaCheck.ShrunkBirthTerminal.slack_delta_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_delta_below_one_eighth +#print axioms KappaCheck.ShrunkBirthTerminal.slack_short_record_fallback +#print axioms KappaCheck.ShrunkBirthTerminal.slack_small_field_exposure +#print axioms KappaCheck.ShrunkBirthTerminal.slack_artificial_boundary +#print axioms KappaCheck.ShrunkBirthTerminal.slack_literal_scalar_guard +#print axioms KappaCheck.ShrunkBirthTerminal.slack_row_product_gap +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g1_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g2_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g3_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g4_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g5_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g6_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g7_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.margins_strict +#print axioms KappaCheck.ShrunkBirthTerminal.balanced_identities +#print axioms KappaCheck.ShrunkBirthTerminal.stopped_parameter_choice +#print axioms KappaCheck.ShrunkBirthTerminal.controlling_margin +#print axioms KappaCheck.ShrunkBirthTerminal.fixed_profile_grid_exclusion +#print axioms KappaCheck.ShrunkBirthTerminal.gain_over_pinned_bounds +#print axioms KappaCheck.ShrunkBirthTerminal.stock_bit_coarse +#print axioms KappaCheck.ShrunkBirthTerminal.stock_complex +#print axioms KappaCheck.ShrunkBirthTerminal.stock_ordinary_leaf +#print axioms KappaCheck.ShrunkBirthTerminal.row_stock +#print axioms KappaCheck.ShrunkBirthTerminal.semantic_constants +#print axioms KappaCheck.ShrunkBirthTerminal.finite_bridge +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_1 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_1 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_2 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_2 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_3 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_3 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_4 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_4 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_5 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_5 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_6 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_6 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_7 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_7 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_8 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_8 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_9 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_9 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_10 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_10 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_11 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_11 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_12 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_12 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_13 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_13 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_14 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_14 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_15 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_15 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_16 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_16 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_17 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_17 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_18 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_18 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_19 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_19 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_20 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_20 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_21 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_21 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_22 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_22 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_23 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_23 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_529 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_529 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_552 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_552 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_554 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_554 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_556 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_556 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_558 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_558 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_560 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_560 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_562 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_562 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_571 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_571 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_572 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_572 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_573 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_573 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_574 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_574 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_profile_link +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_moment +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_paid_moment +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_1 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_1 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_2 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_2 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_3 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_3 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_4 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_4 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_5 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_5 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_6 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_6 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_7 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_7 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_8 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_8 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_9 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_9 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_10 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_10 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_11 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_11 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_12 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_12 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_13 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_13 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_14 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_14 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_15 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_15 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_16 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_16 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_17 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_17 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_18 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_18 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_19 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_19 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_20 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_20 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_21 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_21 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_22 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_22 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_23 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_23 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_529 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_529 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_552 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_552 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_554 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_554 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_556 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_556 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_558 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_558 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_560 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_560 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_562 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_562 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_571 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_571 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_572 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_572 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_573 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_573 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_574 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_574 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_profile_link +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_moment +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_paid_moment diff --git a/research/shrunk-birth-terminal/audit/independent-lean/regeneration/generate.py b/research/shrunk-birth-terminal/audit/independent-lean/regeneration/generate.py new file mode 100644 index 0000000000..ba5871d9b0 --- /dev/null +++ b/research/shrunk-birth-terminal/audit/independent-lean/regeneration/generate.py @@ -0,0 +1,130 @@ +#!/usr/bin/env python3 +"""Generate a scoped Lean rational-arithmetic companion from input.json.""" +import json +from fractions import Fraction +from pathlib import Path +from hashlib import sha256 +HERE=Path(__file__).resolve().parent +data=json.loads((HERE/'input.json').read_text()); cert=data['certificate']; profile=cert['profile'] +out=[] +def emit(s=''):out.append(s) +def q(x): + f=Fraction(x);return str(f.numerator) if f.denominator==1 else f'({f.numerator} / {f.denominator})' +def proof(name,claim,defs=''): + emit(f'theorem {name} : {claim} := by\n norm_num [{defs}]\n') +def pairs(d):return '['+', '.join(f'({k}, {v})' for k,v in sorted(d.items(),key=lambda z:int(z[0])))+']' +emit('''import Mathlib.Tactic.NormNum +import Mathlib.Data.Nat.Choose.Basic + +/-! +Exact arithmetic companion for the shrunk-frame / birth-reuse / terminal-elision +composition. Prepared with OpenAI assistance. Upstream construction and analytic +credits are retained in the accompanying proof and source provenance. + +Scope: supplied physical-count arrays, all 47 parameter slacks, seven margins, +three row stocks, scalar guards and independent degree-eight moment arithmetic. +The physical-array derivation, real logarithm / exponential enclosure validity, +and all-size framed-word, stopped-product, tape, prime and recovery hypotheses +remain external. This is not an unconditional integer-multiplication theorem. +No sorry, native_decide or additional axioms are introduced. +-/ +namespace KappaCheck.ShrunkBirthTerminal +set_option maxRecDepth 20000 +set_option maxHeartbeats 8000000 +''') +for path,digest in data['pins'].items():emit(f'-- Source SHA256 {digest}: {path}') +emit('def h : ℕ := 24\ndef m : ℕ := h*h\ndef v : ℕ := Nat.choose h 3\ndef n : ℕ := v*v') +for name,val in [('virtualRoles',data['virtual_roles']),('births',data['births']),('terminals',data['terminals'])]:emit(f'def {name} : ℕ := {val}') +emit('def roles : ℕ := virtualRoles-births-terminals\ndef width : ℕ := 2*n+2*v*roles') +emit('def forwardHistogram : List (ℕ × ℕ) := '+pairs(data['forward_histogram'])) +emit('def initialDimensionHistogram : List (ℕ × ℕ) := '+pairs(data['initial_frame_dimension_histogram'])) +emit('''def counts : List (ℕ × ℕ) := + (forwardHistogram.map fun p => (p.1, 2*v*p.2)) ++ + (initialDimensionHistogram.map fun p => (m-h+p.1, 2*v*p.2)) ++ + [((h-1)^2, 2*n), (1, n)] +def count (t : ℕ) : ℕ := (counts.map fun p => if p.1=t then p.2 else 0).sum +def mass : ℕ := (counts.map fun p => p.1*p.2).sum +''') +cdefs='h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose' +allc=cdefs+', mass, count, counts, forwardHistogram, initialDimensionHistogram' +proof('network_counts',f'h = 24 ∧ m = 576 ∧ v = 2024 ∧ n = 4096576 ∧ roles = {profile["R"]} ∧ width = {profile["W"]}',cdefs) +proof('initial_dimension_count','(initialDimensionHistogram.map Prod.snd).sum = roles',allc) +proof('rank_mass',f'mass = {profile["total_rank"]} ∧ m*width-mass = {profile["deficit"]} ∧ n-2*v*h*(h-1) = {profile["deficit"]}',allc) +for t,cnt in sorted(profile['child_multiplicities'].items(),key=lambda z:int(z[0])):proof(f'count_{t}',f'count {t} = {cnt}',allc) +sizes=sorted(map(int,profile['child_multiplicities']));emit(f'def childSizes : List ℕ := {sizes}') +proof('complete_child_support','∀ p ∈ counts, p.2 ≠ 0 → p.1 ∈ childSizes',allc+', childSizes') +proof('strict_child_contraction','∀ t ∈ childSizes, 0 < t ∧ t < m','childSizes, h, m') +for name,key in [('a','assembly_bit'),('b','complex_saving'),('kappa','kappa'),('eta','eta'),('beta','beta'),('backoff','backoff'),('actualBitSaving','actual_bit_saving')]:emit(f'def {name} : ℚ := {q(cert[key])}') +emit('''def tau : ℚ := 1-a +def sigma : ℚ := 1-b +def qParam : ℚ := a*(1-2*eta) +def lp : ℚ := 1-qParam +def c : ℚ := qParam+eta/4 +def epsilon : ℚ := (1-eta)/(1+qParam) +def lam : ℚ := (tau+lp)/2 +def g : ℚ := epsilon*qParam +def r : ℚ := (g+1-epsilon)/2 +def delta : ℚ := eta/8 +def internal : ℚ := tau+(1-beta)*max (sigma-tau) 0 +def leaf : ℚ := sigma+beta*(1-sigma) +''') +scalar=cert['finite_bridge']['complex']['scalar_group_upper'] +emit(f'def scalar : ℕ := {scalar}') +emit('''def guardE : ℕ := 64*(width+m+scalar+1)^3 +def guardB : ℕ := mass+guardE +def literal : ℕ := 2*scalar*width^2+8*mass+4*width+4+32*m +def guardC : ℕ := 32*m*guardB^2 +def literalGap : ℚ := (guardE : ℚ)-literal +def rowCoefficient : ℕ := 367*27+200*27+9*28 +def rowGap : ℚ := 32000-(51/25)*rowCoefficient +def margins : List ℚ := [1-epsilon,a,g,a,min (1-epsilon-delta) (r-delta),1-epsilon-delta,epsilon] +''') +defs='a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, '+allc +slacks = {'a_positive': 'a', 'a_below_b': 'b-a', 'b_below_one_over32': '1/32-b', 'beta_positive': 'beta', 'beta_below_one': '1-beta', 'phase_leaf_above_bit': '(1-beta)*b-a', 'q_positive': 'qParam', 'q_below_internal': '1-internal-qParam', 'q_below_leaf': '1-leaf-qParam', 'c_positive': 'c', 'c_below_one': '1-c', 'q_below_reservations': 'c-qParam', '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': 'qParam', 'epsilon_positive': 'epsilon', 'epsilon_below_one': '1-epsilon', 'guard_width': '1-epsilon', 'K_geometry': '1-epsilon*(1+c)', 'K_dominates_log': 'epsilon*c', 'record_suffix': '1-epsilon', 'phase_local': '1-epsilon-delta', 'phase_boundary': 'r-delta', 'gamma_sublinear': '1-epsilon-r', 'cell_above_band': 'epsilon-(1-r)/2', 'prime_interval_packing': '1-epsilon', 'alpha_positive': 'r', 'alpha_below_one': '1-r', 'alpha_below_one_fourth': '1/4-r', 'delta_positive': 'delta', 'delta_below_one_eighth': '1/8-delta', 'short_record_fallback': 'epsilon-a', 'small_field_exposure': '1-epsilon-g', 'artificial_boundary': '8-epsilon+r-delta-g', 'literal_scalar_guard': 'literalGap', 'row_product_gap': 'rowGap'} +margin_expr=['1-epsilon','a','g','a','min (1-epsilon-delta) (r-delta)','1-epsilon-delta','epsilon'] +for i,x in enumerate(margin_expr,1):slacks[f'g{i}_above_kappa']=f'({x})-kappa' +assert set(slacks)==set(cert['assembly']['constraints']) +for name,expr in slacks.items():proof('slack_'+name,f'({expr}) = ({q(cert["assembly"]["constraints"][name])} : ℚ) ∧ (0 : ℚ) < ({expr})',defs) +proof('margins_strict','∀ x ∈ margins, kappa < x','margins, '+defs) +proof('balanced_identities','1-epsilon-g = eta ∧ 1-epsilon-r = eta/2 ∧ 1-epsilon*(1+c) = eta-epsilon*eta/4',defs) +proof('stopped_parameter_choice','a = min actualBitSaving ((1-beta)*b-backoff) ∧ 0 < eta ∧ eta < 1/2',defs) +proof('controlling_margin','kappa < g ∧ g < kappa+1/1000000000000000000',defs) +proof('fixed_profile_grid_exclusion','(b+1/1000000000000000000000000)/(1+b+1/1000000000000000000000000) < kappa+1/1000000000000000000',defs) +proof('gain_over_pinned_bounds','kappa > (384569/10000000000 : ℚ) ∧ kappa > (52789616935221/1000000000000000000 : ℚ) ∧ kappa > (111192082577/1000000000000000 : ℚ) ∧ (1/2^14 : ℚ) < kappa ∧ kappa < (1/2^13 : ℚ)',defs) +bridge=cert['assembly']['finite_bridge'] +for name in ('bit_coarse','complex','ordinary_leaf'): + x=bridge[name];arity=x['m'];child=x['maxchild'];degree=x['halving_degree'];w=x['W'];bits=x['wire_bits'] + proof('stock_'+name,f'({arity}:ℕ)^{degree} > 2*{child}^{degree} ∧ ({arity}:ℕ)^{degree-1} ≤ 2*{child}^{degree-1} ∧ (2:ℕ)^{bits-1} ≤ {w} ∧ {w} < (2:ℕ)^{bits}') +proof('row_stock','rowCoefficient = 15561 ∧ rowGap = (6389/25 : ℚ) ∧ 4*(32000:ℕ) = 128000','rowCoefficient, rowGap') +sem=cert['finite_bridge']['semantic'] +proof('semantic_constants',f'guardE = {sem["E"]} ∧ guardB = {sem["B"]} ∧ guardC = {sem["C0"]} ∧ literal = {sem["literal_charge"]}',defs) +proof('finite_bridge','guardE > literal ∧ 2*guardB*(m-574) ≥ mass+guardE ∧ guardC > 2*guardB+18',defs) +emit('''-- The analytic meaning of supplied log intervals is external. These +-- statements prove exact rational Taylor inequalities and complete paid sums. +def taylor8 (x : ℚ) : ℚ := 1+x+x^2/2+x^3/6+x^4/24+x^5/120+x^6/720+x^7/5040+x^8/40320 +def expUpper (x : ℚ) : ℚ := taylor8 x+x^9/362880/(1-x/10) +''') +for typ,side,saving in [('accepted','upper','b'),('rejected','lower','(b+1/1000000000000000000000000)')]: + moment_data=cert['independent_moment'][typ];terms=moment_data['terms'];moment=[];recomputed=[] + assert Fraction(moment_data['saving'])==Fraction(cert['complex_saving'])+(Fraction(1,10**24) if typ=='rejected' else 0) + for t,item in sorted(terms.items(),key=lambda z:int(z[0])): + lo,hi=q(item['log_lower']),q(item['log_upper']);val=q(item['exp_'+side]);cnt=profile['child_multiplicities'][t] + emit(f'def {typ}_{t} : ℚ := {val}') + proof(f'{typ}_interval_{t}',f'(0 : ℚ) ≤ {saving}*{lo} ∧ {saving}*{lo} ≤ {saving}*{hi} ∧ {saving}*{hi} < 1','b') + expr=f'expUpper ({saving}*{hi}) ≤ {typ}_{t}' if side=='upper' else f'{typ}_{t} ≤ taylor8 ({saving}*{lo})' + proof(f'{typ}_taylor_{t}',expr,'expUpper, taylor8, b, '+f'{typ}_{t}') + assert Fraction(item['weight'])==Fraction(int(t)*cnt,profile['m']*profile['W']) + moment.append(f'(({t}*{cnt} : ℚ)/({profile["m"]}*{profile["W"]}))*{typ}_{t}') + recomputed.append(f'(({t}*(count {t} : ℚ))/(m*width))*{typ}_{t}') + emit(f'def {typ}Moment : ℚ :=\n '+' +\n '.join(moment)) + emit(f'def {typ}FromCounts : ℚ :=\n '+' +\n '.join(recomputed)) + proof(typ+'_profile_link',f'{typ}FromCounts = {typ}Moment',typ+'FromCounts, '+typ+'Moment, '+cdefs+', '+', '.join(f'count_{t}' for t in terms)) + comparison=f'{typ}Moment < 1' if typ=='accepted' else f'1 < {typ}Moment' + proof(typ+'_moment',f'{comparison} ∧ {typ}Moment = {q(moment_data[side])}',typ+'Moment, '+', '.join(f'{typ}_{t}' for t in terms)) + claim=f'{typ}FromCounts < 1' if typ=='accepted' else f'1 < {typ}FromCounts' + emit(f'theorem {typ}_paid_moment : {claim} := by\n rw [{typ}_profile_link]\n exact {typ}_moment.1\n') +emit('end KappaCheck.ShrunkBirthTerminal') +names=[line.split()[1] for line in '\n'.join(out).splitlines() if line.startswith('theorem ')] +for name in names:emit(f'#print axioms KappaCheck.ShrunkBirthTerminal.{name}') +path=HERE/'ShrunkBirthTerminal.lean';path.write_text('\n'.join(out)+'\n') +print(json.dumps({'theorems':len(names),'sha256':sha256(path.read_bytes()).hexdigest(),'input_sha256':sha256((HERE/'input.json').read_bytes()).hexdigest()})) diff --git a/research/shrunk-birth-terminal/audit/independent-lean/regeneration/input.json b/research/shrunk-birth-terminal/audit/independent-lean/regeneration/input.json new file mode 100644 index 0000000000..6b12efa8e6 --- /dev/null +++ b/research/shrunk-birth-terminal/audit/independent-lean/regeneration/input.json @@ -0,0 +1,1693 @@ +{ + "births": 2108, + "certificate": { + "actual_bit_saving": "1240189553/10000000000000", + "assembly": { + "absorption_gap": "51350955350972219636574114327365369448123005318656908856664201698261131/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000", + "constraints": { + "K_dominates_log": "28203699512803856630705756229332904653617608320033448605133911713260786682305862261131/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000", + "K_geometry": "187528016199700303669130893284245532604957286739213317694137738869/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000", + "a_below_b": "56907455433006738869/500000000000000000000000000000000000000000000000", + "a_positive": "56407455433006738868999943092544566993261131/500000000000000000000000000000000000000000000000", + "alpha_below_one": "499999500000499999500000250027953699762803606630893284245532604957286739213317694137738869/500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000", + "alpha_below_one_fourth": "124957569450855794090053910101585400855367676522073307704325996653786739213317694137738869/500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000", + "alpha_positive": "56407399025607713261536540537365447110966847533351142742872780713260786682305862261131/500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000", + "artificial_boundary": "14001791036782819432824377920275575186005677171202332185161413102487860217639953082413216607/2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000", + "b_below_one_over32": "15568592544566993261131/500000000000000000000000", + "beta_below_one": "999999999999999999999999/1000000000000000000000000", + "beta_positive": "1/1000000000000000000000000", + "c_below_one": "249971796272283496630565437584861183149510108303499943092544566993261131/250000000000000000000000000000000000000000000000000000000000000000000000", + "c_positive": "28203727716503369434562415138816850489891696500056907455433006738869/250000000000000000000000000000000000000000000000000000000000000000000000", + "cell_above_band": "499999500000499999499999749972046300237196393369106715754467395042713260786682305862261131/1000111814799051214426523573136982130419829146956853270776550955476000000000000000000000000", + "compact_leaf": "56657455433006738868999943092544566993261131/250000000000000000000000000000000000000000000000000000000000000000000000", + "compact_reservations": "1/4000000000000000000000000", + "delta_below_one_eighth": "999999999999999999999999/8000000000000000000000000", + "delta_positive": "1/8000000000000000000000000", + "epsilon_below_one": "28203699512803856630893284245532604957286739213317694137738869/250027953699762803606630893284245532604957286739213317694137738869", + "epsilon_positive": "249999750000249999750000000000000000000000000000000000000000000000/250027953699762803606630893284245532604957286739213317694137738869", + "g1_above_kappa": "12837801344731479849844430239564663423413902568985912017495473959/62506988424940700901657723321061383151239321684803329423534434717250000000000000000", + "g2_above_kappa": "6362884228738868999943092544566993261131/500000000000000000000000000000000000000000000000", + "g3_above_kappa": "51350955350972219636574114327365369448123005318656908856664201698261131/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000", + "g4_above_kappa": "6362884228738868999943092544566993261131/500000000000000000000000000000000000000000000000", + "g5_above_kappa": "82161678578327771276200746902320561664316371484223097698653339199861131/400044725919620485770609429254792852167931658782741308310620382190400000000000000000000000", + "g6_above_kappa": "410809393003453655432218161035175945303712277250262445346537472550261131/2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000", + "g7_above_kappa": "62492886575184298986180078023670096698605108554761333999879467851735912017495473959/62506988424940700901657723321061383151239321684803329423534434717250000000000000000", + "gamma_sublinear": "1/2000000000000000000000000", + "guard_width": "28203699512803856630893284245532604957286739213317694137738869/250027953699762803606630893284245532604957286739213317694137738869", + "lambda_above_internal": "56407455433006738868999943092544566993261131/500000000000000000000000000000000000000000000000000000000000000000000000", + "lambda_above_sigma": "113314910866013477737999943092544566993261131/500000000000000000000000000000000000000000000000000000000000000000000000", + "lambda_above_tau": "56407455433006738868999943092544566993261131/500000000000000000000000000000000000000000000000000000000000000000000000", + "lambda_prime_above_lambda": "56407455433006738868999943092544566993261131/500000000000000000000000000000000000000000000000000000000000000000000000", + "lambda_prime_below_one": "28203727716503369434499915138816850489891696500056907455433006738869/250000000000000000000000000000000000000000000000000000000000000000000000", + "literal_scalar_guard": "1936723974066543198917496885658826453564", + "phase_boundary": "45125919220486170609179226839152405128052151848024065087777233113260786682305862261131/400044725919620485770609429254792852167931658782741308310620382190400000000000000000000000", + "phase_leaf_above_bit": "1/1000000000000000000000000000000", + "phase_local": "225629596102430853046896246010561076854687282813257307569305994713260786682305862261131/2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000", + "prime_interval_packing": "28203699512803856630893284245532604957286739213317694137738869/250027953699762803606630893284245532604957286739213317694137738869", + "q_below_internal": "56407455433006738868999943092544566993261131/250000000000000000000000000000000000000000000000000000000000000000000000", + "q_below_leaf": 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"W": 114315520, + "halving_degree": 200, + "m": 576, + "maxchild": 574, + "s": 65843877440, + "scalar_group_upper": 3116113870848, + "wire_bits": 27 + }, + "ordinary_leaf": { + "W": 188181929, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "rows": { + "coefficient": 15561, + "degree": 32000, + "degree_gap": "6389/25", + "suffix_slope": 128000 + }, + "semantic": { + "B": 1936723974147986188574068436796202829440, + "C0": 69136584229593344553734547662349298866110568132764137982571664415937240220513075200, + "C1": 1, + "E": 1936723974147986188574068436730358952000, + "induction_gap": 5810171922443958565722205310388608488320, + "literal_charge": 81442989656571551071532498436, + "strict_literal_gap": 1936723974066543198917496885658826453564 + } + }, + "margins": { + "g1": "28203699512803856630893284245532604957286739213317694137738869/250027953699762803606630893284245532604957286739213317694137738869", + "g2": 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b/research/shrunk-birth-terminal/audit/lean-portable-equivalence.json @@ -0,0 +1,30 @@ +{ + "allowed_nonmathematical_changes": [ + "certificate_schema", + "finite_bridge/rows/contract wording", + "finite_bridge/semantic/exact_grid wording", + "research-only discovery metadata omitted; portable source/bit-enclosure metadata added", + "scalar input SHA updated to the metadata-corrected bill with unchanged G" + ], + "equal_fields": [ + "profile", + "complex_saving", + "next_complex_rejected", + "first_moment", + "independent_moment", + "actual_bit_saving", + "assembly_bit", + "beta", + "eta", + "backoff", + "kappa", + "assembly", + "cutoffs", + "fixed_profile_family_ceiling" + ], + "finite_bridge_numerics_equal": true, + "lean_prepackage_certificate_sha256": "89b115978ab95d8e69e58472cde14a588157a3b3a8c577034c39ca0309eab34d", + "portable_certificate_sha256": "63fe0b3d9d53a18ceb316adbd6053cfc9682e699da1f1d01314d408ee742dd4d", + "scope": "No Lean source or Lean input byte changed; audit_lean.py verifies equality anew.", + "status": "PASS exact mathematical equivalence of portable certificate and unchanged Lean input" +} diff --git a/research/shrunk-birth-terminal/audit/portable-arithmetic-validation.json b/research/shrunk-birth-terminal/audit/portable-arithmetic-validation.json new file mode 100644 index 0000000000..d49b8ad07f --- /dev/null +++ b/research/shrunk-birth-terminal/audit/portable-arithmetic-validation.json @@ -0,0 +1,130 @@ +{ + "certificate_sha256": "63fe0b3d9d53a18ceb316adbd6053cfc9682e699da1f1d01314d408ee742dd4d", + "controls": [ + { + "name": "missing old stock", + "rejected": true + }, + { + "name": "zero old stock", + "rejected": true + }, + { + "name": "two-stock coefficient", + "rejected": true + }, + { + "name": "stale coarse child", + "rejected": true + }, + { + "name": "stale scalar charge", + "rejected": true + }, + { + "name": "zero scalar charge", + "rejected": true + }, + { + "name": "stale C0", + "rejected": true + }, + { + "name": "insufficient row stock", + "rejected": true + }, + { + "name": "zero stopped leaf gap", + "rejected": true + }, + { + "name": "next kappa", + "rejected": true + }, + { + "name": "old prefix at selected parameters", + "rejected": true + }, + { + "name": "unpaid singleton deletion", + "rejected": true + }, + { + "name": "top float", + "rejected": true + }, + { + "name": "nested float", + "rejected": true + }, + { + "name": "list float", + "rejected": true + }, + { + "name": "noninteger width", + "rejected": true + }, + { + "name": "inconsistent two-factor dimensions", + "rejected": true + }, + { + "name": "floating child count", + "rejected": true + } + ], + "kappa": "28200546274389/250000000000000000", + "prepackage_agreement": { + "all_fields_match": true, + "fields": [ + "profile", + "complex_saving", + "next_complex_rejected", + "first_moment", + "independent_moment", + "actual_bit_saving", + "assembly_bit", + "beta", + "eta", + "backoff", + "kappa", + "assembly", + "cutoffs", + "fixed_profile_family_ceiling" + ] + }, + "prepackage_reference_sha256": "89b115978ab95d8e69e58472cde14a588157a3b3a8c577034c39ca0309eab34d", + "retained_constraints": 47, + "retained_margins": 7, + "same_backoff_layout_comparison": { + "additional_backoff_gain": "58091633/500000000000000000", + "backoff": "1/100000000000000", + "balanced_kappa": "11280206891429/100000000000000000", + "beta": "1/1000000", + "eta": "1/100000000", + "original_prefix_kappa": "2255786920849/20000000000000000", + "paid_layout_gain": "79517949/6250000000000000" + }, + "scope": "Arithmetic and interface-source audit only; full physical and formal-tool receipts are separately bound.", + "source_sha256": { + "REFERENCE_PINS.json": "fbf75766c9112483e43e9cfca5e339044fe80f1d41481c1d7146080ed4970e6f", + "balanced_stopped.py": "03f5f012ab4eb306320ab8a209c2041addd75b84aa43f45ab80595c8989ce781", + "certificate.py": "30f143d6b2e05dc284b773fafbe831080207ef070d07f222cf2e5b87c9746142", + "inputs/bit-profile.json": "7293f330518b78650bd86d76b93681e43f3a55541cdb8110993714148a4b4a6a", + "interval_moment.py": "9d3d1d28bfb3375958995205179b171fb65c70a3792cf9f7a21ef5ee54f5460b", + "references/pr100/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "references/pr100/refine.py": "e0488c919e76850313ff93d7da704a7fcc14a316eee2cac81e2b8dff9c145b5d", + "references/pr104/balanced_assembly.py": "4d27575dcad2b45a281a34054d311409ecd954f373c0c3a62c29bcc843f06a86", + "references/pr104/copied-centers-network.json": "7dbd675e42e22ac076280360f8750031851564bb7a56079e66236fee5d0a6cdf", + "references/pr104/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d", + "validate.py": "f61d6d19fcfe1e3974a16da3c4cc5c9ce43066a0735416d7a3c827a1083d096c" + }, + "status": "PASS selected exact adverse controls and entire source-adaptation audit", + "three_stock_terms": [ + 9909, + 5400, + 252 + ], + "whole_adapter_normalizes_to_pinned_source": true +} diff --git a/research/shrunk-birth-terminal/audit/scalar-metadata-correction.json b/research/shrunk-birth-terminal/audit/scalar-metadata-correction.json new file mode 100644 index 0000000000..58168fd9f3 --- /dev/null +++ b/research/shrunk-birth-terminal/audit/scalar-metadata-correction.json @@ -0,0 +1,14 @@ +{ + "corrected_scalar_bill_sha256": "5a9abce80ed9021ac0717268d0a1c0eff338cfbfc55936d448ce3df9b6fadae4", + "global_scalar_group_upper": 3116113870848, + "inherited_deferred_readout_terms": 9732, + "original_scalar_bill_sha256": "3203dcb2709c3c8f1513c9ff31faafe9903f7ba14cdd7bbe1aaa38c9edbfcf43", + "scope": "The corrected counts describe exact signed old readout support. The conservative bill pays every virtual response before elimination; counts do not enter G. Original input and discovery receipts are retained unchanged.", + "selected_retained_deferred_readout_terms": 11503, + "selected_retained_deferred_roles": 4344, + "selected_virtual_deferred_readout_terms": 11884, + "selected_virtual_deferred_roles": 4725, + "status": "PASS descriptive scalar metadata corrected with unchanged full word, complete profile and all mathematical charges", + "unchanged_profile_sha256": "6a1ca866ddbb81c62f7fee08358849f2060e170bc48bae771da30d76eb9dc297", + "unchanged_word_sha256": "11dfe85123d23c17b4e1f4309b7c5fdfdac55faef7563881f2f3db5b2dfae82e" +} diff --git a/research/shrunk-birth-terminal/audit_lean.py b/research/shrunk-birth-terminal/audit_lean.py new file mode 100644 index 0000000000..edcf514b06 --- /dev/null +++ b/research/shrunk-birth-terminal/audit_lean.py @@ -0,0 +1,67 @@ +#!/usr/bin/env python3 +"""Bind the unchanged Lean companion to the actual selected word and certificate. + +This checks exact input derivation, generation and saved compile provenance; +fresh Lean kernel compilation belongs to make formal-historical-verify. +""" +from pathlib import Path +from hashlib import sha256 +from collections import Counter +from fractions import Fraction as Q +import gzip, json, re, shutil, subprocess, sys, tempfile +if sys.flags.optimize:raise RuntimeError('Assertions must remain enabled') +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1];L=HERE/'lean' +read=lambda p:json.loads(p.read_text()) +sha=lambda p:sha256(p.read_bytes()).hexdigest() +def require(ok,reason): + if not ok:raise ValueError(reason) +def main(): + source=L/'ShrunkBirthTerminal.lean';verification=read(L/'verification.json');data=read(L/'input.json') + require(sha(source)==verification['source_sha256'],'Lean source digest') + require(sha(L/'generate.py')==verification['generator_sha256'],'Lean generator digest') + require(sha(L/'input.json')==verification['input_sha256'],'Lean input digest') + require(source.read_bytes()==(ROOT/'formal/lean/KappaCheck/ShrunkBirthTerminal.lean').read_bytes(),'Integrated Lean module differs') + aliases={'work/r12-audit/canonical-joint-expansion/joint-expansion/certificate.json':HERE/'audit/independent-prepackage-certificate.json'} + aliases['work/r12-terminal/joint-expansion/word.json.gz']=HERE/'selected/word.json.gz' + aliases['work/r12-terminal/joint-expansion/physical-audit.json']=HERE/'audit/discovery-physical-audit.json' + aliases['work/r12-terminal/joint-expansion/READOUT_COST.json']=HERE/'audit/discovery-scalar-bill.json' + require(set(aliases)==set(data['pins']),'Lean source mapping incomplete') + for name,path in aliases.items():require(sha(path)==data['pins'][name],'Lean pinned input: '+name) + require(data['certificate']==read(HERE/'audit/independent-prepackage-certificate.json'),'Lean certificate snapshot') + current=read(HERE/'certificate.json') + math_fields=['profile','complex_saving','next_complex_rejected','first_moment','independent_moment','actual_bit_saving','assembly_bit','beta','eta','backoff','kappa','assembly','cutoffs','fixed_profile_family_ceiling'] + for key in math_fields: + require(key in current and current[key]==data['certificate'][key],'Lean/current certificate mathematical mismatch: '+key) + bridge=json.loads(json.dumps(current['finite_bridge']));oldbridge=json.loads(json.dumps(data['certificate']['finite_bridge'])) + # Only these two prose contracts were reworded in the portable schema. + for x in [bridge,oldbridge]: + x['rows'].pop('contract');x['semantic'].pop('exact_grid') + require(bridge==oldbridge,'Lean/current finite bridge numeric mismatch') + require(current['finite_bridge']['complex']['scalar_group_upper']==read(HERE/'selected/READOUT_COST.json')['global_scalar_group_upper']==read(HERE/'audit/discovery-scalar-bill.json')['global_scalar_group_upper'],'Corrected billing metadata changed the Lean scalar charge') + word=json.loads(gzip.decompress((HERE/'selected/word.json.gz').read_bytes()));audit=read(HERE/'selected/physical-audit.json') + exterior=Counter(len(word['frames'][word['initial_frames'][2*word['v']+role]]) for role in word['physical_roles']) + forward={int(k):n for k,n in audit['forward_frame']['histogram'].items()} + require({str(k):v for k,v in exterior.items()}==data['initial_frame_dimension_histogram'],'Lean exterior counts not from actual word') + require({str(k):v for k,v in forward.items()}==data['forward_histogram'],'Lean forward counts not from actual audit') + require((word['virtual_roles'],len(word['birth_pairs']),len(word['eliminated_terminal_roles']))==(data['virtual_roles'],data['births'],data['terminals']),'Lean role counts') + h=word['h'];v=word['v'];m=h*h;counts=Counter({k:2*v*n for k,n in forward.items()}) + for k,n in exterior.items():counts[m-h+k]+=2*v*n + counts[(h-1)**2]+=2*v*v;counts[1]+=v*v + require({str(k):n for k,n in counts.items()}==current['profile']['child_multiplicities'],'Lean complete paid histogram') + require(Q(verification['kappa'])==Q(current['kappa']),'Lean kappa') + expected=re.findall(r'^#print axioms (\S+)\s*$',source.read_text(),re.M) + require(len(expected)==len(set(expected))==240,'Lean theorem audit roster') + for name,digest in verification['compile_receipts'].items():require(sha(L/name)==digest,'Lean saved compile receipt: '+name) + require((L/'receipts/compile/exit-code').read_text().strip()=='0','Lean saved compile exit') + output=(L/'receipts/compile/output.log').read_text() + rows=re.findall(r"^'([^']+)' (?:depends on axioms: \[([^\]]*)\]|does not depend on any axioms)",output,re.M) + allowed={'propext','Classical.choice','Quot.sound'} + require(len(rows)==len(expected) and {n for n,_ in rows}==set(expected),'Lean saved axiom coverage') + require(all({x.strip() for x in text.split(',')}-{''}<=allowed for _,text in rows),'Lean forbidden saved axiom') + with tempfile.TemporaryDirectory(prefix='shrunk-terminal-lean-') as folder: + destination=Path(folder) + for name in ['generate.py','input.json']:shutil.copy2(L/name,destination/name) + subprocess.run([sys.executable,str(destination/'generate.py')],check=True,capture_output=True,text=True) + require((destination/'ShrunkBirthTerminal.lean').read_bytes()==source.read_bytes(),'Lean generation differs') + print('PASS unchanged Lean module, actual complete physical-count arrays, exact certificate linkage, deterministic generation and 240 saved axiom records') +if __name__=='__main__':main() diff --git a/research/shrunk-birth-terminal/certificate.json b/research/shrunk-birth-terminal/certificate.json new file mode 100644 index 0000000000..aa62bd14c7 --- /dev/null +++ b/research/shrunk-birth-terminal/certificate.json @@ -0,0 +1,2524 @@ +{ + "actual_bit_saving": "1240189553/10000000000000", + "assembly": { + "absorption_gap": "51350955350972219636574114327365369448123005318656908856664201698261131/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000", + "constraints": { + "K_dominates_log": "28203699512803856630705756229332904653617608320033448605133911713260786682305862261131/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000", + "K_geometry": "187528016199700303669130893284245532604957286739213317694137738869/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000", + "a_below_b": "56907455433006738869/500000000000000000000000000000000000000000000000", + "a_positive": "56407455433006738868999943092544566993261131/500000000000000000000000000000000000000000000000", + "alpha_below_one": "499999500000499999500000250027953699762803606630893284245532604957286739213317694137738869/500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000", + "alpha_below_one_fourth": "124957569450855794090053910101585400855367676522073307704325996653786739213317694137738869/500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000", + "alpha_positive": "56407399025607713261536540537365447110966847533351142742872780713260786682305862261131/500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000", + "artificial_boundary": "14001791036782819432824377920275575186005677171202332185161413102487860217639953082413216607/2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000", + "b_below_one_over32": "15568592544566993261131/500000000000000000000000", + "beta_below_one": "999999999999999999999999/1000000000000000000000000", + "beta_positive": "1/1000000000000000000000000", + "c_below_one": "249971796272283496630565437584861183149510108303499943092544566993261131/250000000000000000000000000000000000000000000000000000000000000000000000", + "c_positive": "28203727716503369434562415138816850489891696500056907455433006738869/250000000000000000000000000000000000000000000000000000000000000000000000", + "cell_above_band": "499999500000499999499999749972046300237196393369106715754467395042713260786682305862261131/1000111814799051214426523573136982130419829146956853270776550955476000000000000000000000000", + "compact_leaf": "56657455433006738868999943092544566993261131/250000000000000000000000000000000000000000000000000000000000000000000000", + "compact_reservations": "1/4000000000000000000000000", + "delta_below_one_eighth": "999999999999999999999999/8000000000000000000000000", + "delta_positive": "1/8000000000000000000000000", + "epsilon_below_one": "28203699512803856630893284245532604957286739213317694137738869/250027953699762803606630893284245532604957286739213317694137738869", + "epsilon_positive": "249999750000249999750000000000000000000000000000000000000000000000/250027953699762803606630893284245532604957286739213317694137738869", + "g1_above_kappa": "12837801344731479849844430239564663423413902568985912017495473959/62506988424940700901657723321061383151239321684803329423534434717250000000000000000", + "g2_above_kappa": "6362884228738868999943092544566993261131/500000000000000000000000000000000000000000000000", + "g3_above_kappa": "51350955350972219636574114327365369448123005318656908856664201698261131/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000", + "g4_above_kappa": "6362884228738868999943092544566993261131/500000000000000000000000000000000000000000000000", + "g5_above_kappa": "82161678578327771276200746902320561664316371484223097698653339199861131/400044725919620485770609429254792852167931658782741308310620382190400000000000000000000000", + "g6_above_kappa": "410809393003453655432218161035175945303712277250262445346537472550261131/2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000", + "g7_above_kappa": "62492886575184298986180078023670096698605108554761333999879467851735912017495473959/62506988424940700901657723321061383151239321684803329423534434717250000000000000000", + "gamma_sublinear": "1/2000000000000000000000000", + "guard_width": "28203699512803856630893284245532604957286739213317694137738869/250027953699762803606630893284245532604957286739213317694137738869", + "lambda_above_internal": "56407455433006738868999943092544566993261131/500000000000000000000000000000000000000000000000000000000000000000000000", + "lambda_above_sigma": "113314910866013477737999943092544566993261131/500000000000000000000000000000000000000000000000000000000000000000000000", + "lambda_above_tau": "56407455433006738868999943092544566993261131/500000000000000000000000000000000000000000000000000000000000000000000000", + "lambda_prime_above_lambda": "56407455433006738868999943092544566993261131/500000000000000000000000000000000000000000000000000000000000000000000000", + "lambda_prime_below_one": "28203727716503369434499915138816850489891696500056907455433006738869/250000000000000000000000000000000000000000000000000000000000000000000000", + "literal_scalar_guard": "1936723974066543198917496885658826453564", + "phase_boundary": "45125919220486170609179226839152405128052151848024065087777233113260786682305862261131/400044725919620485770609429254792852167931658782741308310620382190400000000000000000000000", + "phase_leaf_above_bit": "1/1000000000000000000000000000000", + "phase_local": "225629596102430853046896246010561076854687282813257307569305994713260786682305862261131/2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000", + "prime_interval_packing": "28203699512803856630893284245532604957286739213317694137738869/250027953699762803606630893284245532604957286739213317694137738869", + "q_below_internal": "56407455433006738868999943092544566993261131/250000000000000000000000000000000000000000000000000000000000000000000000", + "q_below_leaf": "56657455433006738868999943092544566993261131/250000000000000000000000000000000000000000000000000000000000000000000000", + "q_below_reservations": "1/4000000000000000000000000", + "q_positive": "28203727716503369434499915138816850489891696500056907455433006738869/250000000000000000000000000000000000000000000000000000000000000000000000", + "record_suffix": "28203699512803856630893284245532604957286739213317694137738869/250027953699762803606630893284245532604957286739213317694137738869", + "row_product_gap": "6389/25", + "short_record_fallback": "124985771559469674632287261529685377995480559442484781152571541385040823194886876611665983695762005501567194399161/125013976849881401803315446642122766302478643369606658847068869434500000000000000000000000000000000000000000000000", + "small_field_exposure": "1/1000000000000000000000000" + }, + "finite_bridge": { + "bit_coarse": { + "W": 108516254, + "halving_degree": 367, + "m": 529, + "maxchild": 528, + "wire_bits": 27 + }, + "complex": { + 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'-28203699512803805279500377303413505275896650061379754949523635769612716700410026261131/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000'}", + "ordinary_leaf_bridge": { + "W": 188181929, + "halving_degree": 9, + "m": 575, + "maxchild": 529, + "wire_bits": 28 + }, + "ordinary_leaf_saving": "384599/10000000000", + "profile": { + "L": 2234496, + "N": 4096576, + "R": 26216, + "W": 114315520, + "child_multiplicities": { + "1": 435042608, + "10": 7735728, + "11": 6658960, + "12": 33578160, + "13": 13184336, + "14": 1821600, + "15": 3238400, + "16": 631488, + "17": 404800, + "18": 202400, + "19": 311696, + "2": 266771296, + "20": 550528, + "21": 1222496, + "22": 64768, + "23": 8383408, + "3": 29060592, + "4": 60639040, + "5": 26643936, + "529": 8193152, + "552": 97071040, + "554": 3456992, + "556": 1481568, + "558": 2384272, + "560": 445280, + "562": 48576, + "571": 740784, + "572": 101200, + "573": 28336, + "574": 364320, + "6": 15333824, + "7": 11743248, + "8": 22069696, + "9": 3938704 + }, + "deficit": 1862080, + "h": 24, + "m": 576, + "maxchild": 574, + "total_rank": 65843877440, + "v": 2024 + }, + "raw_discovery_metadata_in_certificate": false, + "scope": "Exact arithmetic on the supplied complete physical profile. Physical source/dirty/reflection identities, paid positional layout, all-size interfaces and fixed-tape analytic transfer remain separately verified or inherited obligations. Grid optimality is only within this fixed-profile balanced transfer family.", + "source_sha256": { + "REFERENCE_PINS.json": "fbf75766c9112483e43e9cfca5e339044fe80f1d41481c1d7146080ed4970e6f", + "balanced_stopped.py": "03f5f012ab4eb306320ab8a209c2041addd75b84aa43f45ab80595c8989ce781", + "certificate.py": "30f143d6b2e05dc284b773fafbe831080207ef070d07f222cf2e5b87c9746142", + "inputs/bit-profile.json": "7293f330518b78650bd86d76b93681e43f3a55541cdb8110993714148a4b4a6a", + "interval_moment.py": "9d3d1d28bfb3375958995205179b171fb65c70a3792cf9f7a21ef5ee54f5460b", + "references/pr100/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0", + "references/pr100/refine.py": "e0488c919e76850313ff93d7da704a7fcc14a316eee2cac81e2b8dff9c145b5d", + "references/pr104/balanced_assembly.py": "4d27575dcad2b45a281a34054d311409ecd954f373c0c3a62c29bcc843f06a86", + "references/pr104/copied-centers-network.json": "7dbd675e42e22ac076280360f8750031851564bb7a56079e66236fee5d0a6cdf", + "references/pr104/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d", + "validate.py": "f61d6d19fcfe1e3974a16da3c4cc5c9ce43066a0735416d7a3c827a1083d096c" + } +} diff --git a/research/shrunk-birth-terminal/construction/compose_terminal.py b/research/shrunk-birth-terminal/construction/compose_terminal.py new file mode 100644 index 0000000000..a3b0826651 --- /dev/null +++ b/research/shrunk-birth-terminal/construction/compose_terminal.py @@ -0,0 +1,328 @@ +#!/usr/bin/env python3 +"""Compose disjoint terminal elimination with an exact shrunk/birth word. + +Original terminal-elision identity: SovereignSteak, PR122. +Shrunk frames: Joel Pulikkan, PR125. Birth reuse: James Chang, PR124. +PR117 DAG: eumemic; deferred compiler: Avi Eisenberg and Rohan Arun. +This explicit composition, complete word/profile checks and all-column +response audit were prepared with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +from functools import lru_cache +from hashlib import sha256 +import argparse, gzip, json, pickle, resource, subprocess, sys, time + +assert not sys.flags.optimize, 'Assertions must remain enabled' +W=Path(__file__).resolve().parent +p=argparse.ArgumentParser(description=__doc__) +p.add_argument('--frames',type=Path,required=True) +p.add_argument('--matches',type=Path,required=True) +p.add_argument('--readouts',type=Path,required=True) +p.add_argument('--scalar-bill',type=Path,required=True) +p.add_argument('--out',type=Path,required=True) +p.add_argument('--terminal-roles',type=Path,help='JSON list of exact terminal IDs; validated after supplied real birth matches.') +a=p.parse_args();start=time.monotonic();O=a.out.resolve();O.mkdir(parents=True,exist_ok=False) +source_directory=O/'construction-sources';source_directory.mkdir() +source_bytes={q.name:q.read_bytes() for q in [Path(__file__),W/'terminal_inventory.py']} +for name,data in source_bytes.items():(source_directory/name).write_bytes(data) +inputs=O/'inputs';inputs.mkdir();pins={} +for source,name in [(a.frames,'FRAMES.pkl'),(a.matches,'BIRTH_MATCHES.json.gz'),(a.readouts,'READOUTS.pkl'),(a.scalar_bill,'READOUT_COST.json')]: + data=source.read_bytes();(inputs/name).write_bytes(data);assert source.read_bytes()==data + pins[name]={'source_path':str(source.resolve()),'sha256':sha256(data).hexdigest(),'bytes':len(data)} +selection_args=[] +if a.terminal_roles: + data=a.terminal_roles.read_bytes();(inputs/'TERMINAL_ROLES.json').write_bytes(data);assert a.terminal_roles.read_bytes()==data + pins['TERMINAL_ROLES.json']={'source_path':str(a.terminal_roles.resolve()),'sha256':sha256(data).hexdigest(),'bytes':len(data)} + selection_args=['--terminal-roles',str(inputs/'TERMINAL_ROLES.json')] +subprocess.run([sys.executable,str(source_directory/'terminal_inventory.py'),'--frames',str(inputs/'FRAMES.pkl'),'--matches',str(inputs/'BIRTH_MATCHES.json.gz'),'--readouts',str(inputs/'READOUTS.pkl'),'--out',str(O/'inventory.json'),*selection_args],check=True,stdout=subprocess.DEVNULL) +inventory=json.loads((O/'inventory.json').read_text()) +g=pickle.loads((inputs/'FRAMES.pkl').read_bytes());readouts=pickle.loads((inputs/'READOUTS.pkl').read_bytes()) +choice=json.loads(gzip.decompress((inputs/'BIRTH_MATCHES.json.gz').read_bytes())) +bill=json.loads((inputs/'READOUT_COST.json').read_text()) +R=len(g['first']);v=g['v'];h=g['h'];m=h*h;N=v*v +merge={r['recipient']:r['donor'] for r in choice['pairs']} +removed={r['role'] for r in inventory['selected']};selected={r['role']:r for r in inventory['selected']} +assert removed and not removed & (set(merge)|set(merge.values())) +live=set(range(R))-set(merge)-removed +assert len(live)==choice['R']-len(removed) +physical=lambda s:2*v+merge.get(s,s) + +frames=[()];ids={():0} +def fid(F): + F=tuple(F) + if F not in ids:ids[F]=len(frames);frames.append(F) + return ids[F] +def basis(rows): + piv={} + for x in rows: + for q in sorted(piv,reverse=True): + if x>>q&1:x^=piv[q] + if x: + q=x.bit_length()-1 + for r in piv: + if piv[r]>>q&1:piv[r]^=x + piv[q]=x + return tuple(piv[q] for q in sorted(piv,reverse=True)) +FULL=fid(tuple(1<>j&1:x|=1<<(r.bit_length()-1) + out.append(x) + return fid(basis(out)) +@lru_cache(None) +def nested(i,j): + for x in frames[i]: + for r in frames[j]: + if x>>(r.bit_length()-1)&1:x^=r + if x:return False + return True +@lru_cache(None) +def nondeg(i): + A=frames[i] + return len(basis(sum(((x&y).bit_count()&1)<=2*v and d-2*v in live + e=('g',d,s,sign,F);word.append(e) + if remember:forward_workspace.append(e) +def oldread(s,F): + mask=ALL if g['reach_all'][s] else g['reach'][s] + if s in removed: + assert mask==1<0 + hist[r]+=1;current[s]=F;incidences+=1 + if s<2*v: + bank=s//v;counts[bank][old]-=1 + if not counts[bank][old]:del counts[bank][old] + counts[bank][F]+=1 + def targets(bank,mask,F): + assert bank in (0,v) and mask>=0 and not(mask&~ALL) + if len(counts[bank//v])==1 and counts[bank//v].get(F)==v:return + while mask: + b=mask&-mask;mask-=b;promote(bank+b.bit_length()-1,F) + for e in events: + digest.update(repr(e).encode()) + if e[0]=='g': + _,d,s,c,F=e;assert c in (-1,1);promote(d,F);promote(s,F) + elif e[0]=='d': + _,d,s,c,F,idx,role=e;assert c in (-21,21);promote(d,F);promote(s,F) + elif e[0]=='r': + _,s,bank,mask,sign,F,key=e;promote(s,F);targets(bank,mask,F) + elif e[0]=='f': + _,bank,mask,F,key=e;targets(bank,mask,F) + else: + _,s,bank,mask,sign,F,T,key=e;promote(s,F);targets(bank,mask,T) + assert (F==FULL and T==0) or nested(F,T) or nested(T,F) + rank=abs(len(frames[F])-len(frames[T]));assert rank==h-1;hist[rank]+=1;copies+=1 + for s in active:promote(s,end[s]) + assert current==end + return {'histogram':dict(hist),'copies':copies,'transitions':incidences,'word_sha256':digest.hexdigest()} + +forward=scan(word,initial,finish) +def swap(s):return s+v if s=sum(before_sorted[:k]) for k in range(1,5)) + assert before_sorted!=after_sorted + for width in before: + if width:delta[width]-=2*v + # The width-m term is only the padding used to compare changing W. + if F0>M:delta[F0-M]+=2*v + packets.append({'role':row['role'],'target':row['target'],'old':before,'new_with_dummy_m':after}) +expected=Counter(oldH) +expected.update(delta);expected=Counter({r:n for r,n in expected.items() if n}) +assert all(n>=0 for n in expected.values()) and H==expected,('Full profile != exact complete packet sum',H-expected,expected-H) +newR=len(live);newW=2*v*v+2*v*newR;rank=sum(r*n for r,n in H.items()) +assert m*newW-rank==choice['deficit']==g['base_profile']['deficit'] +hinges={k:sum(min(r,k)*n for r,n in H.items())+2*v*len(removed)*min(m,k)-sum(min(r,k)*n for r,n in oldH.items()) for k in range(1,m+1)} +assert all(x<=0 for x in hinges.values()) and min(hinges.values())<0 + +def plus(a,b): + out=[];carry=0 + for i in range(max(len(a),len(b))): + x=a[i] if i>i&1 else 0 for i in range(n.bit_length())) + +def responses(events,inputbank,outputbank,expected_sign): + P,M=[()]*R,[()]*R;XP,XM=[()]*v,[()]*v + def accumulate(aux,positive,negative): + assert aux>=2*v and aux-2*v in live + r=aux-2*v;P[r],M[r]=plus(P[r],positive),plus(M[r],negative) + for e in reversed(events): + kind=e[0] + if kind=='f':continue + if kind in ('r','c'): + aux,bank,sign=e[1],e[2],e[4];assert bank==outputbank + key=e[-1] + if key[0]=='old':s=key[1];seed=False + elif key[0]=='side':s=key[2];seed=True + else:s=next(s for s in g['center_roles'] if g['terminal'][s]==len(g['roots'])-h+key[1]);seed=True + aa=readouts['terminal_positive' if seed else 'positive'][s] + bb=readouts['terminal_negative' if seed else 'negative'][s] + if sign<0:aa,bb=bb,aa + accumulate(aux,aa,bb) + elif kind=='d': + _,dst,src,num,F,idx,role=e + assert outputbank<=dst=2*v + aa,bb=P[dst-2*v],M[dst-2*v] + if sign<0:aa,bb=bb,aa + if src>=2*v:accumulate(src,aa,bb) + else: + assert inputbank<=src0:source_ok=all(aa==plus(bb,scaled(1<=bill['global_scalar_group_upper'] +profile=dict(g['base_profile']);profile.update(R=newR,W=newW,total_rank=rank,maxchild=max(H),child_multiplicities=dict(sorted(H.items())),pre_terminal_physical_roles=choice['R'],virtual_roles=R,birth_reuses=len(merge),terminal_eliminations=len(removed),terminal_direct_updates=len(direct_origins),deferred_roles=len(g['placed'])-len(removed),role_count_scope='Explicit physical birth-reused and terminal-elided word; DAG role formula is the pre-composition virtual count.',replay={'method':'Exact signed bit-plane all-column responses over Q, both orientations','source_columns':v,'dirty_columns':newR,'target_columns':v,'forward_signed_identity':1,'reflected_signed_identity':-1,'scratch_restored':True}) +dd=Counter({int(k):n for k,n in profile['deferred_dims'].items()}) +for row in inventory['selected']:dd[row['sigma']]-=1 +profile['deferred_dims']=dict(sorted((k,n) for k,n in dd.items() if n)) +scalar_bill={**{k:value for k,value in bill.items() if k not in {'rss_KiB','rss_bytes','seconds'}},'status':'PASS conservative scalar upper bound for new terminal composition','inherited_local_scalar_upper':bill['local_scalar_upper'],'terminal_direct_updates':len(direct_origins),'terminal_extra_scalar_charge':extra_scalar,'local_scalar_upper':newlocal,'global_scalar_group_upper':newG,'terminal_charge_rule':'Keep the entire inherited scalar bill and add 29 groups per direct output update: 21 same-frame shears of coefficient +/-1/42, plus eight conservative bookkeeping groups. No new role, source copy or frame incidence is introduced; denominator42 and odd21 grid are unchanged.','expansion':'Each numerator n/42 is |n| same-frame shears of coefficient sign(n)/42, with no new roles, source copies or frame transitions. Reverse all workspace/source gates chronologically. The retained eight-scan allowance, factor16 and explicit endpoint groups conservatively bound scalar bookkeeping/wrappers. Direct terminal updates use the same expansion, with eight additional bookkeeping groups per update.','original_bill_sha256':pins['READOUT_COST.json']['sha256']} +# The inherited bill is a conservative charge for the full virtual graph. +# Its descriptive deferred support count may belong to another placement. +def old_readout_support(role): + positive=readouts['positive'][role];negative=readouts['negative'][role];mask=0 + for i in range(max(len(positive),len(negative))): + mask|=(positive[i] if i>(r.bit_length()-1)&1:x^=r + if x:return False + return True + +incoming=defaultdict(list);outgoing=Counter() +for i,(op,s,t,x) in enumerate(g['ops']): + if op==1:dst,src=s,t + elif op==2:dst,src=t,s + else:continue + incoming[dst].append((i,src,x));outgoing[src]+=1 + +target_front=[() for _ in range(v)] +for s,F in sorted(g['placed'].items(),key=lambda z:(len(z[1]),z[0])): + targets=g['reach'][s] + while targets: + b=targets&-targets;targets-=b;t=b.bit_length()-1 + assert contains(target_front[t],F) + target_front[t]=F + +def scaled(mask,n):return tuple(mask if n>>i&1 else 0 for i in range(n.bit_length())) + +blocked=Counter();eligible=[] +for s,j in sorted(g['terminal'].items()): + if j>=len(g['roots'])-h:blocked['center_root']+=1;continue + if outgoing[s]:blocked['controls_auxiliary']+=1;continue + if s in merge and not a.include_birth_recipients:blocked['physical_slot_shared_as_birth_recipient']+=1;continue + assert s not in set(merge.values()) + if s not in g['placed']:blocked['not_deferred']+=1;continue + if g['first'][s]<=v:blocked['source_injection_excluded_from_this_bounded_pass']+=1;continue + if not incoming[s]:blocked['no_incoming_update']+=1;continue + if any(i in g['phase'] for i,_,_ in incoming[s]):blocked['early_update']+=1;continue + assert s not in g['touched'] + t=g['targets'][j];sign=1 if j0 else ()) + assert readouts['negative'][s]==(expected if sign<0 else ()) + F0=g['U'][incoming[s][0][2]];M=target_front[t];sigma=g['placed'][s] + if not contains(M,F0):blocked['target_front_past_first_update']+=1;continue + fs=[M]+[g['U'][x] for _,_,x in incoming[s]] + assert all(contains(a,b) for a,b in zip(fs,fs[1:])),s + assert contains(sigma,M) and len(fs[-1])<=h-1 + if a.include_birth_recipients and not len(sigma)==len(M)==len(F0):blocked['unequal_packet_dimensions_excluded_from_joint_options']+=1;continue + eligible.append({'role':s,'target':t,'root_index':j,'coefficient_numerator':21*sign,'sigma':len(sigma),'M':len(M),'F0':len(F0),'incoming_operations':[i for i,_,_ in incoming[s]],'incoming_count':len(incoming[s]),'frames':[list(F) for F in fs],'current_birth_donor':merge.get(s),'terminal_local_scalar_charge':29*len(incoming[s]),'packet_replication':2*v,'old_packet':[m-h+len(sigma),1,len(F0)-len(sigma),h-1-len(M)],'padded_new_packet':[m,len(F0)-len(M),0,0]}) + +# One terminal per target gives disjoint target-front packets; this avoids +# treating individually legal but interleaved output paths as simultaneous. +bytarget=defaultdict(list) +for row in eligible:bytarget[row['target']].append(row) +selected=[min(group,key=lambda x:x['role']) for _,group in sorted(bytarget.items())] +if a.terminal_roles: + requested=json.loads(a.terminal_roles.read_text()) + assert isinstance(requested,list) and all(type(s) is int for s in requested), 'Selection must be a JSON list of integer role IDs' + assert len(requested)==len(set(requested)), 'Duplicate terminal role ID' + rows={row['role']:row for row in eligible} + assert set(requested)<=rows.keys(), f'Ineligible requested terminal roles: {sorted(set(requested)-rows.keys())}' + selected=[rows[s] for s in sorted(requested)] + assert len({row['target'] for row in selected})==len(selected), 'Selected terminals must have distinct targets' + assert not set(requested)&(set(merge)|set(merge.values())), 'Selected terminals must have no birth aliases' +record={'status':'PASS exact local eligibility and disjoint-target selection on new composition inputs','base_virtual_roles':R,'base_physical_roles':choice['R'],'birth_merges_preserved':len(merge),'eligible_unshared_terminal_roles':len(eligible),'selected_terminal_roles':len(selected),'selected_targets':len(bytarget),'blocked':dict(blocked),'selection_rule':'Lowest eligible role id per target; no frame, deferral or birth matching changes.','selected':selected,'eligible':eligible,'expected_physical_roles':choice['R']-len(selected),'input_sha256':{str(p):sha256(p.read_bytes()).hexdigest() for p in [a.frames,a.readouts,a.matches]}} +if a.terminal_roles: + record.update(selection_rule='Exact requested role-ID subset, validated against ordinary unshared eligibility and distinct targets',selected_targets=len(selected),selection_sha256=sha256(a.terminal_roles.read_bytes()).hexdigest()) +if a.include_birth_recipients: + record.update(status='PASS virtual eligibility options for joint birth/terminal optimization; not a legal simultaneous elimination selection',joint_optimization_options=True,eligible_virtual_terminal_roles=len(eligible),currently_birth_matched_options=sum(row['current_birth_donor'] is not None for row in eligible),selection_rule='All eligible options retained in eligible; selected is only the lowest role per target and may conflict with existing births. Choose at most one option per target and never choose both a terminal edge and a birth donor edge for the same role. After changing the birth matching, rerun the default inventory and full builder.') + record.pop('eligible_unshared_terminal_roles');record.pop('expected_physical_roles') +a.out.parent.mkdir(parents=True,exist_ok=True) +a.out.write_text(json.dumps(record,indent=2,sort_keys=True)+'\n') +print(json.dumps({k:v for k,v in record.items() if k not in ['selected','eligible','input_sha256']},indent=2)) diff --git a/research/shrunk-birth-terminal/lean/ShrunkBirthTerminal.lean b/research/shrunk-birth-terminal/lean/ShrunkBirthTerminal.lean new file mode 100644 index 0000000000..985b71d41e --- /dev/null +++ b/research/shrunk-birth-terminal/lean/ShrunkBirthTerminal.lean @@ -0,0 +1,1248 @@ +import Mathlib.Tactic.NormNum +import Mathlib.Data.Nat.Choose.Basic + +/-! +Exact arithmetic companion for the shrunk-frame / birth-reuse / terminal-elision +composition. Prepared with OpenAI assistance. Upstream construction and analytic +credits are retained in the accompanying proof and source provenance. + +Scope: supplied physical-count arrays, all 47 parameter slacks, seven margins, +three row stocks, scalar guards and independent degree-eight moment arithmetic. +The physical-array derivation, real logarithm / exponential enclosure validity, +and all-size framed-word, stopped-product, tape, prime and recovery hypotheses +remain external. This is not an unconditional integer-multiplication theorem. +No sorry, native_decide or additional axioms are introduced. +-/ +namespace KappaCheck.ShrunkBirthTerminal +set_option maxRecDepth 20000 +set_option maxHeartbeats 8000000 + +-- Source SHA256 89b115978ab95d8e69e58472cde14a588157a3b3a8c577034c39ca0309eab34d: work/r12-audit/canonical-joint-expansion/joint-expansion/certificate.json +-- Source SHA256 3203dcb2709c3c8f1513c9ff31faafe9903f7ba14cdd7bbe1aaa38c9edbfcf43: work/r12-terminal/joint-expansion/READOUT_COST.json +-- Source SHA256 457287cf9986574cef50235644af77c893b3513e7a0872827b1cce352f4b62d5: work/r12-terminal/joint-expansion/physical-audit.json +-- Source SHA256 11dfe85123d23c17b4e1f4309b7c5fdfdac55faef7563881f2f3db5b2dfae82e: work/r12-terminal/joint-expansion/word.json.gz +def h : ℕ := 24 +def m : ℕ := h*h +def v : ℕ := Nat.choose h 3 +def n : ℕ := v*v +def virtualRoles : ℕ := 28705 +def births : ℕ := 2108 +def terminals : ℕ := 381 +def roles : ℕ := virtualRoles-births-terminals +def width : ℕ := 2*n+2*v*roles +def forwardHistogram : List (ℕ × ℕ) := [(1, 106459), (2, 65902), (3, 7179), (4, 14980), (5, 6582), (6, 3788), (7, 2901), (8, 5452), (9, 973), (10, 1911), (11, 1645), (12, 8295), (13, 3257), (14, 450), (15, 800), (16, 156), (17, 100), (18, 50), (19, 77), (20, 136), (21, 302), (22, 16), (23, 2071)] +def initialDimensionHistogram : List (ℕ × ℕ) := [(0, 23980), (2, 854), (4, 366), (6, 589), (8, 110), (10, 12), (19, 183), (20, 25), (21, 7), (22, 90)] +def counts : List (ℕ × ℕ) := + (forwardHistogram.map fun p => (p.1, 2*v*p.2)) ++ + (initialDimensionHistogram.map fun p => (m-h+p.1, 2*v*p.2)) ++ + [((h-1)^2, 2*n), (1, n)] +def count (t : ℕ) : ℕ := (counts.map fun p => if p.1=t then p.2 else 0).sum +def mass : ℕ := (counts.map fun p => p.1*p.2).sum + +theorem network_counts : h = 24 ∧ m = 576 ∧ v = 2024 ∧ n = 4096576 ∧ roles = 26216 ∧ width = 114315520 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose] + +theorem initial_dimension_count : (initialDimensionHistogram.map Prod.snd).sum = roles := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem rank_mass : mass = 65843877440 ∧ m*width-mass = 1862080 ∧ n-2*v*h*(h-1) = 1862080 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_1 : count 1 = 435042608 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_2 : count 2 = 266771296 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_3 : count 3 = 29060592 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_4 : count 4 = 60639040 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_5 : count 5 = 26643936 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_6 : count 6 = 15333824 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_7 : count 7 = 11743248 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_8 : count 8 = 22069696 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_9 : count 9 = 3938704 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_10 : count 10 = 7735728 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_11 : count 11 = 6658960 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_12 : count 12 = 33578160 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_13 : count 13 = 13184336 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_14 : count 14 = 1821600 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_15 : count 15 = 3238400 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_16 : count 16 = 631488 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_17 : count 17 = 404800 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_18 : count 18 = 202400 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_19 : count 19 = 311696 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_20 : count 20 = 550528 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_21 : count 21 = 1222496 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_22 : count 22 = 64768 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_23 : count 23 = 8383408 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_529 : count 529 = 8193152 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_552 : count 552 = 97071040 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_554 : count 554 = 3456992 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_556 : count 556 = 1481568 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_558 : count 558 = 2384272 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_560 : count 560 = 445280 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_562 : count 562 = 48576 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_571 : count 571 = 740784 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_572 : count 572 = 101200 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_573 : count 573 = 28336 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem count_574 : count 574 = 364320 := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +def childSizes : List ℕ := [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 529, 552, 554, 556, 558, 560, 562, 571, 572, 573, 574] +theorem complete_child_support : ∀ p ∈ counts, p.2 ≠ 0 → p.1 ∈ childSizes := by + norm_num [h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram, childSizes] + +theorem strict_child_contraction : ∀ t ∈ childSizes, 0 < t ∧ t < m := by + norm_num [childSizes, h, m] + +def a : ℚ := (56407455433006738868999943092544566993261131 / 500000000000000000000000000000000000000000000000) +def b : ℚ := (56407455433006738869 / 500000000000000000000000) +def kappa : ℚ := (28200546274389 / 250000000000000000) +def eta : ℚ := (1 / 1000000000000000000000000) +def beta : ℚ := (1 / 1000000000000000000000000) +def backoff : ℚ := (1 / 1000000000000000000000000000000) +def actualBitSaving : ℚ := (1240189553 / 10000000000000) +def tau : ℚ := 1-a +def sigma : ℚ := 1-b +def qParam : ℚ := a*(1-2*eta) +def lp : ℚ := 1-qParam +def c : ℚ := qParam+eta/4 +def epsilon : ℚ := (1-eta)/(1+qParam) +def lam : ℚ := (tau+lp)/2 +def g : ℚ := epsilon*qParam +def r : ℚ := (g+1-epsilon)/2 +def delta : ℚ := eta/8 +def internal : ℚ := tau+(1-beta)*max (sigma-tau) 0 +def leaf : ℚ := sigma+beta*(1-sigma) + +def scalar : ℕ := 3116113870848 +def guardE : ℕ := 64*(width+m+scalar+1)^3 +def guardB : ℕ := mass+guardE +def literal : ℕ := 2*scalar*width^2+8*mass+4*width+4+32*m +def guardC : ℕ := 32*m*guardB^2 +def literalGap : ℚ := (guardE : ℚ)-literal +def rowCoefficient : ℕ := 367*27+200*27+9*28 +def rowGap : ℚ := 32000-(51/25)*rowCoefficient +def margins : List ℚ := [1-epsilon,a,g,a,min (1-epsilon-delta) (r-delta),1-epsilon-delta,epsilon] + +theorem slack_a_positive : (a) = ((56407455433006738868999943092544566993261131 / 500000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (a) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_a_below_b : (b-a) = ((56907455433006738869 / 500000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (b-a) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_b_below_one_over32 : (1/32-b) = ((15568592544566993261131 / 500000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1/32-b) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_beta_positive : (beta) = ((1 / 1000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (beta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_beta_below_one : (1-beta) = ((999999999999999999999999 / 1000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-beta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_phase_leaf_above_bit : ((1-beta)*b-a) = ((1 / 1000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((1-beta)*b-a) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_q_positive : (qParam) = ((28203727716503369434499915138816850489891696500056907455433006738869 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (qParam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_q_below_internal : (1-internal-qParam) = ((56407455433006738868999943092544566993261131 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-internal-qParam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_q_below_leaf : (1-leaf-qParam) = ((56657455433006738868999943092544566993261131 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-leaf-qParam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_c_positive : (c) = ((28203727716503369434562415138816850489891696500056907455433006738869 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (c) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_c_below_one : (1-c) = ((249971796272283496630565437584861183149510108303499943092544566993261131 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-c) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_q_below_reservations : (c-qParam) = ((1 / 4000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (c-qParam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_lambda_above_tau : (lam-tau) = ((56407455433006738868999943092544566993261131 / 500000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lam-tau) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_lambda_above_sigma : (lam-sigma) = ((113314910866013477737999943092544566993261131 / 500000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lam-sigma) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_lambda_above_internal : (lam-internal) = ((56407455433006738868999943092544566993261131 / 500000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lam-internal) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_lambda_prime_above_lambda : (lp-lam) = ((56407455433006738868999943092544566993261131 / 500000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lp-lam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_compact_leaf : (lp-leaf) = ((56657455433006738868999943092544566993261131 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lp-leaf) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_compact_reservations : (lp-(1-c)) = ((1 / 4000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (lp-(1-c)) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_lambda_prime_below_one : (qParam) = ((28203727716503369434499915138816850489891696500056907455433006738869 / 250000000000000000000000000000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (qParam) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_epsilon_positive : (epsilon) = ((249999750000249999750000000000000000000000000000000000000000000000 / 250027953699762803606630893284245532604957286739213317694137738869) : ℚ) ∧ (0 : ℚ) < (epsilon) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_epsilon_below_one : (1-epsilon) = ((28203699512803856630893284245532604957286739213317694137738869 / 250027953699762803606630893284245532604957286739213317694137738869) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_guard_width : (1-epsilon) = ((28203699512803856630893284245532604957286739213317694137738869 / 250027953699762803606630893284245532604957286739213317694137738869) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_K_geometry : (1-epsilon*(1+c)) = ((187528016199700303669130893284245532604957286739213317694137738869 / 250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon*(1+c)) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_K_dominates_log : (epsilon*c) = ((28203699512803856630705756229332904653617608320033448605133911713260786682305862261131 / 250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (epsilon*c) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_record_suffix : (1-epsilon) = ((28203699512803856630893284245532604957286739213317694137738869 / 250027953699762803606630893284245532604957286739213317694137738869) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_phase_local : (1-epsilon-delta) = ((225629596102430853046896246010561076854687282813257307569305994713260786682305862261131 / 2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon-delta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_phase_boundary : (r-delta) = ((45125919220486170609179226839152405128052151848024065087777233113260786682305862261131 / 400044725919620485770609429254792852167931658782741308310620382190400000000000000000000000) : ℚ) ∧ (0 : ℚ) < (r-delta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_gamma_sublinear : (1-epsilon-r) = ((1 / 2000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon-r) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_cell_above_band : (epsilon-(1-r)/2) = ((499999500000499999499999749972046300237196393369106715754467395042713260786682305862261131 / 1000111814799051214426523573136982130419829146956853270776550955476000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (epsilon-(1-r)/2) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_prime_interval_packing : (1-epsilon) = ((28203699512803856630893284245532604957286739213317694137738869 / 250027953699762803606630893284245532604957286739213317694137738869) : ℚ) ∧ (0 : ℚ) < (1-epsilon) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_alpha_positive : (r) = ((56407399025607713261536540537365447110966847533351142742872780713260786682305862261131 / 500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (r) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_alpha_below_one : (1-r) = ((499999500000499999500000250027953699762803606630893284245532604957286739213317694137738869 / 500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-r) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_alpha_below_one_fourth : (1/4-r) = ((124957569450855794090053910101585400855367676522073307704325996653786739213317694137738869 / 500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1/4-r) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_delta_positive : (delta) = ((1 / 8000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (delta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_delta_below_one_eighth : (1/8-delta) = ((999999999999999999999999 / 8000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1/8-delta) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_short_record_fallback : (epsilon-a) = ((124985771559469674632287261529685377995480559442484781152571541385040823194886876611665983695762005501567194399161 / 125013976849881401803315446642122766302478643369606658847068869434500000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (epsilon-a) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_small_field_exposure : (1-epsilon-g) = ((1 / 1000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (1-epsilon-g) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_artificial_boundary : (8-epsilon+r-delta-g) = ((14001791036782819432824377920275575186005677171202332185161413102487860217639953082413216607 / 2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000) : ℚ) ∧ (0 : ℚ) < (8-epsilon+r-delta-g) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_literal_scalar_guard : (literalGap) = (1936723974066543198917496885658826453564 : ℚ) ∧ (0 : ℚ) < (literalGap) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_row_product_gap : (rowGap) = ((6389 / 25) : ℚ) ∧ (0 : ℚ) < (rowGap) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g1_above_kappa : ((1-epsilon)-kappa) = ((12837801344731479849844430239564663423413902568985912017495473959 / 62506988424940700901657723321061383151239321684803329423534434717250000000000000000) : ℚ) ∧ (0 : ℚ) < ((1-epsilon)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g2_above_kappa : ((a)-kappa) = ((6362884228738868999943092544566993261131 / 500000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((a)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g3_above_kappa : ((g)-kappa) = ((51350955350972219636574114327365369448123005318656908856664201698261131 / 250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((g)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g4_above_kappa : ((a)-kappa) = ((6362884228738868999943092544566993261131 / 500000000000000000000000000000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((a)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g5_above_kappa : ((min (1-epsilon-delta) (r-delta))-kappa) = ((82161678578327771276200746902320561664316371484223097698653339199861131 / 400044725919620485770609429254792852167931658782741308310620382190400000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((min (1-epsilon-delta) (r-delta))-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g6_above_kappa : ((1-epsilon-delta)-kappa) = ((410809393003453655432218161035175945303712277250262445346537472550261131 / 2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000) : ℚ) ∧ (0 : ℚ) < ((1-epsilon-delta)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem slack_g7_above_kappa : ((epsilon)-kappa) = ((62492886575184298986180078023670096698605108554761333999879467851735912017495473959 / 62506988424940700901657723321061383151239321684803329423534434717250000000000000000) : ℚ) ∧ (0 : ℚ) < ((epsilon)-kappa) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem margins_strict : ∀ x ∈ margins, kappa < x := by + norm_num [margins, a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem balanced_identities : 1-epsilon-g = eta ∧ 1-epsilon-r = eta/2 ∧ 1-epsilon*(1+c) = eta-epsilon*eta/4 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem stopped_parameter_choice : a = min actualBitSaving ((1-beta)*b-backoff) ∧ 0 < eta ∧ eta < 1/2 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem controlling_margin : kappa < g ∧ g < kappa+1/1000000000000000000 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem fixed_profile_grid_exclusion : (b+1/1000000000000000000000000)/(1+b+1/1000000000000000000000000) < kappa+1/1000000000000000000 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem gain_over_pinned_bounds : kappa > (384569/10000000000 : ℚ) ∧ kappa > (52789616935221/1000000000000000000 : ℚ) ∧ kappa > (111192082577/1000000000000000 : ℚ) ∧ (1/2^14 : ℚ) < kappa ∧ kappa < (1/2^13 : ℚ) := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem stock_bit_coarse : (529:ℕ)^367 > 2*528^367 ∧ (529:ℕ)^366 ≤ 2*528^366 ∧ (2:ℕ)^26 ≤ 108516254 ∧ 108516254 < (2:ℕ)^27 := by + norm_num [] + +theorem stock_complex : (576:ℕ)^200 > 2*574^200 ∧ (576:ℕ)^199 ≤ 2*574^199 ∧ (2:ℕ)^26 ≤ 114315520 ∧ 114315520 < (2:ℕ)^27 := by + norm_num [] + +theorem stock_ordinary_leaf : (575:ℕ)^9 > 2*529^9 ∧ (575:ℕ)^8 ≤ 2*529^8 ∧ (2:ℕ)^27 ≤ 188181929 ∧ 188181929 < (2:ℕ)^28 := by + norm_num [] + +theorem row_stock : rowCoefficient = 15561 ∧ rowGap = (6389/25 : ℚ) ∧ 4*(32000:ℕ) = 128000 := by + norm_num [rowCoefficient, rowGap] + +theorem semantic_constants : guardE = 1936723974147986188574068436730358952000 ∧ guardB = 1936723974147986188574068436796202829440 ∧ guardC = 69136584229593344553734547662349298866110568132764137982571664415937240220513075200 ∧ literal = 81442989656571551071532498436 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +theorem finite_bridge : guardE > literal ∧ 2*guardB*(m-574) ≥ mass+guardE ∧ guardC > 2*guardB+18 := by + norm_num [a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, mass, count, counts, forwardHistogram, initialDimensionHistogram] + +-- The analytic meaning of supplied log intervals is external. These +-- statements prove exact rational Taylor inequalities and complete paid sums. +def taylor8 (x : ℚ) : ℚ := 1+x+x^2/2+x^3/6+x^4/24+x^5/120+x^6/720+x^7/5040+x^8/40320 +def expUpper (x : ℚ) : ℚ := taylor8 x+x^9/362880/(1-x/10) + +def accepted_1 : ℚ := (10007173208708459192443081796658477476273 / 10000000000000000000000000000000000000000) +theorem accepted_interval_1 : (0 : ℚ) ≤ b*(3178053830347945619646941601297 / 500000000000000000000000000000) ∧ b*(3178053830347945619646941601297 / 500000000000000000000000000000) ≤ b*(1271221532139178247858776640519 / 200000000000000000000000000000) ∧ b*(1271221532139178247858776640519 / 200000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_1 : expUpper (b*(1271221532139178247858776640519 / 200000000000000000000000000000)) ≤ accepted_1 := by + norm_num [expUpper, taylor8, b, accepted_1] + +def accepted_2 : ℚ := (2001278141000794096250171811675050044519 / 2000000000000000000000000000000000000000) +theorem accepted_interval_2 : (0 : ℚ) ≤ b*(1132592096027189185975330216227 / 200000000000000000000000000000) ∧ b*(1132592096027189185975330216227 / 200000000000000000000000000000) ≤ b*(353935030008496620617290692571 / 62500000000000000000000000000) ∧ b*(353935030008496620617290692571 / 62500000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_2 : expUpper (b*(353935030008496620617290692571 / 62500000000000000000000000000)) ≤ accepted_2 := by + norm_num [expUpper, taylor8, b, accepted_2] + +def accepted_3 : ℚ := (5002966499022595054406188132806194434321 / 5000000000000000000000000000000000000000) +theorem accepted_interval_3 : (0 : ℚ) ≤ b*(5257495372027781547898637965671 / 1000000000000000000000000000000) ∧ b*(5257495372027781547898637965671 / 1000000000000000000000000000000) ≤ b*(657186921503472693487329745709 / 125000000000000000000000000000) ∧ b*(657186921503472693487329745709 / 125000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_3 : expUpper (b*(657186921503472693487329745709 / 125000000000000000000000000000)) ≤ accepted_3 := by + norm_num [expUpper, taylor8, b, accepted_3] + +def accepted_4 : ℚ := (10005608262486795586682598316938196351633 / 10000000000000000000000000000000000000000) +theorem accepted_interval_4 : (0 : ℚ) ≤ b*(4969813299576000620459418959677 / 1000000000000000000000000000000) ∧ b*(4969813299576000620459418959677 / 1000000000000000000000000000000) ≤ b*(2484906649788000310229709479839 / 500000000000000000000000000000) ∧ b*(2484906649788000310229709479839 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_4 : expUpper (b*(2484906649788000310229709479839 / 500000000000000000000000000000)) ≤ accepted_4 := by + norm_num [expUpper, taylor8, b, accepted_4] + +def accepted_5 : ℚ := (5002678192638354252310939591491486682637 / 5000000000000000000000000000000000000000) +theorem accepted_interval_5 : (0 : ℚ) ≤ b*(4746669748261790864693123869367 / 1000000000000000000000000000000) ∧ b*(4746669748261790864693123869367 / 1000000000000000000000000000000) ≤ b*(593333718532723858086640483671 / 125000000000000000000000000000) ∧ b*(593333718532723858086640483671 / 125000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_5 : expUpper (b*(593333718532723858086640483671 / 125000000000000000000000000000)) ≤ accepted_5 := by + norm_num [expUpper, taylor8, b, accepted_5] + +def accepted_6 : ℚ := (10005150591318081334437472307882593960501 / 10000000000000000000000000000000000000000) +theorem accepted_interval_6 : (0 : ℚ) ≤ b*(4564348191467836238481405844213 / 1000000000000000000000000000000) ∧ b*(4564348191467836238481405844213 / 1000000000000000000000000000000) ≤ b*(2282174095733918119240702922107 / 500000000000000000000000000000) ∧ b*(2282174095733918119240702922107 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_6 : expUpper (b*(2282174095733918119240702922107 / 500000000000000000000000000000)) ≤ accepted_6 := by + norm_num [expUpper, taylor8, b, accepted_6] + +def accepted_7 : ℚ := (10004976598307617933072074586029358175999 / 10000000000000000000000000000000000000000) +theorem accepted_interval_7 : (0 : ℚ) ≤ b*(88203950232811558683770609183 / 20000000000000000000000000000) ∧ b*(88203950232811558683770609183 / 20000000000000000000000000000) ≤ b*(4410197511640577934188530459151 / 1000000000000000000000000000000) ∧ b*(4410197511640577934188530459151 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_7 : expUpper (b*(4410197511640577934188530459151 / 1000000000000000000000000000000)) ≤ accepted_7 := by + norm_num [expUpper, taylor8, b, accepted_7] + +def accepted_8 : ℚ := (1250603235144018751348201924633183002973 / 1250000000000000000000000000000000000000) +theorem accepted_interval_8 : (0 : ℚ) ≤ b*(4276666119016055311042186838219 / 1000000000000000000000000000000) ∧ b*(4276666119016055311042186838219 / 1000000000000000000000000000000) ≤ b*(213833305950802765552109341911 / 50000000000000000000000000000) ∧ b*(213833305950802765552109341911 / 50000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_8 : expUpper (b*(213833305950802765552109341911 / 50000000000000000000000000000)) ≤ accepted_8 := by + norm_num [expUpper, taylor8, b, accepted_8] + +def accepted_9 : ℚ := (10004692941083916304711037875234252480853 / 10000000000000000000000000000000000000000) +theorem accepted_interval_9 : (0 : ℚ) ≤ b*(4158883083359671856503392728749 / 1000000000000000000000000000000) ∧ b*(4158883083359671856503392728749 / 1000000000000000000000000000000) ≤ b*(3327106466687737485202714183 / 800000000000000000000000000) ∧ b*(3327106466687737485202714183 / 800000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_9 : expUpper (b*(3327106466687737485202714183 / 800000000000000000000000000)) ≤ accepted_9 := by + norm_num [expUpper, taylor8, b, accepted_9] + +def accepted_10 : ℚ := (2000914804727484006991228354413582185253 / 2000000000000000000000000000000000000000) +theorem accepted_interval_10 : (0 : ℚ) ≤ b*(4053522567701845555275891747909 / 1000000000000000000000000000000) ∧ b*(4053522567701845555275891747909 / 1000000000000000000000000000000) ≤ b*(405352256770184555527589174791 / 100000000000000000000000000000) ∧ b*(405352256770184555527589174791 / 100000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_10 : expUpper (b*(405352256770184555527589174791 / 100000000000000000000000000000)) ≤ accepted_10 := by + norm_num [expUpper, taylor8, b, accepted_10] + +def accepted_11 : ℚ := (10004466450939586496552205020318496489341 / 10000000000000000000000000000000000000000) +theorem accepted_interval_11 : (0 : ℚ) ≤ b*(989553096974380173807984906157 / 250000000000000000000000000000) ∧ b*(989553096974380173807984906157 / 250000000000000000000000000000) ≤ b*(3958212387897520695231939624629 / 1000000000000000000000000000000) ∧ b*(3958212387897520695231939624629 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_11 : expUpper (b*(3958212387897520695231939624629 / 1000000000000000000000000000000)) ≤ accepted_11 := by + norm_num [expUpper, taylor8, b, accepted_11] + +def accepted_12 : ℚ := (2501092061442675825070071222311488555861 / 2500000000000000000000000000000000000000) +theorem accepted_interval_12 : (0 : ℚ) ≤ b*(774240202181578185812834744551 / 200000000000000000000000000000) ∧ b*(774240202181578185812834744551 / 200000000000000000000000000000) ≤ b*(967800252726972732266043430689 / 250000000000000000000000000000) ∧ b*(967800252726972732266043430689 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_12 : expUpper (b*(967800252726972732266043430689 / 250000000000000000000000000000)) ≤ accepted_12 := by + norm_num [expUpper, taylor8, b, accepted_12] + +def accepted_13 : ℚ := (1000427790662396194996233470122394286203 / 1000000000000000000000000000000000000000) +theorem accepted_interval_13 : (0 : ℚ) ≤ b*(947789575808588625810098940257 / 250000000000000000000000000000) ∧ b*(947789575808588625810098940257 / 250000000000000000000000000000) ≤ b*(3791158303234354503240395761029 / 1000000000000000000000000000000) ∧ b*(3791158303234354503240395761029 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_13 : expUpper (b*(3791158303234354503240395761029 / 1000000000000000000000000000000)) ≤ accepted_13 := by + norm_num [expUpper, taylor8, b, accepted_13] + +def accepted_14 : ℚ := (1250524283295687260942300726950585983367 / 1250000000000000000000000000000000000000) +theorem accepted_interval_14 : (0 : ℚ) ≤ b*(929262582770158156192824584423 / 250000000000000000000000000000) ∧ b*(929262582770158156192824584423 / 250000000000000000000000000000) ≤ b*(3717050331080632624771298337693 / 1000000000000000000000000000000) ∧ b*(3717050331080632624771298337693 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_14 : expUpper (b*(3717050331080632624771298337693 / 1000000000000000000000000000000)) ≤ accepted_14 := by + norm_num [expUpper, taylor8, b, accepted_14] + +def accepted_15 : ℚ := (10004116399776304731797587454524115614907 / 10000000000000000000000000000000000000000) +theorem accepted_interval_15 : (0 : ℚ) ≤ b*(729611491918736234659575726489 / 200000000000000000000000000000) ∧ b*(729611491918736234659575726489 / 200000000000000000000000000000) ≤ b*(1824028729796840586648939316223 / 500000000000000000000000000000) ∧ b*(1824028729796840586648939316223 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_15 : expUpper (b*(1824028729796840586648939316223 / 500000000000000000000000000000)) ≤ accepted_15 := by + norm_num [expUpper, taylor8, b, accepted_15] + +def accepted_16 : ℚ := (5002021780497624814863799490608923226717 / 5000000000000000000000000000000000000000) +theorem accepted_interval_16 : (0 : ℚ) ≤ b*(3583518938456110001624954716761 / 1000000000000000000000000000000) ∧ b*(3583518938456110001624954716761 / 1000000000000000000000000000000) ≤ b*(1791759469228055000812477358381 / 500000000000000000000000000000) ∧ b*(1791759469228055000812477358381 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_16 : expUpper (b*(1791759469228055000812477358381 / 500000000000000000000000000000)) ≤ accepted_16 := by + norm_num [expUpper, taylor8, b, accepted_16] + +def accepted_17 : ℚ := (1000397513996078830412133154494488397217 / 1000000000000000000000000000000000000000) +theorem accepted_interval_17 : (0 : ℚ) ≤ b*(44036178957995939488054357309 / 12500000000000000000000000000) ∧ b*(44036178957995939488054357309 / 12500000000000000000000000000) ≤ b*(3522894316639675159044348584721 / 1000000000000000000000000000000) ∧ b*(3522894316639675159044348584721 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_17 : expUpper (b*(3522894316639675159044348584721 / 1000000000000000000000000000000)) ≤ accepted_17 := by + norm_num [expUpper, taylor8, b, accepted_17] + +def accepted_18 : ℚ := (2500977657830542212572203647666043033353 / 2500000000000000000000000000000000000000) +theorem accepted_interval_18 : (0 : ℚ) ≤ b*(346573590279972654708616060729 / 100000000000000000000000000000) ∧ b*(346573590279972654708616060729 / 100000000000000000000000000000) ≤ b*(3465735902799726547086160607291 / 1000000000000000000000000000000) ∧ b*(3465735902799726547086160607291 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_18 : expUpper (b*(3465735902799726547086160607291 / 1000000000000000000000000000000)) ≤ accepted_18 := by + norm_num [expUpper, taylor8, b, accepted_18] + +def accepted_19 : ℚ := (10003849611767539530251041249190273494001 / 10000000000000000000000000000000000000000) +theorem accepted_interval_19 : (0 : ℚ) ≤ b*(1705834340764725389642427885353 / 500000000000000000000000000000) ∧ b*(1705834340764725389642427885353 / 500000000000000000000000000000) ≤ b*(3411668681529450779284855770707 / 1000000000000000000000000000000) ∧ b*(3411668681529450779284855770707 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_19 : expUpper (b*(3411668681529450779284855770707 / 1000000000000000000000000000000)) ≤ accepted_19 := by + norm_num [expUpper, taylor8, b, accepted_19] + +def accepted_20 : ℚ := (10003791723174336695859928379092107147311 / 10000000000000000000000000000000000000000) +theorem accepted_interval_20 : (0 : ℚ) ≤ b*(3360375387141900245858659626451 / 1000000000000000000000000000000) ∧ b*(3360375387141900245858659626451 / 1000000000000000000000000000000) ≤ b*(840093846785475061464664906613 / 250000000000000000000000000000) ∧ b*(840093846785475061464664906613 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_20 : expUpper (b*(840093846785475061464664906613 / 250000000000000000000000000000)) ≤ accepted_20 := by + norm_num [expUpper, taylor8, b, accepted_20] + +def accepted_21 : ℚ := (10003736659875036312749799798518888013029 / 10000000000000000000000000000000000000000) +theorem accepted_interval_21 : (0 : ℚ) ≤ b*(827896305743117060698321305557 / 250000000000000000000000000000) ∧ b*(827896305743117060698321305557 / 250000000000000000000000000000) ≤ b*(3311585222972468242793285222229 / 1000000000000000000000000000000) ∧ b*(3311585222972468242793285222229 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_21 : expUpper (b*(3311585222972468242793285222229 / 1000000000000000000000000000000)) ≤ accepted_21 := by + norm_num [expUpper, taylor8, b, accepted_21] + +def accepted_22 : ℚ := (5001842079444036409320152786470891628601 / 5000000000000000000000000000000000000000) +theorem accepted_interval_22 : (0 : ℚ) ≤ b*(326506520733757538581470750317 / 100000000000000000000000000000) ∧ b*(326506520733757538581470750317 / 100000000000000000000000000000) ≤ b*(3265065207337575385814707503171 / 1000000000000000000000000000000) ∧ b*(3265065207337575385814707503171 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_22 : expUpper (b*(3265065207337575385814707503171 / 1000000000000000000000000000000)) ≤ accepted_22 := by + norm_num [expUpper, taylor8, b, accepted_22] + +def accepted_23 : ℚ := (10003633992322138767059090899422809010713 / 10000000000000000000000000000000000000000) +theorem accepted_interval_23 : (0 : ℚ) ≤ b*(3220613444766741548487130370783 / 1000000000000000000000000000000) ∧ b*(3220613444766741548487130370783 / 1000000000000000000000000000000) ≤ b*(100644170148960673390222824087 / 31250000000000000000000000000) ∧ b*(100644170148960673390222824087 / 31250000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_23 : expUpper (b*(100644170148960673390222824087 / 31250000000000000000000000000)) ≤ accepted_23 := by + norm_num [expUpper, taylor8, b, accepted_23] + +def accepted_529 : ℚ := (2500024006910801357156667820225605837451 / 2500000000000000000000000000000000000000) +theorem accepted_interval_529 : (0 : ℚ) ≤ b*(85119228837591857680377538973 / 1000000000000000000000000000000) ∧ b*(85119228837591857680377538973 / 1000000000000000000000000000000) ≤ b*(42559614418795928840188769487 / 500000000000000000000000000000) ∧ b*(42559614418795928840188769487 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_529 : expUpper (b*(42559614418795928840188769487 / 500000000000000000000000000000)) ≤ accepted_529 := by + norm_num [expUpper, taylor8, b, accepted_529] + +def accepted_552 : ℚ := (10000048013706336914502962445538143648637 / 10000000000000000000000000000000000000000) +theorem accepted_interval_552 : (0 : ℚ) ≤ b*(21279807209397964420094384743 / 500000000000000000000000000000) ∧ b*(21279807209397964420094384743 / 500000000000000000000000000000) ≤ b*(42559614418795928840188769487 / 1000000000000000000000000000000) ∧ b*(42559614418795928840188769487 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_552 : expUpper (b*(42559614418795928840188769487 / 1000000000000000000000000000000)) ≤ accepted_552 := by + norm_num [expUpper, taylor8, b, accepted_552] + +def accepted_554 : ℚ := (400001757343114255072912651180621264047 / 400000000000000000000000000000000000000) +theorem accepted_interval_554 : (0 : ℚ) ≤ b*(38942973948607430007253531611 / 1000000000000000000000000000000) ∧ b*(38942973948607430007253531611 / 1000000000000000000000000000000) ≤ b*(9735743487151857501813382903 / 250000000000000000000000000000) ∧ b*(9735743487151857501813382903 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_554 : expUpper (b*(9735743487151857501813382903 / 250000000000000000000000000000)) ≤ accepted_554 := by + norm_num [expUpper, taylor8, b, accepted_554] + +def accepted_556 : ℚ := (5000019934077114581960794678319392907493 / 5000000000000000000000000000000000000000) +theorem accepted_interval_556 : (0 : ℚ) ≤ b*(17669683222654431635317020401 / 500000000000000000000000000000) ∧ b*(17669683222654431635317020401 / 500000000000000000000000000000) ≤ b*(35339366445308863270634040803 / 1000000000000000000000000000000) ∧ b*(35339366445308863270634040803 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_556 : expUpper (b*(35339366445308863270634040803 / 1000000000000000000000000000000)) ≤ accepted_556 := by + norm_num [expUpper, taylor8, b, accepted_556] + +def accepted_558 : ℚ := (10000035817329848616000090876431682424381 / 10000000000000000000000000000000000000000) +theorem accepted_interval_558 : (0 : ℚ) ≤ b*(7937174578645075289249070687 / 250000000000000000000000000000) ∧ b*(7937174578645075289249070687 / 250000000000000000000000000000) ≤ b*(31748698314580301156996282749 / 1000000000000000000000000000000) ∧ b*(31748698314580301156996282749 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_558 : expUpper (b*(31748698314580301156996282749 / 1000000000000000000000000000000)) ≤ accepted_558 := by + norm_num [expUpper, taylor8, b, accepted_558] + +def accepted_560 : ℚ := (2000006356200048328919135749948149107147 / 2000000000000000000000000000000000000000) +theorem accepted_interval_560 : (0 : ℚ) ≤ b*(7042719241674080479710660023 / 250000000000000000000000000000) ∧ b*(7042719241674080479710660023 / 250000000000000000000000000000) ≤ b*(28170876966696321918842640093 / 1000000000000000000000000000000) ∧ b*(28170876966696321918842640093 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_560 : expUpper (b*(28170876966696321918842640093 / 1000000000000000000000000000000)) ≤ accepted_560 := by + norm_num [expUpper, taylor8, b, accepted_560] + +def accepted_562 : ℚ := (5000013879531026283516616597127113348633 / 5000000000000000000000000000000000000000) +theorem accepted_interval_562 : (0 : ℚ) ≤ b*(12302905401100082385006378221 / 500000000000000000000000000000) ∧ b*(12302905401100082385006378221 / 500000000000000000000000000000) ≤ b*(24605810802200164770012756443 / 1000000000000000000000000000000) ∧ b*(24605810802200164770012756443 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_562 : expUpper (b*(24605810802200164770012756443 / 1000000000000000000000000000000)) ≤ accepted_562 := by + norm_num [expUpper, taylor8, b, accepted_562] + +def accepted_571 : ℚ := (2500002458929401650667719229571399047519 / 2500000000000000000000000000000000000000) +theorem accepted_interval_571 : (0 : ℚ) ≤ b*(4359225519940511281958503327 / 500000000000000000000000000000) ∧ b*(4359225519940511281958503327 / 500000000000000000000000000000) ≤ b*(1743690207976204512783401331 / 200000000000000000000000000000) ∧ b*(1743690207976204512783401331 / 200000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_571 : expUpper (b*(1743690207976204512783401331 / 200000000000000000000000000000)) ≤ accepted_571 := by + norm_num [expUpper, taylor8, b, accepted_571] + +def accepted_572 : ℚ := (2500001965425291953393961431121574574217 / 2500000000000000000000000000000000000000) +theorem accepted_interval_572 : (0 : ℚ) ≤ b*(6968669316093340343987940147 / 1000000000000000000000000000000) ∧ b*(6968669316093340343987940147 / 1000000000000000000000000000000) ≤ b*(1742167329023335085996985037 / 250000000000000000000000000000) ∧ b*(1742167329023335085996985037 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_572 : expUpper (b*(1742167329023335085996985037 / 250000000000000000000000000000)) ≤ accepted_572 := by + norm_num [expUpper, taylor8, b, accepted_572] + +def accepted_573 : ℚ := (5000002945566591540622685978536652726911 / 5000000000000000000000000000000000000000) +theorem accepted_interval_573 : (0 : ℚ) ≤ b*(5221943981151675048688013469 / 1000000000000000000000000000000) ∧ b*(5221943981151675048688013469 / 1000000000000000000000000000000) ≤ b*(522194398115167504868801347 / 100000000000000000000000000000) ∧ b*(522194398115167504868801347 / 100000000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_573 : expUpper (b*(522194398115167504868801347 / 100000000000000000000000000000)) ≤ accepted_573 := by + norm_num [expUpper, taylor8, b, accepted_573] + +def accepted_574 : ℚ := (5000001962000812862191416361841862291317 / 5000000000000000000000000000000000000000) +theorem accepted_interval_574 : (0 : ℚ) ≤ b*(695652875264964180906992931 / 200000000000000000000000000000) ∧ b*(695652875264964180906992931 / 200000000000000000000000000000) ≤ b*(217391523520301306533435291 / 62500000000000000000000000000) ∧ b*(217391523520301306533435291 / 62500000000000000000000000000) < 1 := by + norm_num [b] + +theorem accepted_taylor_574 : expUpper (b*(217391523520301306533435291 / 62500000000000000000000000000)) ≤ accepted_574 := by + norm_num [expUpper, taylor8, b, accepted_574] + +def acceptedMoment : ℚ := + ((1*435042608 : ℚ)/(576*114315520))*accepted_1 + + ((2*266771296 : ℚ)/(576*114315520))*accepted_2 + + ((3*29060592 : ℚ)/(576*114315520))*accepted_3 + + ((4*60639040 : ℚ)/(576*114315520))*accepted_4 + + ((5*26643936 : ℚ)/(576*114315520))*accepted_5 + + ((6*15333824 : ℚ)/(576*114315520))*accepted_6 + + ((7*11743248 : ℚ)/(576*114315520))*accepted_7 + + ((8*22069696 : ℚ)/(576*114315520))*accepted_8 + + ((9*3938704 : ℚ)/(576*114315520))*accepted_9 + + ((10*7735728 : ℚ)/(576*114315520))*accepted_10 + + ((11*6658960 : ℚ)/(576*114315520))*accepted_11 + + ((12*33578160 : ℚ)/(576*114315520))*accepted_12 + + ((13*13184336 : ℚ)/(576*114315520))*accepted_13 + + ((14*1821600 : ℚ)/(576*114315520))*accepted_14 + + ((15*3238400 : ℚ)/(576*114315520))*accepted_15 + + ((16*631488 : ℚ)/(576*114315520))*accepted_16 + + ((17*404800 : ℚ)/(576*114315520))*accepted_17 + + ((18*202400 : ℚ)/(576*114315520))*accepted_18 + + ((19*311696 : ℚ)/(576*114315520))*accepted_19 + + ((20*550528 : ℚ)/(576*114315520))*accepted_20 + + ((21*1222496 : ℚ)/(576*114315520))*accepted_21 + + ((22*64768 : ℚ)/(576*114315520))*accepted_22 + + ((23*8383408 : ℚ)/(576*114315520))*accepted_23 + + ((529*8193152 : ℚ)/(576*114315520))*accepted_529 + + ((552*97071040 : ℚ)/(576*114315520))*accepted_552 + + ((554*3456992 : ℚ)/(576*114315520))*accepted_554 + + ((556*1481568 : ℚ)/(576*114315520))*accepted_556 + + ((558*2384272 : ℚ)/(576*114315520))*accepted_558 + + ((560*445280 : ℚ)/(576*114315520))*accepted_560 + + ((562*48576 : ℚ)/(576*114315520))*accepted_562 + + ((571*740784 : ℚ)/(576*114315520))*accepted_571 + + ((572*101200 : ℚ)/(576*114315520))*accepted_572 + + ((573*28336 : ℚ)/(576*114315520))*accepted_573 + + ((574*364320 : ℚ)/(576*114315520))*accepted_574 +def acceptedFromCounts : ℚ := + ((1*(count 1 : ℚ))/(m*width))*accepted_1 + + ((2*(count 2 : ℚ))/(m*width))*accepted_2 + + ((3*(count 3 : ℚ))/(m*width))*accepted_3 + + ((4*(count 4 : ℚ))/(m*width))*accepted_4 + + ((5*(count 5 : ℚ))/(m*width))*accepted_5 + + ((6*(count 6 : ℚ))/(m*width))*accepted_6 + + ((7*(count 7 : ℚ))/(m*width))*accepted_7 + + ((8*(count 8 : ℚ))/(m*width))*accepted_8 + + ((9*(count 9 : ℚ))/(m*width))*accepted_9 + + ((10*(count 10 : ℚ))/(m*width))*accepted_10 + + ((11*(count 11 : ℚ))/(m*width))*accepted_11 + + ((12*(count 12 : ℚ))/(m*width))*accepted_12 + + ((13*(count 13 : ℚ))/(m*width))*accepted_13 + + ((14*(count 14 : ℚ))/(m*width))*accepted_14 + + ((15*(count 15 : ℚ))/(m*width))*accepted_15 + + ((16*(count 16 : ℚ))/(m*width))*accepted_16 + + ((17*(count 17 : ℚ))/(m*width))*accepted_17 + + ((18*(count 18 : ℚ))/(m*width))*accepted_18 + + ((19*(count 19 : ℚ))/(m*width))*accepted_19 + + ((20*(count 20 : ℚ))/(m*width))*accepted_20 + + ((21*(count 21 : ℚ))/(m*width))*accepted_21 + + ((22*(count 22 : ℚ))/(m*width))*accepted_22 + + ((23*(count 23 : ℚ))/(m*width))*accepted_23 + + ((529*(count 529 : ℚ))/(m*width))*accepted_529 + + ((552*(count 552 : ℚ))/(m*width))*accepted_552 + + ((554*(count 554 : ℚ))/(m*width))*accepted_554 + + ((556*(count 556 : ℚ))/(m*width))*accepted_556 + + ((558*(count 558 : ℚ))/(m*width))*accepted_558 + + ((560*(count 560 : ℚ))/(m*width))*accepted_560 + + ((562*(count 562 : ℚ))/(m*width))*accepted_562 + + ((571*(count 571 : ℚ))/(m*width))*accepted_571 + + ((572*(count 572 : ℚ))/(m*width))*accepted_572 + + ((573*(count 573 : ℚ))/(m*width))*accepted_573 + + ((574*(count 574 : ℚ))/(m*width))*accepted_574 +theorem accepted_profile_link : acceptedFromCounts = acceptedMoment := by + norm_num [acceptedFromCounts, acceptedMoment, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, count_1, count_10, count_11, count_12, count_13, count_14, count_15, count_16, count_17, count_18, count_19, count_2, count_20, count_21, count_22, count_23, count_3, count_4, count_5, count_529, count_552, count_554, count_556, count_558, count_560, count_562, count_571, count_572, count_573, count_574, count_6, count_7, count_8, count_9] + +theorem accepted_moment : acceptedMoment < 1 ∧ acceptedMoment = (40665599999999999999999992105609200772387856393 / 40665600000000000000000000000000000000000000000) := by + norm_num [acceptedMoment, accepted_1, accepted_10, accepted_11, accepted_12, accepted_13, accepted_14, accepted_15, accepted_16, accepted_17, accepted_18, accepted_19, accepted_2, accepted_20, accepted_21, accepted_22, accepted_23, accepted_3, accepted_4, accepted_5, accepted_529, accepted_552, accepted_554, accepted_556, accepted_558, accepted_560, accepted_562, accepted_571, accepted_572, accepted_573, accepted_574, accepted_6, accepted_7, accepted_8, accepted_9] + +theorem accepted_paid_moment : acceptedFromCounts < 1 := by + rw [accepted_profile_link] + exact accepted_moment.1 + +def rejected_1 : ℚ := (5003586604354229596221572701664384374267 / 5000000000000000000000000000000000000000) +theorem rejected_interval_1 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(3178053830347945619646941601297 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3178053830347945619646941601297 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(1271221532139178247858776640519 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1271221532139178247858776640519 / 200000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_1 : rejected_1 ≤ taylor8 ((b+1/1000000000000000000000000)*(3178053830347945619646941601297 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_1] + +def rejected_2 : ℚ := (10006390705003970481250915724170359842273 / 10000000000000000000000000000000000000000) +theorem rejected_interval_2 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(1132592096027189185975330216227 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1132592096027189185975330216227 / 200000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(353935030008496620617290692571 / 62500000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(353935030008496620617290692571 / 62500000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_2 : rejected_2 ≤ taylor8 ((b+1/1000000000000000000000000)*(1132592096027189185975330216227 / 200000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_2] + +def rejected_3 : ℚ := (10005932998045190108812428871758817532111 / 10000000000000000000000000000000000000000) +theorem rejected_interval_3 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(5257495372027781547898637965671 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(5257495372027781547898637965671 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(657186921503472693487329745709 / 125000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(657186921503472693487329745709 / 125000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_3 : rejected_3 ≤ taylor8 ((b+1/1000000000000000000000000)*(5257495372027781547898637965671 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_3] + +def rejected_4 : ℚ := (1000560826248679558668264804294320832637 / 1000000000000000000000000000000000000000) +theorem rejected_interval_4 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4969813299576000620459418959677 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4969813299576000620459418959677 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(2484906649788000310229709479839 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(2484906649788000310229709479839 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_4 : rejected_4 ≤ taylor8 ((b+1/1000000000000000000000000)*(4969813299576000620459418959677 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_4] + +def rejected_5 : ℚ := (10005356385276708504621926675105446707631 / 10000000000000000000000000000000000000000) +theorem rejected_interval_5 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4746669748261790864693123869367 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4746669748261790864693123869367 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(593333718532723858086640483671 / 125000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(593333718532723858086640483671 / 125000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_5 : rejected_5 ≤ taylor8 ((b+1/1000000000000000000000000)*(4746669748261790864693123869367 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_5] + +def rejected_6 : ℚ := (5002575295659040667218758987436799803833 / 5000000000000000000000000000000000000000) +theorem rejected_interval_6 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4564348191467836238481405844213 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4564348191467836238481405844213 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(2282174095733918119240702922107 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(2282174095733918119240702922107 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_6 : rejected_6 ≤ taylor8 ((b+1/1000000000000000000000000)*(4564348191467836238481405844213 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_6] + +def rejected_7 : ℚ := (5002488299153808966536059354976127437137 / 5000000000000000000000000000000000000000) +theorem rejected_interval_7 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(88203950232811558683770609183 / 20000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(88203950232811558683770609183 / 20000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(4410197511640577934188530459151 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4410197511640577934188530459151 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_7 : rejected_7 ≤ taylor8 ((b+1/1000000000000000000000000)*(88203950232811558683770609183 / 20000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_7] + +def rejected_8 : ℚ := (10004825881152150010785658184365335434401 / 10000000000000000000000000000000000000000) +theorem rejected_interval_8 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4276666119016055311042186838219 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4276666119016055311042186838219 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(213833305950802765552109341911 / 50000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(213833305950802765552109341911 / 50000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_8 : rejected_8 ≤ taylor8 ((b+1/1000000000000000000000000)*(4276666119016055311042186838219 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_8] + +def rejected_9 : ℚ := (625293308817744769044442467723904887727 / 625000000000000000000000000000000000000) +theorem rejected_interval_9 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4158883083359671856503392728749 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4158883083359671856503392728749 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3327106466687737485202714183 / 800000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3327106466687737485202714183 / 800000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_9 : rejected_9 ≤ taylor8 ((b+1/1000000000000000000000000)*(4158883083359671856503392728749 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_9] + +def rejected_10 : ℚ := (10004574023637420034956182325834494831437 / 10000000000000000000000000000000000000000) +theorem rejected_interval_10 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4053522567701845555275891747909 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4053522567701845555275891747909 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(405352256770184555527589174791 / 100000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(405352256770184555527589174791 / 100000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_10 : rejected_10 ≤ taylor8 ((b+1/1000000000000000000000000)*(4053522567701845555275891747909 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_10] + +def rejected_11 : ℚ := (5002233225469793248276122310060767877723 / 5000000000000000000000000000000000000000) +theorem rejected_interval_11 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(989553096974380173807984906157 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(989553096974380173807984906157 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3958212387897520695231939624629 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3958212387897520695231939624629 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_11 : rejected_11 ≤ taylor8 ((b+1/1000000000000000000000000)*(989553096974380173807984906157 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_11] + +def rejected_12 : ℚ := (10004368245770703300280323618166419601223 / 10000000000000000000000000000000000000000) +theorem rejected_interval_12 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(774240202181578185812834744551 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(774240202181578185812834744551 / 200000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(967800252726972732266043430689 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(967800252726972732266043430689 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_12 : rejected_12 ≤ taylor8 ((b+1/1000000000000000000000000)*(774240202181578185812834744551 / 200000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_12] + +def rejected_13 : ℚ := (10004277906623961949962372629025195281639 / 10000000000000000000000000000000000000000) +theorem rejected_interval_13 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(947789575808588625810098940257 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(947789575808588625810098940257 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3791158303234354503240395761029 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3791158303234354503240395761029 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_13 : rejected_13 ≤ taylor8 ((b+1/1000000000000000000000000)*(947789575808588625810098940257 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_13] + +def rejected_14 : ℚ := (2000838853273099617507688600339659343221 / 2000000000000000000000000000000000000000) +theorem rejected_interval_14 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(929262582770158156192824584423 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(929262582770158156192824584423 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3717050331080632624771298337693 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3717050331080632624771298337693 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_14 : rejected_14 ≤ taylor8 ((b+1/1000000000000000000000000)*(929262582770158156192824584423 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_14] + +def rejected_15 : ℚ := (10004116399776304731797623950115573324387 / 10000000000000000000000000000000000000000) +theorem rejected_interval_15 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(729611491918736234659575726489 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(729611491918736234659575726489 / 200000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(1824028729796840586648939316223 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1824028729796840586648939316223 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_15 : rejected_15 ≤ taylor8 ((b+1/1000000000000000000000000)*(729611491918736234659575726489 / 200000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_15] + +def rejected_16 : ℚ := (5002021780497624814863817415448703641629 / 5000000000000000000000000000000000000000) +theorem rejected_interval_16 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(3583518938456110001624954716761 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3583518938456110001624954716761 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(1791759469228055000812477358381 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1791759469228055000812477358381 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_16 : rejected_16 ≤ taylor8 ((b+1/1000000000000000000000000)*(3583518938456110001624954716761 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_16] + +def rejected_17 : ℚ := (10003975139960788304121366787892047209213 / 10000000000000000000000000000000000000000) +theorem rejected_interval_17 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(44036178957995939488054357309 / 12500000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(44036178957995939488054357309 / 12500000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3522894316639675159044348584721 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3522894316639675159044348584721 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_17 : rejected_17 ≤ taylor8 ((b+1/1000000000000000000000000)*(44036178957995939488054357309 / 12500000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_17] + +def rejected_18 : ℚ := (1250488828915271106286106157697051796507 / 1250000000000000000000000000000000000000) +theorem rejected_interval_18 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(346573590279972654708616060729 / 100000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(346573590279972654708616060729 / 100000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3465735902799726547086160607291 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3465735902799726547086160607291 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_18 : rejected_18 ≤ taylor8 ((b+1/1000000000000000000000000)*(346573590279972654708616060729 / 100000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_18] + +def rejected_19 : ℚ := (5001924805883769765125537689505343779089 / 5000000000000000000000000000000000000000) +theorem rejected_interval_19 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(1705834340764725389642427885353 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1705834340764725389642427885353 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3411668681529450779284855770707 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3411668681529450779284855770707 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_19 : rejected_19 ≤ taylor8 ((b+1/1000000000000000000000000)*(1705834340764725389642427885353 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_19] + +def rejected_20 : ℚ := (400151668926973467834398479823503626527 / 400000000000000000000000000000000000000) +theorem rejected_interval_20 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(3360375387141900245858659626451 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3360375387141900245858659626451 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(840093846785475061464664906613 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(840093846785475061464664906613 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_20 : rejected_20 ≤ taylor8 ((b+1/1000000000000000000000000)*(3360375387141900245858659626451 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_20] + +def rejected_21 : ℚ := (10003736659875036312749832926745384230677 / 10000000000000000000000000000000000000000) +theorem rejected_interval_21 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(827896305743117060698321305557 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(827896305743117060698321305557 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3311585222972468242793285222229 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3311585222972468242793285222229 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_21 : rejected_21 ≤ taylor8 ((b+1/1000000000000000000000000)*(827896305743117060698321305557 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_21] + +def rejected_22 : ℚ := (100036841588880728186403382356228745047 / 100000000000000000000000000000000000000) +theorem rejected_interval_22 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(326506520733757538581470750317 / 100000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(326506520733757538581470750317 / 100000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(3265065207337575385814707503171 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3265065207337575385814707503171 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_22 : rejected_22 ≤ taylor8 ((b+1/1000000000000000000000000)*(326506520733757538581470750317 / 100000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_22] + +def rejected_23 : ℚ := (5001816996161069383529561558630470038693 / 5000000000000000000000000000000000000000) +theorem rejected_interval_23 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(3220613444766741548487130370783 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(3220613444766741548487130370783 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(100644170148960673390222824087 / 31250000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(100644170148960673390222824087 / 31250000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_23 : rejected_23 ≤ taylor8 ((b+1/1000000000000000000000000)*(3220613444766741548487130370783 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_23] + +def rejected_529 : ℚ := (10000096027643205428626672132102884396499 / 10000000000000000000000000000000000000000) +theorem rejected_interval_529 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(85119228837591857680377538973 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(85119228837591857680377538973 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(42559614418795928840188769487 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(42559614418795928840188769487 / 500000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_529 : rejected_529 ≤ taylor8 ((b+1/1000000000000000000000000)*(85119228837591857680377538973 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_529] + +def rejected_552 : ℚ := (10000048013706336914502962871136330153269 / 10000000000000000000000000000000000000000) +theorem rejected_interval_552 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(21279807209397964420094384743 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(21279807209397964420094384743 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(42559614418795928840188769487 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(42559614418795928840188769487 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_552 : rejected_552 ≤ taylor8 ((b+1/1000000000000000000000000)*(21279807209397964420094384743 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_552] + +def rejected_554 : ℚ := (1250005491697232047102852083618372607909 / 1250000000000000000000000000000000000000) +theorem rejected_interval_554 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(38942973948607430007253531611 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(38942973948607430007253531611 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(9735743487151857501813382903 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(9735743487151857501813382903 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_554 : rejected_554 ≤ taylor8 ((b+1/1000000000000000000000000)*(38942973948607430007253531611 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_554] + +def rejected_556 : ℚ := (156250622939909830686274839219279032113 / 156250000000000000000000000000000000000) +theorem rejected_interval_556 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(17669683222654431635317020401 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(17669683222654431635317020401 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(35339366445308863270634040803 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(35339366445308863270634040803 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_556 : rejected_556 ≤ taylor8 ((b+1/1000000000000000000000000)*(17669683222654431635317020401 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_556] + +def rejected_558 : ℚ := (1000003581732984861600009119391980159563 / 1000000000000000000000000000000000000000) +theorem rejected_interval_558 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(7937174578645075289249070687 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(7937174578645075289249070687 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(31748698314580301156996282749 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(31748698314580301156996282749 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_558 : rejected_558 ≤ taylor8 ((b+1/1000000000000000000000000)*(7937174578645075289249070687 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_558] + +def rejected_560 : ℚ := (10000031781000241644595679031450409373193 / 10000000000000000000000000000000000000000) +theorem rejected_interval_560 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(7042719241674080479710660023 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(7042719241674080479710660023 / 250000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(28170876966696321918842640093 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(28170876966696321918842640093 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_560 : rejected_560 ≤ taylor8 ((b+1/1000000000000000000000000)*(7042719241674080479710660023 / 250000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_560] + +def rejected_562 : ℚ := (10000027759062052567033233440313016625343 / 10000000000000000000000000000000000000000) +theorem rejected_interval_562 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(12302905401100082385006378221 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(12302905401100082385006378221 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(24605810802200164770012756443 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(24605810802200164770012756443 / 1000000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_562 : rejected_562 ≤ taylor8 ((b+1/1000000000000000000000000)*(12302905401100082385006378221 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_562] + +def rejected_571 : ℚ := (10000009835717606602670877005470191212957 / 10000000000000000000000000000000000000000) +theorem rejected_interval_571 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(4359225519940511281958503327 / 500000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(4359225519940511281958503327 / 500000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(1743690207976204512783401331 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1743690207976204512783401331 / 200000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_571 : rejected_571 ≤ taylor8 ((b+1/1000000000000000000000000)*(4359225519940511281958503327 / 500000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_571] + +def rejected_572 : ℚ := (5000003930850583906787922897086522557623 / 5000000000000000000000000000000000000000) +theorem rejected_interval_572 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(6968669316093340343987940147 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(6968669316093340343987940147 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(1742167329023335085996985037 / 250000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(1742167329023335085996985037 / 250000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_572 : rejected_572 ≤ taylor8 ((b+1/1000000000000000000000000)*(6968669316093340343987940147 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_572] + +def rejected_573 : ℚ := (2000001178226636616249074401858554980071 / 2000000000000000000000000000000000000000) +theorem rejected_interval_573 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(5221943981151675048688013469 / 1000000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(5221943981151675048688013469 / 1000000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(522194398115167504868801347 / 100000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(522194398115167504868801347 / 100000000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_573 : rejected_573 ≤ taylor8 ((b+1/1000000000000000000000000)*(5221943981151675048688013469 / 1000000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_573] + +def rejected_574 : ℚ := (10000003924001625724382832758466380866447 / 10000000000000000000000000000000000000000) +theorem rejected_interval_574 : (0 : ℚ) ≤ (b+1/1000000000000000000000000)*(695652875264964180906992931 / 200000000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(695652875264964180906992931 / 200000000000000000000000000000) ≤ (b+1/1000000000000000000000000)*(217391523520301306533435291 / 62500000000000000000000000000) ∧ (b+1/1000000000000000000000000)*(217391523520301306533435291 / 62500000000000000000000000000) < 1 := by + norm_num [b] + +theorem rejected_taylor_574 : rejected_574 ≤ taylor8 ((b+1/1000000000000000000000000)*(695652875264964180906992931 / 200000000000000000000000000000)) := by + norm_num [expUpper, taylor8, b, rejected_574] + +def rejectedMoment : ℚ := + ((1*435042608 : ℚ)/(576*114315520))*rejected_1 + + ((2*266771296 : ℚ)/(576*114315520))*rejected_2 + + ((3*29060592 : ℚ)/(576*114315520))*rejected_3 + + ((4*60639040 : ℚ)/(576*114315520))*rejected_4 + + ((5*26643936 : ℚ)/(576*114315520))*rejected_5 + + ((6*15333824 : ℚ)/(576*114315520))*rejected_6 + + ((7*11743248 : ℚ)/(576*114315520))*rejected_7 + + ((8*22069696 : ℚ)/(576*114315520))*rejected_8 + + ((9*3938704 : ℚ)/(576*114315520))*rejected_9 + + ((10*7735728 : ℚ)/(576*114315520))*rejected_10 + + ((11*6658960 : ℚ)/(576*114315520))*rejected_11 + + ((12*33578160 : ℚ)/(576*114315520))*rejected_12 + + ((13*13184336 : ℚ)/(576*114315520))*rejected_13 + + ((14*1821600 : ℚ)/(576*114315520))*rejected_14 + + ((15*3238400 : ℚ)/(576*114315520))*rejected_15 + + ((16*631488 : ℚ)/(576*114315520))*rejected_16 + + ((17*404800 : ℚ)/(576*114315520))*rejected_17 + + ((18*202400 : ℚ)/(576*114315520))*rejected_18 + + ((19*311696 : ℚ)/(576*114315520))*rejected_19 + + ((20*550528 : ℚ)/(576*114315520))*rejected_20 + + ((21*1222496 : ℚ)/(576*114315520))*rejected_21 + + ((22*64768 : ℚ)/(576*114315520))*rejected_22 + + ((23*8383408 : ℚ)/(576*114315520))*rejected_23 + + ((529*8193152 : ℚ)/(576*114315520))*rejected_529 + + ((552*97071040 : ℚ)/(576*114315520))*rejected_552 + + ((554*3456992 : ℚ)/(576*114315520))*rejected_554 + + ((556*1481568 : ℚ)/(576*114315520))*rejected_556 + + ((558*2384272 : ℚ)/(576*114315520))*rejected_558 + + ((560*445280 : ℚ)/(576*114315520))*rejected_560 + + ((562*48576 : ℚ)/(576*114315520))*rejected_562 + + ((571*740784 : ℚ)/(576*114315520))*rejected_571 + + ((572*101200 : ℚ)/(576*114315520))*rejected_572 + + ((573*28336 : ℚ)/(576*114315520))*rejected_573 + + ((574*364320 : ℚ)/(576*114315520))*rejected_574 +def rejectedFromCounts : ℚ := + ((1*(count 1 : ℚ))/(m*width))*rejected_1 + + ((2*(count 2 : ℚ))/(m*width))*rejected_2 + + ((3*(count 3 : ℚ))/(m*width))*rejected_3 + + ((4*(count 4 : ℚ))/(m*width))*rejected_4 + + ((5*(count 5 : ℚ))/(m*width))*rejected_5 + + ((6*(count 6 : ℚ))/(m*width))*rejected_6 + + ((7*(count 7 : ℚ))/(m*width))*rejected_7 + + ((8*(count 8 : ℚ))/(m*width))*rejected_8 + + ((9*(count 9 : ℚ))/(m*width))*rejected_9 + + ((10*(count 10 : ℚ))/(m*width))*rejected_10 + + ((11*(count 11 : ℚ))/(m*width))*rejected_11 + + ((12*(count 12 : ℚ))/(m*width))*rejected_12 + + ((13*(count 13 : ℚ))/(m*width))*rejected_13 + + ((14*(count 14 : ℚ))/(m*width))*rejected_14 + + ((15*(count 15 : ℚ))/(m*width))*rejected_15 + + ((16*(count 16 : ℚ))/(m*width))*rejected_16 + + ((17*(count 17 : ℚ))/(m*width))*rejected_17 + + ((18*(count 18 : ℚ))/(m*width))*rejected_18 + + ((19*(count 19 : ℚ))/(m*width))*rejected_19 + + ((20*(count 20 : ℚ))/(m*width))*rejected_20 + + ((21*(count 21 : ℚ))/(m*width))*rejected_21 + + ((22*(count 22 : ℚ))/(m*width))*rejected_22 + + ((23*(count 23 : ℚ))/(m*width))*rejected_23 + + ((529*(count 529 : ℚ))/(m*width))*rejected_529 + + ((552*(count 552 : ℚ))/(m*width))*rejected_552 + + ((554*(count 554 : ℚ))/(m*width))*rejected_554 + + ((556*(count 556 : ℚ))/(m*width))*rejected_556 + + ((558*(count 558 : ℚ))/(m*width))*rejected_558 + + ((560*(count 560 : ℚ))/(m*width))*rejected_560 + + ((562*(count 562 : ℚ))/(m*width))*rejected_562 + + ((571*(count 571 : ℚ))/(m*width))*rejected_571 + + ((572*(count 572 : ℚ))/(m*width))*rejected_572 + + ((573*(count 573 : ℚ))/(m*width))*rejected_573 + + ((574*(count 574 : ℚ))/(m*width))*rejected_574 +theorem rejected_profile_link : rejectedFromCounts = rejectedMoment := by + norm_num [rejectedFromCounts, rejectedMoment, h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose, count_1, count_10, count_11, count_12, count_13, count_14, count_15, count_16, count_17, count_18, count_19, count_2, count_20, count_21, count_22, count_23, count_3, count_4, count_5, count_529, count_552, count_554, count_556, count_558, count_560, count_562, count_571, count_572, count_573, count_574, count_6, count_7, count_8, count_9] + +theorem rejected_moment : 1 < rejectedMoment ∧ rejectedMoment = (40665600000000000000000002301675639985445787697 / 40665600000000000000000000000000000000000000000) := by + norm_num [rejectedMoment, rejected_1, rejected_10, rejected_11, rejected_12, rejected_13, rejected_14, rejected_15, rejected_16, rejected_17, rejected_18, rejected_19, rejected_2, rejected_20, rejected_21, rejected_22, rejected_23, rejected_3, rejected_4, rejected_5, rejected_529, rejected_552, rejected_554, rejected_556, rejected_558, rejected_560, rejected_562, rejected_571, rejected_572, rejected_573, rejected_574, rejected_6, rejected_7, rejected_8, rejected_9] + +theorem rejected_paid_moment : 1 < rejectedFromCounts := by + rw [rejected_profile_link] + exact rejected_moment.1 + +end KappaCheck.ShrunkBirthTerminal +#print axioms KappaCheck.ShrunkBirthTerminal.network_counts +#print axioms KappaCheck.ShrunkBirthTerminal.initial_dimension_count +#print axioms KappaCheck.ShrunkBirthTerminal.rank_mass +#print axioms KappaCheck.ShrunkBirthTerminal.count_1 +#print axioms KappaCheck.ShrunkBirthTerminal.count_2 +#print axioms KappaCheck.ShrunkBirthTerminal.count_3 +#print axioms KappaCheck.ShrunkBirthTerminal.count_4 +#print axioms KappaCheck.ShrunkBirthTerminal.count_5 +#print axioms KappaCheck.ShrunkBirthTerminal.count_6 +#print axioms KappaCheck.ShrunkBirthTerminal.count_7 +#print axioms KappaCheck.ShrunkBirthTerminal.count_8 +#print axioms KappaCheck.ShrunkBirthTerminal.count_9 +#print axioms KappaCheck.ShrunkBirthTerminal.count_10 +#print axioms KappaCheck.ShrunkBirthTerminal.count_11 +#print axioms KappaCheck.ShrunkBirthTerminal.count_12 +#print axioms KappaCheck.ShrunkBirthTerminal.count_13 +#print axioms KappaCheck.ShrunkBirthTerminal.count_14 +#print axioms KappaCheck.ShrunkBirthTerminal.count_15 +#print axioms KappaCheck.ShrunkBirthTerminal.count_16 +#print axioms KappaCheck.ShrunkBirthTerminal.count_17 +#print axioms KappaCheck.ShrunkBirthTerminal.count_18 +#print axioms KappaCheck.ShrunkBirthTerminal.count_19 +#print axioms KappaCheck.ShrunkBirthTerminal.count_20 +#print axioms KappaCheck.ShrunkBirthTerminal.count_21 +#print axioms KappaCheck.ShrunkBirthTerminal.count_22 +#print axioms KappaCheck.ShrunkBirthTerminal.count_23 +#print axioms KappaCheck.ShrunkBirthTerminal.count_529 +#print axioms KappaCheck.ShrunkBirthTerminal.count_552 +#print axioms KappaCheck.ShrunkBirthTerminal.count_554 +#print axioms KappaCheck.ShrunkBirthTerminal.count_556 +#print axioms KappaCheck.ShrunkBirthTerminal.count_558 +#print axioms KappaCheck.ShrunkBirthTerminal.count_560 +#print axioms KappaCheck.ShrunkBirthTerminal.count_562 +#print axioms KappaCheck.ShrunkBirthTerminal.count_571 +#print axioms KappaCheck.ShrunkBirthTerminal.count_572 +#print axioms KappaCheck.ShrunkBirthTerminal.count_573 +#print axioms KappaCheck.ShrunkBirthTerminal.count_574 +#print axioms KappaCheck.ShrunkBirthTerminal.complete_child_support +#print axioms KappaCheck.ShrunkBirthTerminal.strict_child_contraction +#print axioms KappaCheck.ShrunkBirthTerminal.slack_a_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_a_below_b +#print axioms KappaCheck.ShrunkBirthTerminal.slack_b_below_one_over32 +#print axioms KappaCheck.ShrunkBirthTerminal.slack_beta_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_beta_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_phase_leaf_above_bit +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_below_internal +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_below_leaf +#print axioms KappaCheck.ShrunkBirthTerminal.slack_c_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_c_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_q_below_reservations +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_above_tau +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_above_sigma +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_above_internal +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_prime_above_lambda +#print axioms KappaCheck.ShrunkBirthTerminal.slack_compact_leaf +#print axioms KappaCheck.ShrunkBirthTerminal.slack_compact_reservations +#print axioms KappaCheck.ShrunkBirthTerminal.slack_lambda_prime_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_epsilon_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_epsilon_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_guard_width +#print axioms KappaCheck.ShrunkBirthTerminal.slack_K_geometry +#print axioms KappaCheck.ShrunkBirthTerminal.slack_K_dominates_log +#print axioms KappaCheck.ShrunkBirthTerminal.slack_record_suffix +#print axioms KappaCheck.ShrunkBirthTerminal.slack_phase_local +#print axioms KappaCheck.ShrunkBirthTerminal.slack_phase_boundary +#print axioms KappaCheck.ShrunkBirthTerminal.slack_gamma_sublinear +#print axioms KappaCheck.ShrunkBirthTerminal.slack_cell_above_band +#print axioms KappaCheck.ShrunkBirthTerminal.slack_prime_interval_packing +#print axioms KappaCheck.ShrunkBirthTerminal.slack_alpha_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_alpha_below_one +#print axioms KappaCheck.ShrunkBirthTerminal.slack_alpha_below_one_fourth +#print axioms KappaCheck.ShrunkBirthTerminal.slack_delta_positive +#print axioms KappaCheck.ShrunkBirthTerminal.slack_delta_below_one_eighth +#print axioms KappaCheck.ShrunkBirthTerminal.slack_short_record_fallback +#print axioms KappaCheck.ShrunkBirthTerminal.slack_small_field_exposure +#print axioms KappaCheck.ShrunkBirthTerminal.slack_artificial_boundary +#print axioms KappaCheck.ShrunkBirthTerminal.slack_literal_scalar_guard +#print axioms KappaCheck.ShrunkBirthTerminal.slack_row_product_gap +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g1_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g2_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g3_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g4_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g5_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g6_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.slack_g7_above_kappa +#print axioms KappaCheck.ShrunkBirthTerminal.margins_strict +#print axioms KappaCheck.ShrunkBirthTerminal.balanced_identities +#print axioms KappaCheck.ShrunkBirthTerminal.stopped_parameter_choice +#print axioms KappaCheck.ShrunkBirthTerminal.controlling_margin +#print axioms KappaCheck.ShrunkBirthTerminal.fixed_profile_grid_exclusion +#print axioms KappaCheck.ShrunkBirthTerminal.gain_over_pinned_bounds +#print axioms KappaCheck.ShrunkBirthTerminal.stock_bit_coarse +#print axioms KappaCheck.ShrunkBirthTerminal.stock_complex +#print axioms KappaCheck.ShrunkBirthTerminal.stock_ordinary_leaf +#print axioms KappaCheck.ShrunkBirthTerminal.row_stock +#print axioms KappaCheck.ShrunkBirthTerminal.semantic_constants +#print axioms KappaCheck.ShrunkBirthTerminal.finite_bridge +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_1 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_1 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_2 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_2 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_3 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_3 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_4 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_4 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_5 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_5 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_6 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_6 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_7 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_7 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_8 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_8 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_9 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_9 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_10 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_10 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_11 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_11 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_12 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_12 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_13 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_13 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_14 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_14 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_15 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_15 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_16 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_16 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_17 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_17 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_18 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_18 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_19 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_19 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_20 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_20 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_21 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_21 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_22 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_22 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_23 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_23 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_529 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_529 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_552 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_552 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_554 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_554 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_556 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_556 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_558 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_558 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_560 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_560 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_562 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_562 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_571 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_571 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_572 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_572 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_573 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_573 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_interval_574 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_taylor_574 +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_profile_link +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_moment +#print axioms KappaCheck.ShrunkBirthTerminal.accepted_paid_moment +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_1 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_1 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_2 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_2 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_3 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_3 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_4 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_4 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_5 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_5 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_6 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_6 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_7 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_7 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_8 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_8 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_9 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_9 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_10 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_10 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_11 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_11 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_12 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_12 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_13 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_13 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_14 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_14 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_15 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_15 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_16 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_16 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_17 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_17 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_18 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_18 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_19 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_19 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_20 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_20 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_21 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_21 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_22 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_22 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_23 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_23 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_529 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_529 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_552 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_552 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_554 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_554 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_556 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_556 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_558 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_558 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_560 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_560 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_562 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_562 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_571 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_571 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_572 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_572 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_573 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_573 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_interval_574 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_taylor_574 +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_profile_link +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_moment +#print axioms KappaCheck.ShrunkBirthTerminal.rejected_paid_moment diff --git a/research/shrunk-birth-terminal/lean/generate.py b/research/shrunk-birth-terminal/lean/generate.py new file mode 100644 index 0000000000..ba5871d9b0 --- /dev/null +++ b/research/shrunk-birth-terminal/lean/generate.py @@ -0,0 +1,130 @@ +#!/usr/bin/env python3 +"""Generate a scoped Lean rational-arithmetic companion from input.json.""" +import json +from fractions import Fraction +from pathlib import Path +from hashlib import sha256 +HERE=Path(__file__).resolve().parent +data=json.loads((HERE/'input.json').read_text()); cert=data['certificate']; profile=cert['profile'] +out=[] +def emit(s=''):out.append(s) +def q(x): + f=Fraction(x);return str(f.numerator) if f.denominator==1 else f'({f.numerator} / {f.denominator})' +def proof(name,claim,defs=''): + emit(f'theorem {name} : {claim} := by\n norm_num [{defs}]\n') +def pairs(d):return '['+', '.join(f'({k}, {v})' for k,v in sorted(d.items(),key=lambda z:int(z[0])))+']' +emit('''import Mathlib.Tactic.NormNum +import Mathlib.Data.Nat.Choose.Basic + +/-! +Exact arithmetic companion for the shrunk-frame / birth-reuse / terminal-elision +composition. Prepared with OpenAI assistance. Upstream construction and analytic +credits are retained in the accompanying proof and source provenance. + +Scope: supplied physical-count arrays, all 47 parameter slacks, seven margins, +three row stocks, scalar guards and independent degree-eight moment arithmetic. +The physical-array derivation, real logarithm / exponential enclosure validity, +and all-size framed-word, stopped-product, tape, prime and recovery hypotheses +remain external. This is not an unconditional integer-multiplication theorem. +No sorry, native_decide or additional axioms are introduced. +-/ +namespace KappaCheck.ShrunkBirthTerminal +set_option maxRecDepth 20000 +set_option maxHeartbeats 8000000 +''') +for path,digest in data['pins'].items():emit(f'-- Source SHA256 {digest}: {path}') +emit('def h : ℕ := 24\ndef m : ℕ := h*h\ndef v : ℕ := Nat.choose h 3\ndef n : ℕ := v*v') +for name,val in [('virtualRoles',data['virtual_roles']),('births',data['births']),('terminals',data['terminals'])]:emit(f'def {name} : ℕ := {val}') +emit('def roles : ℕ := virtualRoles-births-terminals\ndef width : ℕ := 2*n+2*v*roles') +emit('def forwardHistogram : List (ℕ × ℕ) := '+pairs(data['forward_histogram'])) +emit('def initialDimensionHistogram : List (ℕ × ℕ) := '+pairs(data['initial_frame_dimension_histogram'])) +emit('''def counts : List (ℕ × ℕ) := + (forwardHistogram.map fun p => (p.1, 2*v*p.2)) ++ + (initialDimensionHistogram.map fun p => (m-h+p.1, 2*v*p.2)) ++ + [((h-1)^2, 2*n), (1, n)] +def count (t : ℕ) : ℕ := (counts.map fun p => if p.1=t then p.2 else 0).sum +def mass : ℕ := (counts.map fun p => p.1*p.2).sum +''') +cdefs='h, m, v, n, roles, width, virtualRoles, births, terminals, Nat.choose' +allc=cdefs+', mass, count, counts, forwardHistogram, initialDimensionHistogram' +proof('network_counts',f'h = 24 ∧ m = 576 ∧ v = 2024 ∧ n = 4096576 ∧ roles = {profile["R"]} ∧ width = {profile["W"]}',cdefs) +proof('initial_dimension_count','(initialDimensionHistogram.map Prod.snd).sum = roles',allc) +proof('rank_mass',f'mass = {profile["total_rank"]} ∧ m*width-mass = {profile["deficit"]} ∧ n-2*v*h*(h-1) = {profile["deficit"]}',allc) +for t,cnt in sorted(profile['child_multiplicities'].items(),key=lambda z:int(z[0])):proof(f'count_{t}',f'count {t} = {cnt}',allc) +sizes=sorted(map(int,profile['child_multiplicities']));emit(f'def childSizes : List ℕ := {sizes}') +proof('complete_child_support','∀ p ∈ counts, p.2 ≠ 0 → p.1 ∈ childSizes',allc+', childSizes') +proof('strict_child_contraction','∀ t ∈ childSizes, 0 < t ∧ t < m','childSizes, h, m') +for name,key in [('a','assembly_bit'),('b','complex_saving'),('kappa','kappa'),('eta','eta'),('beta','beta'),('backoff','backoff'),('actualBitSaving','actual_bit_saving')]:emit(f'def {name} : ℚ := {q(cert[key])}') +emit('''def tau : ℚ := 1-a +def sigma : ℚ := 1-b +def qParam : ℚ := a*(1-2*eta) +def lp : ℚ := 1-qParam +def c : ℚ := qParam+eta/4 +def epsilon : ℚ := (1-eta)/(1+qParam) +def lam : ℚ := (tau+lp)/2 +def g : ℚ := epsilon*qParam +def r : ℚ := (g+1-epsilon)/2 +def delta : ℚ := eta/8 +def internal : ℚ := tau+(1-beta)*max (sigma-tau) 0 +def leaf : ℚ := sigma+beta*(1-sigma) +''') +scalar=cert['finite_bridge']['complex']['scalar_group_upper'] +emit(f'def scalar : ℕ := {scalar}') +emit('''def guardE : ℕ := 64*(width+m+scalar+1)^3 +def guardB : ℕ := mass+guardE +def literal : ℕ := 2*scalar*width^2+8*mass+4*width+4+32*m +def guardC : ℕ := 32*m*guardB^2 +def literalGap : ℚ := (guardE : ℚ)-literal +def rowCoefficient : ℕ := 367*27+200*27+9*28 +def rowGap : ℚ := 32000-(51/25)*rowCoefficient +def margins : List ℚ := [1-epsilon,a,g,a,min (1-epsilon-delta) (r-delta),1-epsilon-delta,epsilon] +''') +defs='a, b, kappa, eta, beta, backoff, actualBitSaving, tau, sigma, qParam, lp, c, epsilon, lam, g, r, delta, internal, leaf, literalGap, rowGap, rowCoefficient, guardE, guardB, guardC, literal, scalar, '+allc +slacks = {'a_positive': 'a', 'a_below_b': 'b-a', 'b_below_one_over32': '1/32-b', 'beta_positive': 'beta', 'beta_below_one': '1-beta', 'phase_leaf_above_bit': '(1-beta)*b-a', 'q_positive': 'qParam', 'q_below_internal': '1-internal-qParam', 'q_below_leaf': '1-leaf-qParam', 'c_positive': 'c', 'c_below_one': '1-c', 'q_below_reservations': 'c-qParam', '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': 'qParam', 'epsilon_positive': 'epsilon', 'epsilon_below_one': '1-epsilon', 'guard_width': '1-epsilon', 'K_geometry': '1-epsilon*(1+c)', 'K_dominates_log': 'epsilon*c', 'record_suffix': '1-epsilon', 'phase_local': '1-epsilon-delta', 'phase_boundary': 'r-delta', 'gamma_sublinear': '1-epsilon-r', 'cell_above_band': 'epsilon-(1-r)/2', 'prime_interval_packing': '1-epsilon', 'alpha_positive': 'r', 'alpha_below_one': '1-r', 'alpha_below_one_fourth': '1/4-r', 'delta_positive': 'delta', 'delta_below_one_eighth': '1/8-delta', 'short_record_fallback': 'epsilon-a', 'small_field_exposure': '1-epsilon-g', 'artificial_boundary': '8-epsilon+r-delta-g', 'literal_scalar_guard': 'literalGap', 'row_product_gap': 'rowGap'} +margin_expr=['1-epsilon','a','g','a','min (1-epsilon-delta) (r-delta)','1-epsilon-delta','epsilon'] +for i,x in enumerate(margin_expr,1):slacks[f'g{i}_above_kappa']=f'({x})-kappa' +assert set(slacks)==set(cert['assembly']['constraints']) +for name,expr in slacks.items():proof('slack_'+name,f'({expr}) = ({q(cert["assembly"]["constraints"][name])} : ℚ) ∧ (0 : ℚ) < ({expr})',defs) +proof('margins_strict','∀ x ∈ margins, kappa < x','margins, '+defs) +proof('balanced_identities','1-epsilon-g = eta ∧ 1-epsilon-r = eta/2 ∧ 1-epsilon*(1+c) = eta-epsilon*eta/4',defs) +proof('stopped_parameter_choice','a = min actualBitSaving ((1-beta)*b-backoff) ∧ 0 < eta ∧ eta < 1/2',defs) +proof('controlling_margin','kappa < g ∧ g < kappa+1/1000000000000000000',defs) +proof('fixed_profile_grid_exclusion','(b+1/1000000000000000000000000)/(1+b+1/1000000000000000000000000) < kappa+1/1000000000000000000',defs) +proof('gain_over_pinned_bounds','kappa > (384569/10000000000 : ℚ) ∧ kappa > (52789616935221/1000000000000000000 : ℚ) ∧ kappa > (111192082577/1000000000000000 : ℚ) ∧ (1/2^14 : ℚ) < kappa ∧ kappa < (1/2^13 : ℚ)',defs) +bridge=cert['assembly']['finite_bridge'] +for name in ('bit_coarse','complex','ordinary_leaf'): + x=bridge[name];arity=x['m'];child=x['maxchild'];degree=x['halving_degree'];w=x['W'];bits=x['wire_bits'] + proof('stock_'+name,f'({arity}:ℕ)^{degree} > 2*{child}^{degree} ∧ ({arity}:ℕ)^{degree-1} ≤ 2*{child}^{degree-1} ∧ (2:ℕ)^{bits-1} ≤ {w} ∧ {w} < (2:ℕ)^{bits}') +proof('row_stock','rowCoefficient = 15561 ∧ rowGap = (6389/25 : ℚ) ∧ 4*(32000:ℕ) = 128000','rowCoefficient, rowGap') +sem=cert['finite_bridge']['semantic'] +proof('semantic_constants',f'guardE = {sem["E"]} ∧ guardB = {sem["B"]} ∧ guardC = {sem["C0"]} ∧ literal = {sem["literal_charge"]}',defs) +proof('finite_bridge','guardE > literal ∧ 2*guardB*(m-574) ≥ mass+guardE ∧ guardC > 2*guardB+18',defs) +emit('''-- The analytic meaning of supplied log intervals is external. These +-- statements prove exact rational Taylor inequalities and complete paid sums. +def taylor8 (x : ℚ) : ℚ := 1+x+x^2/2+x^3/6+x^4/24+x^5/120+x^6/720+x^7/5040+x^8/40320 +def expUpper (x : ℚ) : ℚ := taylor8 x+x^9/362880/(1-x/10) +''') +for typ,side,saving in [('accepted','upper','b'),('rejected','lower','(b+1/1000000000000000000000000)')]: + moment_data=cert['independent_moment'][typ];terms=moment_data['terms'];moment=[];recomputed=[] + assert Fraction(moment_data['saving'])==Fraction(cert['complex_saving'])+(Fraction(1,10**24) if typ=='rejected' else 0) + for t,item in sorted(terms.items(),key=lambda z:int(z[0])): + lo,hi=q(item['log_lower']),q(item['log_upper']);val=q(item['exp_'+side]);cnt=profile['child_multiplicities'][t] + emit(f'def {typ}_{t} : ℚ := {val}') + proof(f'{typ}_interval_{t}',f'(0 : ℚ) ≤ {saving}*{lo} ∧ {saving}*{lo} ≤ {saving}*{hi} ∧ {saving}*{hi} < 1','b') + expr=f'expUpper ({saving}*{hi}) ≤ {typ}_{t}' if side=='upper' else f'{typ}_{t} ≤ taylor8 ({saving}*{lo})' + proof(f'{typ}_taylor_{t}',expr,'expUpper, taylor8, b, '+f'{typ}_{t}') + assert Fraction(item['weight'])==Fraction(int(t)*cnt,profile['m']*profile['W']) + moment.append(f'(({t}*{cnt} : ℚ)/({profile["m"]}*{profile["W"]}))*{typ}_{t}') + recomputed.append(f'(({t}*(count {t} : ℚ))/(m*width))*{typ}_{t}') + emit(f'def {typ}Moment : ℚ :=\n '+' +\n '.join(moment)) + emit(f'def {typ}FromCounts : ℚ :=\n '+' +\n '.join(recomputed)) + proof(typ+'_profile_link',f'{typ}FromCounts = {typ}Moment',typ+'FromCounts, '+typ+'Moment, '+cdefs+', '+', '.join(f'count_{t}' for t in terms)) + comparison=f'{typ}Moment < 1' if typ=='accepted' else f'1 < {typ}Moment' + proof(typ+'_moment',f'{comparison} ∧ {typ}Moment = {q(moment_data[side])}',typ+'Moment, '+', '.join(f'{typ}_{t}' for t in terms)) + claim=f'{typ}FromCounts < 1' if typ=='accepted' else f'1 < {typ}FromCounts' + emit(f'theorem {typ}_paid_moment : {claim} := by\n rw [{typ}_profile_link]\n exact {typ}_moment.1\n') +emit('end KappaCheck.ShrunkBirthTerminal') +names=[line.split()[1] for line in '\n'.join(out).splitlines() if line.startswith('theorem ')] +for name in names:emit(f'#print axioms KappaCheck.ShrunkBirthTerminal.{name}') +path=HERE/'ShrunkBirthTerminal.lean';path.write_text('\n'.join(out)+'\n') +print(json.dumps({'theorems':len(names),'sha256':sha256(path.read_bytes()).hexdigest(),'input_sha256':sha256((HERE/'input.json').read_bytes()).hexdigest()})) diff --git a/research/shrunk-birth-terminal/lean/input.json b/research/shrunk-birth-terminal/lean/input.json new file mode 100644 index 0000000000..6b12efa8e6 --- /dev/null +++ b/research/shrunk-birth-terminal/lean/input.json @@ -0,0 +1,1693 @@ +{ + "births": 2108, + "certificate": { + "actual_bit_saving": "1240189553/10000000000000", + "assembly": { + "absorption_gap": "51350955350972219636574114327365369448123005318656908856664201698261131/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000", + "constraints": { + "K_dominates_log": "28203699512803856630705756229332904653617608320033448605133911713260786682305862261131/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000", + "K_geometry": "187528016199700303669130893284245532604957286739213317694137738869/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000", + "a_below_b": "56907455433006738869/500000000000000000000000000000000000000000000000", + "a_positive": "56407455433006738868999943092544566993261131/500000000000000000000000000000000000000000000000", + "alpha_below_one": "499999500000499999500000250027953699762803606630893284245532604957286739213317694137738869/500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000", + "alpha_below_one_fourth": "124957569450855794090053910101585400855367676522073307704325996653786739213317694137738869/500055907399525607213261786568491065209914573478426635388275477738000000000000000000000000", + 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'-198676998348790583970056778956880163156834281420556408837473537170738869/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000', 'g5_above_kappa': '-317883047341292714494408682352472290503615287298518210611967042990538869/400044725919620485770609429254792852167931658782741308310620382190400000000000000000000000', 'g6_above_kappa': '-1589414236594648773420828985238788315535946016663444096206564438401738869/2000223629598102428853047146273964260839658293913706541553101910952000000000000000000000000'}", + "old_prefix_rejection": "{'g1_above_kappa': '-28203699512803805279500377303413505275896650061379754949523635769612716700410026261131/250027953699762803606630893284245532604957286739213317694137738869000000000000000000000000'}", + "profile": { + "L": 2234496, + "N": 4096576, + "R": 26216, + "W": 114315520, + "child_multiplicities": { + "1": 435042608, + "10": 7735728, + "11": 6658960, + "12": 33578160, + "13": 13184336, + "14": 1821600, + "15": 3238400, + "16": 631488, + "17": 404800, + "18": 202400, + "19": 311696, + "2": 266771296, + "20": 550528, + "21": 1222496, + "22": 64768, + "23": 8383408, + "3": 29060592, + "4": 60639040, + "5": 26643936, + "529": 8193152, + "552": 97071040, + "554": 3456992, + "556": 1481568, + "558": 2384272, + "560": 445280, + "562": 48576, + "571": 740784, + "572": 101200, + "573": 28336, + "574": 364320, + "6": 15333824, + "7": 11743248, + "8": 22069696, + "9": 3938704 + }, + "deficit": 1862080, + "h": 24, + "m": 576, + "maxchild": 574, + "total_rank": 65843877440, + "v": 2024 + }, + "raw_discovery_metadata_in_certificate": false, + "raw_discovery_profile_sha256": "6a1ca866ddbb81c62f7fee08358849f2060e170bc48bae771da30d76eb9dc297" + }, + "forward_histogram": { + "1": 106459, + "2": 65902, + "3": 7179, + "4": 14980, + "5": 6582, + "6": 3788, + "7": 2901, + "8": 5452, + "9": 973, + "10": 1911, + "11": 1645, + "12": 8295, + "13": 3257, + "14": 450, + "15": 800, + "16": 156, + "17": 100, + "18": 50, + "19": 77, + "20": 136, + "21": 302, + "22": 16, + "23": 2071 + }, + "initial_frame_dimension_histogram": { + "0": 23980, + "2": 854, + "4": 366, + "6": 589, + "8": 110, + "10": 12, + "19": 183, + "20": 25, + "21": 7, + "22": 90 + }, + "pins": { + "work/r12-audit/canonical-joint-expansion/joint-expansion/certificate.json": "89b115978ab95d8e69e58472cde14a588157a3b3a8c577034c39ca0309eab34d", + "work/r12-terminal/joint-expansion/READOUT_COST.json": "3203dcb2709c3c8f1513c9ff31faafe9903f7ba14cdd7bbe1aaa38c9edbfcf43", + "work/r12-terminal/joint-expansion/physical-audit.json": "457287cf9986574cef50235644af77c893b3513e7a0872827b1cce352f4b62d5", + "work/r12-terminal/joint-expansion/word.json.gz": "11dfe85123d23c17b4e1f4309b7c5fdfdac55faef7563881f2f3db5b2dfae82e" + }, + "terminals": 381, + "virtual_roles": 28705 +} diff --git a/research/shrunk-birth-terminal/lean/receipts/compile/command.txt b/research/shrunk-birth-terminal/lean/receipts/compile/command.txt new file mode 100644 index 0000000000..7abe15821b --- /dev/null +++ b/research/shrunk-birth-terminal/lean/receipts/compile/command.txt @@ -0,0 +1 @@ +/bin/sh -c export\ PATH=/home/cfky/research/integer-mult/src/lean-arithmetic-20261009/lean-4.21.0-linux_aarch64/bin:\$PATH\;\ /usr/bin/time\ -v\ lake\ env\ lean\ ShrunkBirthTerminal.lean diff --git a/research/shrunk-birth-terminal/lean/receipts/compile/cwd.txt b/research/shrunk-birth-terminal/lean/receipts/compile/cwd.txt new file mode 100644 index 0000000000..96c46af568 --- /dev/null +++ b/research/shrunk-birth-terminal/lean/receipts/compile/cwd.txt @@ -0,0 +1 @@ +/home/cfky/research/integer-mult/src/lean-arithmetic-20261009/mathlib diff --git a/research/shrunk-birth-terminal/lean/receipts/compile/exit-code b/research/shrunk-birth-terminal/lean/receipts/compile/exit-code new file mode 100644 index 0000000000..573541ac97 --- /dev/null +++ b/research/shrunk-birth-terminal/lean/receipts/compile/exit-code @@ -0,0 +1 @@ +0 diff --git a/research/shrunk-birth-terminal/lean/receipts/compile/finished-at b/research/shrunk-birth-terminal/lean/receipts/compile/finished-at new file mode 100644 index 0000000000..9aed9befb3 --- /dev/null +++ b/research/shrunk-birth-terminal/lean/receipts/compile/finished-at @@ -0,0 +1 @@ +2026-10-09T02:09:30Z diff --git a/research/shrunk-birth-terminal/lean/receipts/compile/output.log b/research/shrunk-birth-terminal/lean/receipts/compile/output.log new file mode 100644 index 0000000000..f1b5779c9d --- /dev/null +++ b/research/shrunk-birth-terminal/lean/receipts/compile/output.log @@ -0,0 +1,265 @@ +'KappaCheck.ShrunkBirthTerminal.network_counts' depends on axioms: [propext] +'KappaCheck.ShrunkBirthTerminal.initial_dimension_count' depends on axioms: [propext] +'KappaCheck.ShrunkBirthTerminal.rank_mass' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_1' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_2' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_3' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_4' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_5' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_6' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_7' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_8' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_9' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_10' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_11' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_12' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_13' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_14' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_15' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_16' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_17' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_18' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_19' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_20' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_21' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_22' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_23' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_529' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_552' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_554' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_556' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_558' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_560' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_562' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_571' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_572' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_573' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.count_574' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.complete_child_support' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.strict_child_contraction' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_a_positive' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_a_below_b' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_b_below_one_over32' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_beta_positive' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_beta_below_one' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_phase_leaf_above_bit' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_q_positive' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_q_below_internal' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_q_below_leaf' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_c_positive' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_c_below_one' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_q_below_reservations' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_lambda_above_tau' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_lambda_above_sigma' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_lambda_above_internal' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_lambda_prime_above_lambda' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_compact_leaf' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_compact_reservations' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_lambda_prime_below_one' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_epsilon_positive' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_epsilon_below_one' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_guard_width' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_K_geometry' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_K_dominates_log' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_record_suffix' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_phase_local' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_phase_boundary' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_gamma_sublinear' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_cell_above_band' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_prime_interval_packing' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_alpha_positive' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_alpha_below_one' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_alpha_below_one_fourth' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_delta_positive' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_delta_below_one_eighth' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_short_record_fallback' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_small_field_exposure' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_artificial_boundary' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_literal_scalar_guard' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_row_product_gap' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_g1_above_kappa' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_g2_above_kappa' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_g3_above_kappa' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_g4_above_kappa' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_g5_above_kappa' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_g6_above_kappa' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.slack_g7_above_kappa' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.margins_strict' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.balanced_identities' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.stopped_parameter_choice' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.controlling_margin' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.fixed_profile_grid_exclusion' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.gain_over_pinned_bounds' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.stock_bit_coarse' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.stock_complex' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.stock_ordinary_leaf' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.row_stock' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.semantic_constants' depends on axioms: [propext, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.finite_bridge' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_1' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_1' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_2' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_2' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_3' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_3' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_4' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_4' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_5' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_5' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_6' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_6' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_7' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_7' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_8' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_8' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_9' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_9' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_10' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_10' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_11' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_11' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_12' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_12' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_13' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_13' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_14' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_14' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_15' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_15' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_16' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_16' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_17' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_17' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_18' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_18' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_19' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_19' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_20' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_20' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_21' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_21' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_22' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_22' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_23' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_23' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_529' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_529' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_552' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_552' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_554' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_554' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_556' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_556' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_558' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_558' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_560' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_560' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_562' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_562' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_571' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_571' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_572' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_572' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_573' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_573' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_interval_574' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_taylor_574' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_profile_link' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_moment' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.accepted_paid_moment' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_1' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_1' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_2' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_2' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_3' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_3' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_4' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_4' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_5' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_5' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_6' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_6' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_7' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_7' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_8' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_8' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_9' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_9' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_10' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_10' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_11' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_11' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_12' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_12' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_13' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_13' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_14' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_14' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_15' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_15' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_16' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_16' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_17' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_17' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_18' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_18' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_19' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_19' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_20' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_20' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_21' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_21' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_22' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_22' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_23' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_23' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_529' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_529' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_552' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_552' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_554' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_554' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_556' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_556' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_558' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_558' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_560' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_560' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_562' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_562' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_571' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_571' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_572' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_572' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_573' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_573' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_interval_574' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_taylor_574' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_profile_link' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_moment' depends on axioms: [propext, Classical.choice, Quot.sound] +'KappaCheck.ShrunkBirthTerminal.rejected_paid_moment' depends on axioms: [propext, Classical.choice, Quot.sound] + Command being timed: "lake env lean ShrunkBirthTerminal.lean" + User time (seconds): 93.43 + System time (seconds): 5.37 + Percent of CPU this job got: 528% + Elapsed (wall clock) time (h:mm:ss or m:ss): 0:18.71 + Average shared text size (kbytes): 0 + Average unshared data size (kbytes): 0 + Average stack size (kbytes): 0 + Average total size (kbytes): 0 + Maximum resident set size (kbytes): 1739568 + Average resident set size (kbytes): 0 + Major (requiring I/O) page faults: 0 + Minor (reclaiming a frame) page faults: 139632 + Voluntary context switches: 211341 + Involuntary context switches: 7841 + Swaps: 0 + File system inputs: 0 + File system outputs: 56 + Socket messages sent: 0 + Socket messages received: 0 + Signals delivered: 0 + Page size (bytes): 4096 + Exit status: 0 diff --git a/research/shrunk-birth-terminal/lean/receipts/compile/started-at b/research/shrunk-birth-terminal/lean/receipts/compile/started-at new file mode 100644 index 0000000000..6434ae25c6 --- /dev/null +++ b/research/shrunk-birth-terminal/lean/receipts/compile/started-at @@ -0,0 +1 @@ +2026-10-09T02:09:12Z diff --git a/research/shrunk-birth-terminal/lean/verification.json b/research/shrunk-birth-terminal/lean/verification.json new file mode 100644 index 0000000000..75fea25b44 --- /dev/null +++ b/research/shrunk-birth-terminal/lean/verification.json @@ -0,0 +1,27 @@ +{ + "allowed_axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "axiom_entries": 240, + "command": "lake env lean ShrunkBirthTerminal.lean", + "compile_receipts": { + "receipts/compile/command.txt": "0bc5d3265de4a8afb73591a2d5c313ffcc4210855e88a9247679d5113295c68d", + "receipts/compile/cwd.txt": "242fa456d9a4de42222da1163b40484b1c27e92be6abdfdba560024beaebcc54", + "receipts/compile/exit-code": "9a271f2a916b0b6ee6cecb2426f0b3206ef074578be55d9bc94f6f3fe3ab86aa", + "receipts/compile/finished-at": "0d2f6f65ebece2f9e00ba3d78a42a01f4165f89d551893473cfa7f731b743e80", + "receipts/compile/output.log": "cfa07d18b40149f8d3439017ae271463e5d1be8bd862c2634cf14907147e71b4", + "receipts/compile/started-at": "0ef9c485cf6b03d86a03c268efd04a438a374d941f7631dfc7b61a0de195165a" + }, + "exit_code": 0, + "generator_sha256": "e9d34fb5179c7d4fd7f4c12da813b7e3779a7e88286aee751fa9adb5b888bc95", + "input_sha256": "ecd604ec8f7185e7d23f2f2671f11b8aa9c1e3420e89e597d3a958fe613e9abf", + "kappa": "28200546274389/250000000000000000", + "lean": "4.21.0", + "mathlib_commit": "308445d7985027f538e281e18df29ca16ede2ba3", + "scope": "Rational arithmetic only; physical array derivation, real log/exp enclosure validity and all-size transfer remain external", + "source_sha256": "8c69d10ece16816edaef9df72182c9eecef3b464f88c82e0b8435f09c94ad095", + "status": "PASS", + "theorems": 240 +} diff --git a/research/shrunk-birth-terminal/pin_sources.py b/research/shrunk-birth-terminal/pin_sources.py new file mode 100644 index 0000000000..4c5dc4efb6 --- /dev/null +++ b/research/shrunk-birth-terminal/pin_sources.py @@ -0,0 +1,18 @@ +#!/usr/bin/env python3 +"""Explicitly freeze the complete portable source/input closure before verification.""" +from pathlib import Path +from hashlib import sha256 +import json +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +REPOSITORY_FILES=['.gitattributes','Makefile','.github/workflows/verify.yml','README.md','NOTICE','LICENSE','scripts/check_lean_axioms.py','tests/test_shrunk_birth_terminal.py','formal/lean/KappaCheck.lean','formal/lean/KappaCheck/ShrunkBirthTerminal.lean','formal/lean/AuditAll.lean','formal/lean/sources.py','formal/lean/SOURCES.md','research/joint-dual/SOURCE.json','certificates/joint-dual-kappa.json','certificates/joint-dual-validation.json'] +def sha(p):return sha256(p.read_bytes()).hexdigest() +def main(): + files={str(p.relative_to(HERE)):sha(p) for p in sorted(HERE.rglob('*')) if p.is_file() and p.name!='SOURCE.json' and '__pycache__' not in p.parts and p.suffix!='.pyc'} + # Archived source manifests are data and must themselves be pinned. + for p in HERE.rglob('SOURCE.json'): + if p!=HERE/'SOURCE.json':files[str(p.relative_to(HERE))]=sha(p) + record={'schema':1,'author':'Chafik Boukhalfa with OpenAI Codex assistance','base_commit':'56b66d58297deca1d7dd130247d720e960f77a37','scope':'Complete selected finite construction, portable reproduction, exact arithmetic, original sources and scoped Lean companion. Repository-validation receipts are derived and excluded from this freeze.','package_files':dict(sorted(files.items())),'repository_files':{p:sha(ROOT/p) for p in sorted(REPOSITORY_FILES)}} + (HERE/'SOURCE.json').write_text(json.dumps(record,indent=2,sort_keys=True)+'\n') + print('Pinned',len(files),'package files and',len(REPOSITORY_FILES),'repository integration files') +if __name__=='__main__':main() diff --git a/research/shrunk-birth-terminal/references/CONTRIBUTOR-PINS.json b/research/shrunk-birth-terminal/references/CONTRIBUTOR-PINS.json new file mode 100644 index 0000000000..ebdaee0e63 --- /dev/null +++ b/research/shrunk-birth-terminal/references/CONTRIBUTOR-PINS.json @@ -0,0 +1,108 @@ +{ + "bit_word_repository": { + "author_login": "Swapnil-jain", + "role": "Repository owner of the retained round-seven bit word; pinned scientific source remains the archived commit", + "url": "https://github.com/Swapnil-jain/integer-mult-kappa" + }, + "pull_requests": [ + { + "author_login": "jacklightChen", + "head_when_credit_checked": "661ebabc1076c9f525d7ce4967c876b203fa9827", + "number": 23, + "title": "Semantic precision and bulk resampling for a conditional 1099/10^8 > 2^-17 bound", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/23" + }, + { + "author_login": "jacklightChen", + "head_when_credit_checked": "9d963275075fa98f1da821e27757b238dafd6b3c", + "number": 29, + "title": "Two-stage controlled corners for a conditional 15536/10^9 > 2^-16 bound", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/29" + }, + { + "author_login": "jamesyc", + "head_when_credit_checked": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "number": 34, + "title": "Reversed two-stage basis and balanced assembly for conditional \u03ba = 1.639226629e-5", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/34" + }, + { + "author_login": "hipotures", + "head_when_credit_checked": "03bde70c0c2a453f1ceae20c619b602841405467", + "number": 41, + "title": "Alternating pair-block networks for conditional \u03ba = 4.034168124 \u00d7 10\u207b\u2075 > 2\u207b\u00b9\u2075", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/41" + }, + { + "author_login": "rohanarun", + "head_when_credit_checked": "22dc19dd7123dd582110a912a6ca687e31e2243f", + "number": 100, + "title": "Balanced transfer of deferred signed networks: conditional \u03ba = 6.3978919675787e-5", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/100" + }, + { + "author_login": "rohanarun", + "head_when_credit_checked": "75ab1f70d146c21c7611ce0df9eb5f645f51ac0e", + "number": 103, + "title": "Saturated readouts with complete signed/balanced integration: conditional \u03ba = 6.398282083297e-5", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/103" + }, + { + "author_login": "icekylinx", + "head_when_credit_checked": "948ce1510df750f4c18b96bdaef436a86f8bf834", + "number": 104, + "title": "Stopped product-ring interchange and rational centers for conditional kappa = 7.79476e-5", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/104" + }, + { + "author_login": "ikeboy", + "head_when_credit_checked": "09775e9f3fbf1900175010bcd0c3d6d1dbf65ffe", + "number": 110, + "title": "Deferred readouts on both stopped networks: conditional \u03ba = 8.58478e-5", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/110" + }, + { + "author_login": "eumemic", + "head_when_credit_checked": "cbb05ce504d571546d9b7794c186a613c659c3bf", + "number": 117, + "title": "Deferred bit word and a 28,705-role complex producer under stopped-product accounting: conditional \u03ba = 1.044939e-4", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/117" + }, + { + "author_login": "rohanarun", + "head_when_credit_checked": "6ec868e8568ca9a74b7245494de1b187c7be78fe", + "number": 118, + "title": "Deferred readouts on PR117\u2019s complex producer: conditional \u03ba = 1.085428e-4", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/118" + }, + { + "author_login": "SovereignSteak", + "head_when_credit_checked": "b1a6f24e57141637b3ff040d6f2ce9d896ffb9bb", + "number": 122, + "title": "Terminal accumulator elimination with exact majorization audit", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/122" + }, + { + "author_login": "jamesyc", + "head_when_credit_checked": "3657b5d62fabc0bd2b1c596ad86b97002e437ea8", + "number": 124, + "title": "Birth-read slot recycling: conditional kappa 1.1038332094346e-4", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/124" + }, + { + "author_login": "GamingPuzzled", + "head_when_credit_checked": "dda535bdcfc321a13a1ebd3c2d70e2b5bb72368e", + "number": 125, + "title": "Shrunk lifted frames with saturated deferral: conditional \u03ba = 1.10591581647e-4", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/125" + }, + { + "author_login": "DanieleCorso", + "head_when_credit_checked": "31ceb5ead3055ea780e13654b05b546d26c3d6ed", + "number": 126, + "title": "Physical operation frames with deferred readouts: conditional \u03ba = 1.11192082577e-4", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/126" + } + ], + "scope": "Actual GitHub account attribution verified from submitted PR metadata and the bit-word repository owner. These are GitHub handles, not inferred identities or review endorsements. This narrow attribution check is not the final PR frontier refresh." +} diff --git a/research/shrunk-birth-terminal/references/ORIGINAL-NOTICES.json b/research/shrunk-birth-terminal/references/ORIGINAL-NOTICES.json new file mode 100644 index 0000000000..96e321cd20 --- /dev/null +++ b/research/shrunk-birth-terminal/references/ORIGINAL-NOTICES.json @@ -0,0 +1,65 @@ +[ + { + "author": "SovereignSteak", + "commit": "b1a6f24e57141637b3ff040d6f2ce9d896ffb9bb", + "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64", + "path": "LICENSE", + "pull_request": 122, + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "stored_path": "references/pr122/LICENSE" + }, + { + "author": "SovereignSteak", + "commit": "b1a6f24e57141637b3ff040d6f2ce9d896ffb9bb", + "git_blob": "50c6d1236d1b47caf32bb1e9eafa0804722267e9", + "path": "NOTICE", + "pull_request": 122, + "sha256": "46b84a2254d554c8adbe67ddaf33640e1b99e31168a1d90305d470e4fdab8e23", + "stored_path": "references/pr122/NOTICE" + }, + { + "author": "jamesyc", + "commit": "f36782865dfe81abaa40254e8f41b8ccb3c54556", + "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64", + "path": "LICENSE", + "pull_request": 124, + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "stored_path": "references/pr124/LICENSE" + }, + { + "author": "jamesyc", + "commit": "f36782865dfe81abaa40254e8f41b8ccb3c54556", + "git_blob": "50c6d1236d1b47caf32bb1e9eafa0804722267e9", + "path": "NOTICE", + "pull_request": 124, + "sha256": "46b84a2254d554c8adbe67ddaf33640e1b99e31168a1d90305d470e4fdab8e23", + "stored_path": "references/pr124/NOTICE" + }, + { + "author": "jamesyc", + "commit": "f36782865dfe81abaa40254e8f41b8ccb3c54556", + "git_blob": "2f65bed9a8133ed74a2f08c65a20e6b26ba38a7d", + "path": "research/birth-read-reuse/PROOF.md", + "pull_request": 124, + "sha256": "b9182866812a046563da3ab3c7f0a0f29ccf9abe7a20816343a07c7a3d997126", + "stored_path": "references/pr124/research/birth-read-reuse/PROOF.md" + }, + { + "author": "GamingPuzzled", + "commit": "dda535bdcfc321a13a1ebd3c2d70e2b5bb72368e", + "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64", + "path": "LICENSE", + "pull_request": 125, + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "stored_path": "references/pr125/LICENSE" + }, + { + "author": "GamingPuzzled", + "commit": "dda535bdcfc321a13a1ebd3c2d70e2b5bb72368e", + "git_blob": "50c6d1236d1b47caf32bb1e9eafa0804722267e9", + "path": "NOTICE", + "pull_request": 125, + "sha256": "46b84a2254d554c8adbe67ddaf33640e1b99e31168a1d90305d470e4fdab8e23", + "stored_path": "references/pr125/NOTICE" + } +] diff --git a/research/shrunk-birth-terminal/references/discovery-construction/compose_terminal.py b/research/shrunk-birth-terminal/references/discovery-construction/compose_terminal.py new file mode 100644 index 0000000000..ce9b30c8bd --- /dev/null +++ b/research/shrunk-birth-terminal/references/discovery-construction/compose_terminal.py @@ -0,0 +1,317 @@ +#!/usr/bin/env python3 +"""Compose disjoint terminal elimination with an exact shrunk/birth word. + +Original terminal-elision identity: SovereignSteak, PR122. +Shrunk frames: Joel Pulikkan, PR125. Birth reuse: James Chang, PR124. +PR117 DAG: eumemic; deferred compiler: Avi Eisenberg and Rohan Arun. +This explicit composition, complete word/profile checks and all-column +response audit were prepared with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +from functools import lru_cache +from hashlib import sha256 +import argparse, gzip, json, pickle, resource, subprocess, sys, time + +assert not sys.flags.optimize, 'Assertions must remain enabled' +W=Path(__file__).resolve().parent +p=argparse.ArgumentParser(description=__doc__) +p.add_argument('--frames',type=Path,required=True) +p.add_argument('--matches',type=Path,required=True) +p.add_argument('--readouts',type=Path,default=W/'baseline/READOUTS.pkl') +p.add_argument('--scalar-bill',type=Path,default=W/'baseline/READOUT_COST.json') +p.add_argument('--out',type=Path,required=True) +p.add_argument('--terminal-roles',type=Path,help='JSON list of exact terminal IDs; validated after supplied real birth matches.') +a=p.parse_args();start=time.monotonic();O=a.out.resolve();O.mkdir(parents=True,exist_ok=False) +source_directory=O/'construction-sources';source_directory.mkdir() +source_bytes={q.name:q.read_bytes() for q in [Path(__file__),W/'terminal_inventory.py']} +for name,data in source_bytes.items():(source_directory/name).write_bytes(data) +inputs=O/'inputs';inputs.mkdir();pins={} +for source,name in [(a.frames,'FRAMES.pkl'),(a.matches,'BIRTH_MATCHES.json.gz'),(a.readouts,'READOUTS.pkl'),(a.scalar_bill,'READOUT_COST.json')]: + data=source.read_bytes();(inputs/name).write_bytes(data);assert source.read_bytes()==data + pins[name]={'source_path':str(source.resolve()),'sha256':sha256(data).hexdigest(),'bytes':len(data)} +selection_args=[] +if a.terminal_roles: + data=a.terminal_roles.read_bytes();(inputs/'TERMINAL_ROLES.json').write_bytes(data);assert a.terminal_roles.read_bytes()==data + pins['TERMINAL_ROLES.json']={'source_path':str(a.terminal_roles.resolve()),'sha256':sha256(data).hexdigest(),'bytes':len(data)} + selection_args=['--terminal-roles',str(inputs/'TERMINAL_ROLES.json')] +subprocess.run([sys.executable,str(source_directory/'terminal_inventory.py'),'--frames',str(inputs/'FRAMES.pkl'),'--matches',str(inputs/'BIRTH_MATCHES.json.gz'),'--readouts',str(inputs/'READOUTS.pkl'),'--out',str(O/'inventory.json'),*selection_args],check=True,stdout=subprocess.DEVNULL) +inventory=json.loads((O/'inventory.json').read_text()) +g=pickle.loads((inputs/'FRAMES.pkl').read_bytes());readouts=pickle.loads((inputs/'READOUTS.pkl').read_bytes()) +choice=json.loads(gzip.decompress((inputs/'BIRTH_MATCHES.json.gz').read_bytes())) +bill=json.loads((inputs/'READOUT_COST.json').read_text()) +R=len(g['first']);v=g['v'];h=g['h'];m=h*h;N=v*v +merge={r['recipient']:r['donor'] for r in choice['pairs']} +removed={r['role'] for r in inventory['selected']};selected={r['role']:r for r in inventory['selected']} +assert removed and not removed & (set(merge)|set(merge.values())) +live=set(range(R))-set(merge)-removed +assert len(live)==choice['R']-len(removed) +physical=lambda s:2*v+merge.get(s,s) + +frames=[()];ids={():0} +def fid(F): + F=tuple(F) + if F not in ids:ids[F]=len(frames);frames.append(F) + return ids[F] +def basis(rows): + piv={} + for x in rows: + for q in sorted(piv,reverse=True): + if x>>q&1:x^=piv[q] + if x: + q=x.bit_length()-1 + for r in piv: + if piv[r]>>q&1:piv[r]^=x + piv[q]=x + return tuple(piv[q] for q in sorted(piv,reverse=True)) +FULL=fid(tuple(1<>j&1:x|=1<<(r.bit_length()-1) + out.append(x) + return fid(basis(out)) +@lru_cache(None) +def nested(i,j): + for x in frames[i]: + for r in frames[j]: + if x>>(r.bit_length()-1)&1:x^=r + if x:return False + return True +@lru_cache(None) +def nondeg(i): + A=frames[i] + return len(basis(sum(((x&y).bit_count()&1)<=2*v and d-2*v in live + e=('g',d,s,sign,F);word.append(e) + if remember:forward_workspace.append(e) +def oldread(s,F): + mask=ALL if g['reach_all'][s] else g['reach'][s] + if s in removed: + assert mask==1<0 + hist[r]+=1;current[s]=F;incidences+=1 + if s<2*v: + bank=s//v;counts[bank][old]-=1 + if not counts[bank][old]:del counts[bank][old] + counts[bank][F]+=1 + def targets(bank,mask,F): + assert bank in (0,v) and mask>=0 and not(mask&~ALL) + if len(counts[bank//v])==1 and counts[bank//v].get(F)==v:return + while mask: + b=mask&-mask;mask-=b;promote(bank+b.bit_length()-1,F) + for e in events: + digest.update(repr(e).encode()) + if e[0]=='g': + _,d,s,c,F=e;assert c in (-1,1);promote(d,F);promote(s,F) + elif e[0]=='d': + _,d,s,c,F,idx,role=e;assert c in (-21,21);promote(d,F);promote(s,F) + elif e[0]=='r': + _,s,bank,mask,sign,F,key=e;promote(s,F);targets(bank,mask,F) + elif e[0]=='f': + _,bank,mask,F,key=e;targets(bank,mask,F) + else: + _,s,bank,mask,sign,F,T,key=e;promote(s,F);targets(bank,mask,T) + assert (F==FULL and T==0) or nested(F,T) or nested(T,F) + rank=abs(len(frames[F])-len(frames[T]));assert rank==h-1;hist[rank]+=1;copies+=1 + for s in active:promote(s,end[s]) + assert current==end + return {'histogram':dict(hist),'copies':copies,'transitions':incidences,'word_sha256':digest.hexdigest()} + +forward=scan(word,initial,finish) +def swap(s):return s+v if s=sum(before_sorted[:k]) for k in range(1,5)) + assert before_sorted!=after_sorted + for width in before: + if width:delta[width]-=2*v + # The width-m term is only the padding used to compare changing W. + if F0>M:delta[F0-M]+=2*v + packets.append({'role':row['role'],'target':row['target'],'old':before,'new_with_dummy_m':after}) +expected=Counter(oldH) +expected.update(delta);expected=Counter({r:n for r,n in expected.items() if n}) +assert all(n>=0 for n in expected.values()) and H==expected,('Full profile != exact complete packet sum',H-expected,expected-H) +newR=len(live);newW=2*v*v+2*v*newR;rank=sum(r*n for r,n in H.items()) +assert m*newW-rank==choice['deficit']==g['base_profile']['deficit'] +hinges={k:sum(min(r,k)*n for r,n in H.items())+2*v*len(removed)*min(m,k)-sum(min(r,k)*n for r,n in oldH.items()) for k in range(1,m+1)} +assert all(x<=0 for x in hinges.values()) and min(hinges.values())<0 + +def plus(a,b): + out=[];carry=0 + for i in range(max(len(a),len(b))): + x=a[i] if i>i&1 else 0 for i in range(n.bit_length())) + +def responses(events,inputbank,outputbank,expected_sign): + P,M=[()]*R,[()]*R;XP,XM=[()]*v,[()]*v + def accumulate(aux,positive,negative): + assert aux>=2*v and aux-2*v in live + r=aux-2*v;P[r],M[r]=plus(P[r],positive),plus(M[r],negative) + for e in reversed(events): + kind=e[0] + if kind=='f':continue + if kind in ('r','c'): + aux,bank,sign=e[1],e[2],e[4];assert bank==outputbank + key=e[-1] + if key[0]=='old':s=key[1];seed=False + elif key[0]=='side':s=key[2];seed=True + else:s=next(s for s in g['center_roles'] if g['terminal'][s]==len(g['roots'])-h+key[1]);seed=True + aa=readouts['terminal_positive' if seed else 'positive'][s] + bb=readouts['terminal_negative' if seed else 'negative'][s] + if sign<0:aa,bb=bb,aa + accumulate(aux,aa,bb) + elif kind=='d': + _,dst,src,num,F,idx,role=e + assert outputbank<=dst=2*v + aa,bb=P[dst-2*v],M[dst-2*v] + if sign<0:aa,bb=bb,aa + if src>=2*v:accumulate(src,aa,bb) + else: + assert inputbank<=src0:source_ok=all(aa==plus(bb,scaled(1<=bill['global_scalar_group_upper'] +profile=dict(g['base_profile']);profile.update(R=newR,W=newW,total_rank=rank,maxchild=max(H),child_multiplicities=dict(sorted(H.items())),pre_terminal_physical_roles=choice['R'],virtual_roles=R,birth_reuses=len(merge),terminal_eliminations=len(removed),terminal_direct_updates=len(direct_origins),deferred_roles=len(g['placed'])-len(removed),role_count_scope='Explicit physical birth-reused and terminal-elided word; DAG role formula is the pre-composition virtual count.',replay={'method':'Exact signed bit-plane all-column responses over Q, both orientations','source_columns':v,'dirty_columns':newR,'target_columns':v,'forward_signed_identity':1,'reflected_signed_identity':-1,'scratch_restored':True}) +dd=Counter({int(k):n for k,n in profile['deferred_dims'].items()}) +for row in inventory['selected']:dd[row['sigma']]-=1 +profile['deferred_dims']=dict(sorted((k,n) for k,n in dd.items() if n)) +scalar_bill={**{k:value for k,value in bill.items() if k not in {'rss_KiB','rss_bytes','seconds'}},'status':'PASS conservative scalar upper bound for new terminal composition','inherited_local_scalar_upper':bill['local_scalar_upper'],'terminal_direct_updates':len(direct_origins),'terminal_extra_scalar_charge':extra_scalar,'local_scalar_upper':newlocal,'global_scalar_group_upper':newG,'terminal_charge_rule':'Keep the entire inherited scalar bill and add 29 groups per direct output update: 21 same-frame shears of coefficient +/-1/42, plus eight conservative bookkeeping groups. No new role, source copy or frame incidence is introduced; denominator42 and odd21 grid are unchanged.','expansion':'Each numerator n/42 is |n| same-frame shears of coefficient sign(n)/42, with no new roles, source copies or frame transitions. Reverse all workspace/source gates chronologically. The retained eight-scan allowance, factor16 and explicit endpoint groups conservatively bound scalar bookkeeping/wrappers. Direct terminal updates use the same expansion, with eight additional bookkeeping groups per update.','original_bill_sha256':pins['READOUT_COST.json']['sha256']} +physical_record={'status':'PASS new composed literal word, full exact source/dirty responses and complete paid frames in both orientations','physical_roles':newR,'virtual_roles':R,'birth_reuses_preserved':len(merge),'terminal_roles_eliminated':len(removed),'distinct_terminal_targets':len({r['target'] for r in inventory['selected']}),'source_columns':v,'dirty_columns':newR,'target_columns':v,'coefficient_denominator':42,'direct_output_coefficient_numerators':[-21,21],'word_blocks':len(word),'forward_workspace_gates':len(forward_workspace),'forward_frame':forward,'reflected_frame':backward,'forward_scalar':forward_scalar,'reflected_scalar':reverse_scalar,'mutations':{'omitted_redirect_rejected':True,'wrong_redirect_sign_rejected':True,'illegal_redirect_frame_rejected':illegal_frame_rejected},'no_birth_slot_removed':True,'source_reads_at_original_operation_indices':True,'target_never_controls':True,'inverse_exact_reverse_of_actual_retained_workspace_events':True,'rank_deficit_preserved':True,'complete_profile_equals_packet_sum':True,'all_integer_hinges_nonpositive':True,'minimum_hinge':min(hinges.values()),'all_packets_sigma_equal_M_equal_F0':all(r['sigma']==r['M']==r['F0'] for r in inventory['selected']),'seconds':time.monotonic()-start,'input_pins':pins,'scope':'Finite exact composed physical witness and conservative scalar accounting; inherited all-size, fixed-tape, stopped-product and analytic transfer remain hypotheses. New kappa must be assembled separately.'} +payload={'h':h,'v':v,'virtual_roles':R,'physical_roles':sorted(live),'eliminated_terminal_roles':sorted(removed),'birth_pairs':choice['pairs'],'frames':[list(F) for F in frames],'initial_frames':initial,'final_frames':finish,'word':word,'direct_source_bindings':direct_origins,'input_sha256':{k:x['sha256'] for k,x in pins.items()}} +wordbytes=gzip.compress(json.dumps(payload,separators=(',',':')).encode(),mtime=0);(O/'word.json.gz').write_bytes(wordbytes) +physical_record['word_file_sha256']=sha256(wordbytes).hexdigest() +physical_record['seconds']=time.monotonic()-start +physical_record['rss_bytes']=resource.getrusage(resource.RUSAGE_SELF).ru_maxrss*(1024 if sys.platform=='linux' else 1) +for name,x in [('complex-profile.json',profile),('READOUT_COST.json',scalar_bill),('physical-audit.json',physical_record),('majorization.json',{'packets':packets,'hinges':hinges,'profile_delta':dict(sorted(delta.items())),'padding_per_removed_role':m,'replication':2*v})]: + (O/name).write_text(json.dumps(x,indent=2,sort_keys=True)+'\n') +assert all((W/name).read_bytes()==data for name,data in source_bytes.items()), 'Construction sources changed during this run' +sources={str(Path('construction-sources')/name):sha256(data).hexdigest() for name,data in source_bytes.items()} +(O/'SOURCE.json').write_text(json.dumps({'inputs':pins,'construction_sources':sources,'source_attribution':'PR122 terminal-elision identity; PR125 shrunk frames; PR124 birth reuse; PR117 scalar DAG; this new explicit composition and audits with OpenAI Codex assistance.'},indent=2,sort_keys=True)+'\n') +print(json.dumps({k:physical_record[k] for k in ['status','physical_roles','birth_reuses_preserved','terminal_roles_eliminated','source_columns','dirty_columns','word_blocks','all_packets_sigma_equal_M_equal_F0','seconds','word_file_sha256']}|{'W':newW,'total_rank':rank,'deficit':m*newW-rank,'G':newG,'output':str(O)},indent=2)) diff --git a/research/shrunk-birth-terminal/references/discovery-construction/terminal_inventory.py b/research/shrunk-birth-terminal/references/discovery-construction/terminal_inventory.py new file mode 100644 index 0000000000..519b0e4dd4 --- /dev/null +++ b/research/shrunk-birth-terminal/references/discovery-construction/terminal_inventory.py @@ -0,0 +1,101 @@ +"""Bounded PR122-style terminal inventory on our shrunk+birth composition. + +PR122 terminal identity: SovereignSteak; PR125 frames: Joel Pulikkan; +PR124 birth reuse: James Chang; PR117 DAG: eumemic. This compatibility +inventory and conservative disjoint selection are new composition work. +""" +from pathlib import Path +from collections import Counter, defaultdict +from functools import lru_cache +from hashlib import sha256 +import argparse, gzip, json, pickle + +W=Path(__file__).resolve().parent +B=W/'baseline' +p=argparse.ArgumentParser(description=__doc__) +p.add_argument('--frames',type=Path,default=B/'FRAMES.pkl') +p.add_argument('--matches',type=Path,default=B/'BIRTH_MATCHES.json.gz') +p.add_argument('--readouts',type=Path,default=B/'READOUTS.pkl') +p.add_argument('--out',type=Path,default=W/'inventory.json') +p.add_argument('--include-birth-recipients',action='store_true',help='Expose virtual terminal options for joint optimization; these options are not a simultaneous legal elimination selection.') +p.add_argument('--terminal-roles',type=Path,help='JSON list of exact terminal role IDs to eliminate; requires ordinary disjoint eligibility.') +a=p.parse_args() +assert not (a.include_birth_recipients and a.terminal_roles), 'Joint options and a validated physical selection are distinct modes' +g=pickle.loads(a.frames.read_bytes()) +readouts=pickle.loads(a.readouts.read_bytes()) +choice=json.loads(gzip.decompress(a.matches.read_bytes())) +assert choice['source_frame_checkpoint_sha256']==sha256(a.frames.read_bytes()).hexdigest() +R=len(g['first']);v=g['v'];h=g['h'];m=h*h +merge={r['recipient']:r['donor'] for r in choice['pairs']} + +@lru_cache(None) +def contains(A,B): + for x in A: + for r in B: + if x>>(r.bit_length()-1)&1:x^=r + if x:return False + return True + +incoming=defaultdict(list);outgoing=Counter() +for i,(op,s,t,x) in enumerate(g['ops']): + if op==1:dst,src=s,t + elif op==2:dst,src=t,s + else:continue + incoming[dst].append((i,src,x));outgoing[src]+=1 + +target_front=[() for _ in range(v)] +for s,F in sorted(g['placed'].items(),key=lambda z:(len(z[1]),z[0])): + targets=g['reach'][s] + while targets: + b=targets&-targets;targets-=b;t=b.bit_length()-1 + assert contains(target_front[t],F) + target_front[t]=F + +def scaled(mask,n):return tuple(mask if n>>i&1 else 0 for i in range(n.bit_length())) + +blocked=Counter();eligible=[] +for s,j in sorted(g['terminal'].items()): + if j>=len(g['roots'])-h:blocked['center_root']+=1;continue + if outgoing[s]:blocked['controls_auxiliary']+=1;continue + if s in merge and not a.include_birth_recipients:blocked['physical_slot_shared_as_birth_recipient']+=1;continue + assert s not in set(merge.values()) + if s not in g['placed']:blocked['not_deferred']+=1;continue + if g['first'][s]<=v:blocked['source_injection_excluded_from_this_bounded_pass']+=1;continue + if not incoming[s]:blocked['no_incoming_update']+=1;continue + if any(i in g['phase'] for i,_,_ in incoming[s]):blocked['early_update']+=1;continue + assert s not in g['touched'] + t=g['targets'][j];sign=1 if j0 else ()) + assert readouts['negative'][s]==(expected if sign<0 else ()) + F0=g['U'][incoming[s][0][2]];M=target_front[t];sigma=g['placed'][s] + if not contains(M,F0):blocked['target_front_past_first_update']+=1;continue + fs=[M]+[g['U'][x] for _,_,x in incoming[s]] + assert all(contains(a,b) for a,b in zip(fs,fs[1:])),s + assert contains(sigma,M) and len(fs[-1])<=h-1 + if a.include_birth_recipients and not len(sigma)==len(M)==len(F0):blocked['unequal_packet_dimensions_excluded_from_joint_options']+=1;continue + eligible.append({'role':s,'target':t,'root_index':j,'coefficient_numerator':21*sign,'sigma':len(sigma),'M':len(M),'F0':len(F0),'incoming_operations':[i for i,_,_ in incoming[s]],'incoming_count':len(incoming[s]),'frames':[list(F) for F in fs],'current_birth_donor':merge.get(s),'terminal_local_scalar_charge':29*len(incoming[s]),'packet_replication':2*v,'old_packet':[m-h+len(sigma),1,len(F0)-len(sigma),h-1-len(M)],'padded_new_packet':[m,len(F0)-len(M),0,0]}) + +# One terminal per target gives disjoint target-front packets; this avoids +# treating individually legal but interleaved output paths as simultaneous. +bytarget=defaultdict(list) +for row in eligible:bytarget[row['target']].append(row) +selected=[min(group,key=lambda x:x['role']) for _,group in sorted(bytarget.items())] +if a.terminal_roles: + requested=json.loads(a.terminal_roles.read_text()) + assert isinstance(requested,list) and all(type(s) is int for s in requested), 'Selection must be a JSON list of integer role IDs' + assert len(requested)==len(set(requested)), 'Duplicate terminal role ID' + rows={row['role']:row for row in eligible} + assert set(requested)<=rows.keys(), f'Ineligible requested terminal roles: {sorted(set(requested)-rows.keys())}' + selected=[rows[s] for s in sorted(requested)] + assert len({row['target'] for row in selected})==len(selected), 'Selected terminals must have distinct targets' + assert not set(requested)&(set(merge)|set(merge.values())), 'Selected terminals must have no birth aliases' +record={'status':'PASS exact local eligibility and disjoint-target selection on new composition inputs','base_virtual_roles':R,'base_physical_roles':choice['R'],'birth_merges_preserved':len(merge),'eligible_unshared_terminal_roles':len(eligible),'selected_terminal_roles':len(selected),'selected_targets':len(bytarget),'blocked':dict(blocked),'selection_rule':'Lowest eligible role id per target; no frame, deferral or birth matching changes.','selected':selected,'eligible':eligible,'expected_physical_roles':choice['R']-len(selected),'input_sha256':{str(p):sha256(p.read_bytes()).hexdigest() for p in [a.frames,a.readouts,a.matches]}} +if a.terminal_roles: + record.update(selection_rule='Exact requested role-ID subset, validated against ordinary unshared eligibility and distinct targets',selected_targets=len(selected),selection_sha256=sha256(a.terminal_roles.read_bytes()).hexdigest()) +if a.include_birth_recipients: + record.update(status='PASS virtual eligibility options for joint birth/terminal optimization; not a legal simultaneous elimination selection',joint_optimization_options=True,eligible_virtual_terminal_roles=len(eligible),currently_birth_matched_options=sum(row['current_birth_donor'] is not None for row in eligible),selection_rule='All eligible options retained in eligible; selected is only the lowest role per target and may conflict with existing births. Choose at most one option per target and never choose both a terminal edge and a birth donor edge for the same role. After changing the birth matching, rerun the default inventory and full builder.') + record.pop('eligible_unshared_terminal_roles');record.pop('expected_physical_roles') +a.out.parent.mkdir(parents=True,exist_ok=True) +a.out.write_text(json.dumps(record,indent=2,sort_keys=True)+'\n') +print(json.dumps({k:v for k,v in record.items() if k not in ['selected','eligible','input_sha256']},indent=2)) diff --git a/research/shrunk-birth-terminal/references/pr122-fetch.json b/research/shrunk-birth-terminal/references/pr122-fetch.json new file mode 100644 index 0000000000..5796ff585f --- /dev/null +++ b/research/shrunk-birth-terminal/references/pr122-fetch.json @@ -0,0 +1,191 @@ +{ + "files": [ + { + "bytes": 4115, + "git_blob_sha1": "ff5b4e3496dca2c04a7ecfcf45f53bdcd2771892", + "path": "research/terminal-elision/CHECKPOINT.md", + "sha256": "cdb7873d0eaeec326598d8525b9eb7e40bb87b33e92db53acae306125f9b65c0" + }, + { + "bytes": 695, + "git_blob_sha1": "8229745e984d1d2da1d11d2e365f099d2f186ea2", + 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+ } + ], + "head": "b1a6f24e57141637b3ff040d6f2ce9d896ffb9bb" +} diff --git a/research/shrunk-birth-terminal/references/pr122/LICENSE b/research/shrunk-birth-terminal/references/pr122/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/shrunk-birth-terminal/references/pr122/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 + + 1. 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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. + +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. + +Stopped product-ring extension, 9 October 2026 +Copyright 2026 icekylinx + +The opposite-bank generic projector factorization, componentwise atom-ring +adapters, stopped recurrence and outer ordinary-interchange conversion, +aligned pair-star producer with rational centers, exact denominator-21 +grid and selected (23,23)/(24,24) composition are contributed by icekylinx +with substantial OpenAI GPT-6 Astra and Codex assistance. This extension +builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is +integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37. + +The retained ordinary leaf uses the preceding projector, corner and +copied-center proofs. The selected two-stage topology retains Aurel Prosz +(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly +retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching, +original source notices and each imported license remain unchanged. diff --git a/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/CHECKPOINT.md b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/CHECKPOINT.md new file mode 100644 index 0000000000..ff5b4e3496 --- /dev/null +++ b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/CHECKPOINT.md @@ -0,0 +1,69 @@ +# Round 15 active checkpoint — 2026-10-09 00:55 UTC + +User asked to keep going to try to take the lead, including continuing when +overtaken before finishing. Do not claim any current lead from the older +results below. No new external push/PR is authorized by this research turn. + +Strongest own surviving mechanism: terminal-accumulator elision with exact +source-time redirects. For distinct targets the complete charged comparison +(including width reduction via a dummy child) is + + new [m,F-M,0,0] versus old [m-h+sigma,1,F-sigma,h-1-M]. + +For 0<=sigma<=M<=F<=h-1 the new packet strictly majorizes the old. This +strictly improves every concave-power characteristic cost. Full scalar, +forward/reflected frame, profile and mutation audits pass on several bases. +Publication novelty is unresolved; linear cancellation itself is elementary. + +Latest checked public frontier: PR118 ec862a5af51537495c745d9f2323e8a5736ee265, +kappa1.085428059680e-4, later overtaken by updated PR114 head +7dfa16edfa5d6452f2b10dadcbef20d26222827e at 1.09281094468e-4. The latest +checked own candidate is 1.0941620808215e-4, about 0.12364% over that public +head. PR120 bfc5466 is the public refined-replayed comparison at +1.0911630664e-4. PR118 uses PR117's replayed28,705-role graph. Pinned at +worktrees/pr118. Graph-only exact regeneration/matching is complete at +workers/baseline/pr118-graph. Pair-root order is NUMERIC i, not paired-first. + +ACTIVE root producer: session90802, command: + + python3 round15/defer_exact_only.py --compiler-repo round15/worktrees/pr110 --case round15/workers/baseline/pr118-graph --out round15/deferred-replayed --order numeric + +The exact-only exporter intentionally omits two modular scalar samples; it +keeps integer adjoints, exact clean supports, all frame and rank checks. A +separate all-input audit remains mandatory. Control exact-only-cube-control +has identical word SHA to the old sampled exporter; only replay metadata +differs. No sampled test is falsely recorded as executed. + +Completed latest path: exact-only deferred export → PR114 refined placement +(5633a22443940f424dc2a09f44b2f447890e0074) → 393-role terminal elimination. +The final word SHA is 9e22581a3d9badf302307e90fe8c13d19010305a5b2e8d0a3b6d691cee912c4a. +Baseline exact pricing and critic full physical/mutation audits pass. The +portable receipts and local branch are frozen; no further validation is +needed unless the public frontier moves again. + +Current workers: r10_baseline (arithmetic/graphs/portable118 pricing), +r10_construction (frozen terminal-elision template), r10_critic (independent +exact words/frames). Use followup_task if an agent has finished. + +Completed latest own intermediate (overtaken): refined-cube plus1,179 elided +roles at workers/construction/terminal-elided-refined-cube, kappa +10075368759929/1e17. R34499,W147845104,s85156917824,2476 redirects. Exact +critic full audit passed at workers/critic/terminal-refined-cube-audit. +Parent refined-cube uses116 scalar graph and114 refined placement; all +prior dependencies credited. Source-bound packet majorization passes576 +hinges. Removing target-front events of dead readouts gives NO cost gain: +all are needed again at the first live redirect. Keep that negative control. + +Earlier paired-block, mixed-center, deferral, frame-enlargement and +terminal experiments are preserved in LEDGER.md and worker notes. Both +single-node fixed-sigma hinge-filter campaigns accept zero moves. Maximal +dimension alone worsened the power moment. Our append-compatible deferral +improvement is subsumed by the later114 placement on the tested core basis. + +Additive packaging worktree already exists: worktrees/terminal-elision, +branch review/terminal-elision, based on118. It is still empty of our files. +Never edit pinned worktrees or overwrite earlier receipts. Final report +should be ROUND15_RESEARCH_REPORT.md, with current comparison timestamp, +precise attribution, complete recurrence, proof scope, reproduction commands, +local reviewable patch and checkpoint. Refresh public progress before claiming +a lead; include updated heads without changing experimental pins. diff --git a/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/README.md b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/README.md new file mode 100644 index 0000000000..8229745e98 --- /dev/null +++ b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/README.md @@ -0,0 +1,12 @@ +# Round 15 terminal-elision artifact + +This additive package preserves the exact finite candidate and its independent +receipts. It is based on public PR118 (`ec862a5af51537495c745d9f2323e8a5736ee265`), +with PR114 saturated placement (`7dfa16edfa5d6452f2b10dadcbef20d26222827e`) +reproduced and then 393 terminal roles removed by source-time redirects. + +Read `ROUND15_RESEARCH_REPORT.md` and `CHECKPOINT.md` at the project root. +The word/profile/source hashes are in `artifacts/`; arithmetic, physical, and +mutation receipts are in `audit/`. The public all-size stopped-product and +fixed-tape interfaces remain assumptions. This branch is a reviewable local +checkpoint, not an upstream submission. diff --git a/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/ROUND15_RESEARCH_REPORT.md b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/ROUND15_RESEARCH_REPORT.md new file mode 100644 index 0000000000..8c0fb54afe --- /dev/null +++ b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/ROUND15_RESEARCH_REPORT.md @@ -0,0 +1,122 @@ +# Round 15 research report — terminal elimination on the moving frontier + +## Result + +The strongest surviving result is a finite, conditional improvement to the +replayed h=24 complex producer. A terminal auxiliary accumulator that is not +an input to any later auxiliary operation can be removed. Its incoming updates +are redirected to its unique output at their original gate times and frames; +the old target-front moves and all surviving auxiliary operations remain +charged. This preserves arbitrary dirty state and the reflected inverse word. + +Applied after the pinned PR118 replayed graph and the pinned PR114 saturated +placement, the construction removes 393 roles and redirects 1,221 updates: + +| quantity | value | +|---|---:| +| active roles R | 28,312 | +| complex width W | 122,800,128 | +| rank sum | 70,731,011,648 | +| maximum child | 574 | +| deferred roles | 4,560 | +| exact κ | 2,188,324,161,643 / 20,000,000,000,000,000 | +| decimal κ | 0.00010941620808215 | + +The common published-bit control is κ = 0.00010854280649816; the full exact +common-control comparison is +κ = 1,356,785,081,227 / 12,500,000,000,000,000. The candidate improves that +control by 87,340,158,399 / 10^17, and improves the public PR118 value by +17,468,042,283 / 2·10^16. The current public PR114 head claims +1.09281094468·10^-4; this candidate is approximately 0.124% higher. These are +conditional assembly bounds, not an unconditional new multiplication theorem. + +## Identity and cost proof + +For a removed role with initial frame dimension σ, first frame F, and last old +target-readout dimension M, write h=24 and m=h². Distinct targets and the +checked chronology give the before/after packets (zero entries omitted): + + old = [m-h+σ, 1, F-σ, h-1-M] + new = [m, F-M, 0, 0]. + +They have equal rank mass. For 0≤σ≤M≤F≤h−1, the sorted partial sums of `new` +dominate those of `old`; at least one inequality is strict. 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b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/producer.py new file mode 100644 index 0000000000..a93a265f01 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/producer.py @@ -0,0 +1,17 @@ +"""Pinned PR117 scalar DAG adapter for the saturated deferred compiler. + +The searched graph is upstream PR117 work credited to eumemic with Anthropic +Claude assistance. This adapter preserves that witness and producer unchanged; +saturation integration is separate OpenAI Codex-assisted work. Apache-2.0. +""" +from hashlib import sha256 +from pathlib import Path +from replayed_producer import build as replayed_build + +WITNESS_SHA256 = '3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b' + +def build(h, prefix, central_disjoint, base=2): + assert (h, central_disjoint, base) == (24,24,2) + witness=Path(__file__).resolve().parent/'inputs/complex-dag.json.gz' + assert sha256(witness.read_bytes()).hexdigest() == WITNESS_SHA256, 'PR117 DAG pin mismatch' + return replayed_build(witness,prefix) diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/reflection-audit.json b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/reflection-audit.json new file mode 100644 index 0000000000..caace0ada6 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/reflection-audit.json @@ -0,0 +1,82 @@ +{ + "R": 28705, + "all_frames_nondegenerate": true, + "audit_sha256": "6761fb01f93ef89f2455388b2f5a71f19c0bbd870e6aaeba457ede0a949a163b", + "bounded_chunk_coefficients": true, + "bounded_readout_chunks_sha256": "bb2ad510e5f5113eba2fd520f99bb05725087ae47e1566b7e63eafdefc69d809", + "child_multiplicities": { + "1": 435601232, + "10": 7375456, + "11": 7019232, + "12": 31788944, + "13": 12536656, + "14": 1497760, + "15": 3440800, + "16": 854128, + "17": 506000, + "18": 2906464, + "19": 2092816, + "2": 267192288, + "20": 817696, + "21": 1230592, + "22": 64768, + "23": 8363168, + "3": 29238704, + "4": 61145040, + "5": 26425344, + "529": 8193152, + "552": 97147952, + "554": 3493424, + "556": 1445136, + "558": 2319504, + "560": 582912, + "562": 101200, + "564": 1307504, + "566": 975568, + "568": 1364176, + "569": 4048, + "570": 3643200, + "571": 2444992, + "572": 837936, + "573": 44528, + "574": 485760, + "6": 15734576, + "7": 11876832, + "8": 22077792, + "9": 4562096 + }, + "conservative_local_G": 14907958248, + "exact_arbitrary_dirty_cancellation_by_dependency_cut": true, + "exact_chunk_reconstruction": true, + "exact_fresh_source_map": true, + "exact_integer_old_readout_transpose": true, + "expanded_old_readout_additions": 11862944, + "expanded_scalar_operations_per_stage": 12160614, + "forward_incidence_sha256": "46a00e3137729d00cafcf32969d1f3bc4e4cd293552f74eb47f61e64cf1524c1", + "h": 24, + "largest_bounded_chunk_numerator_over_42": 42, + "largest_readout_numerator_over_42": 55, + "literal_frame_incidences_both_directions": true, + "literal_global_scalar_groups": 49230262048, + "old_readout_coefficients_over_42_sha256": "e0666f81e1d35e002d61b8f2b2b1ca0d1d79cc7fbcbc76063eb333294d875e5e", + "reflected_incidence_sha256": "a6de908519fbdfabb1b8c05fd111321fa00181375bfa1cca537161d424ed6515", + "reflected_residual_rank_histogram_equal": true, + "reflected_scalar_map": "X becomes X-Y; Y unchanged; all auxiliary coordinates restored.", + "reflected_word_rule": "Reverse literal order including each bounded readout chunk, negate every shear, swap X/Y ports, complement every frame; auxiliary bank is separate.", + "rejected_controls": [ + "oversized-readout-chunk", + "split-readout-sum", + "reflected-chunk-order", + "inverse-sign", + "uncomplemented-frame", + "signed-root-readout" + ], + "scalar_readout_normalization": "Each exact numerator n/42 becomes signed42 chunks plus a signed remainder. Exact reconstruction and chunk magnitude<=1 checked; every same-frame shear is charged; reflection reverses chunk order.", + "scope": "Exact finite source coefficients, dirty cancellation algebra and literal reflected frame/charge ledger. Copied-centre transforms, endpoint correction and residual-to-child/all-size transfer retain their stated inherited contracts.", + "source_sha256": "fa1125e85ec73b185dc9eee117f62d10356bb6422c07ec793a7f77296c87707e", + "split_readout_macros": 32, + "two_stage_scalar_map": "(X,Y) becomes (-Y,X+Y) before inherited endpoint correction.", + "unsplit_old_readout_macros": 11862912, + "v": 2024, + "word_blocks": 277775 +} diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/reflection_audit.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/reflection_audit.py new file mode 100644 index 0000000000..9da639268b --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/reflection_audit.py @@ -0,0 +1,365 @@ +#!/usr/bin/env python3 +"""Literal inverse/reflection and exact finite scalar/frame audit. + +Captures an unchanged deferred producer before its output write, then checks +the scalar computation on every source symbol, the exact signed old-readout +transpose, the dependency cut and the complete complemented incidence ledger. +This is finite verification; the inherited residual-to-child implementation, +all-size transfer and analytic interfaces are not proved by this script. +""" +import ast +from collections import Counter +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import argparse,json,pickle,struct,sys +from pathlib import Path +sys.dont_write_bytecode=True +assert not sys.flags.optimize,'Assertions must remain enabled' + + +def capture(source): + source=Path(source).resolve();sys.path.insert(0,str(source.parent)) + tree=ast.parse(source.read_text(),filename=str(source)) + main=next(n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name=='main') + at=next(i for i,n in enumerate(main.body) if isinstance(n,ast.Expr) and isinstance(n.value,ast.Call) and isinstance(n.value.func,ast.Attribute) and n.value.func.attr=='write_text') + main.body[at:]=[ast.Return(ast.Call(ast.Name('locals',ast.Load()),[],[]))] + ast.fix_missing_locations(tree) + ns={'__file__':str(source),'__name__':'reflection_capture'} + exec(compile(tree,str(source)+' [read-only capture]','exec'),ns) + data=ns['main']();data['source']=str(source);return data + + +def basis(vectors): + piv={} + for x in vectors: + for p in sorted(piv,reverse=True): + if x>>p&1:x^=piv[p] + if x: + p=x.bit_length()-1 + for q in piv: + if piv[q]>>p&1:piv[q]^=x + piv[p]=x + return tuple(piv[p] for p in sorted(piv,reverse=True)) + + +def dot(a,b):return (a&b).bit_count()&1 + + +@lru_cache(None) +def contained(A,B):return len(basis(A+B))==len(B) + + +@lru_cache(None) +def complement(A,h): + A=basis(A);piv={x.bit_length()-1:x for x in A};result=[] + for j in range(h): + if j not in piv: + x=1<>j&1:x|=1<

      =0 else -1 + parts=(sign*42,)*q+((sign*r,) if r else ()) + check_chunks(numerator,parts) + return parts + +def reverse_row(row): + if row[0]=='old':return (row[0],row[1],row[3],row[2]) + return row + + +def check_reflection(forward,backward,h,v): + def bank(s):return s+v if s1) + readcount+=len(parts);maxchunk=max(maxchunk,max(map(abs,parts))) + for part in parts: + reached.append(t);records.append(struct.pack('len(old):hist[len(F)-len(old)]+=1 + current[s]=F + for event in events: + k,a,b,c,F,*rest=event + assert c in (-1,1) + promote(a,F) + if k=='gate':promote(b,F);scalar+=1 + elif k=='read': + for t in b:promote(t,F) + scalar+=len(b) + else: + assert k=='centre';G=rest[0] + assert contained(G,F) or contained(F,G) + assert nondeg(G);copies[abs(len(F)-len(G))]+=1 + for t in b:promote(t,G) + scalar+=len(b)+2 # temporary copy and erasure + digest.update(repr(event).encode()+b'\n') + # Each literal role cleanup reaches full space; any unused final + # endpoint is still represented explicitly in the expected chain. + for s,F in enumerate(expected):promote(s,F) + assert current==expected + return hist,copies,scalar,digest.hexdigest() + start=tm+[ZERO]*v+[sigma.get(s,ZERO) for s in range(R)] + finish=[FULL]*v+[complement(T,h) for T in tm]+[FULL]*R + H,C,scalar,digest=framescan(word,start,finish) + revstart=[None]*len(start);revfinish=[None]*len(start) + for s in range(len(start)): + revstart[swap(s)]=complement(finish[s],h);revfinish[swap(s)]=complement(start[s],h) + HR,CR,scalarR,reverse_digest=framescan(reverse,revstart,revfinish) + assert (H,C,scalar)==(HR,CR,scalarR) + z=Counter({r:2*v*n for r,n in (H+C).items()}) + for s in range(R):z[h*h-h+len(sigma.get(s,ZERO))]+=2*v + z[(h-1)**2]+=2*v*v;z[1]+=v*v + z.pop(0,None) + assert dict(sorted(z.items()))=={int(r):n for r,n in d['out']['child_multiplicities'].items()},'Literal reflected child histogram' + assert sum(r*n for r,n in z.items())==d['out']['total_rank'] + G=v*v+2*v*scalar + safe=8*(d['c_add']+2*R+(R+q)*v*(h+1)+h*h+h+1) if 'c_add' in d else 8*(d['out']['additions']+2*R+(R+q)*v*(h+1)+h*h+h+1) + assert safe>=scalar + return dict(h=h,v=v,R=R,exact_fresh_source_map=True,exact_integer_old_readout_transpose=True, + exact_arbitrary_dirty_cancellation_by_dependency_cut=True, + reflected_word_rule='Reverse literal order including each bounded readout chunk, negate every shear, swap X/Y ports, complement every frame; auxiliary bank is separate.', + reflected_scalar_map='X becomes X-Y; Y unchanged; all auxiliary coordinates restored.', + two_stage_scalar_map='(X,Y) becomes (-Y,X+Y) before inherited endpoint correction.', + literal_frame_incidences_both_directions=True,all_frames_nondegenerate=True, + reflected_residual_rank_histogram_equal=True,child_multiplicities=dict(sorted(z.items())), + word_blocks=len(word),expanded_scalar_operations_per_stage=scalar, + expanded_old_readout_additions=readcount,largest_readout_numerator_over_42=maxcoef, + unsplit_old_readout_macros=unsplit_readcount,split_readout_macros=split_macros, + largest_bounded_chunk_numerator_over_42=maxchunk, + bounded_readout_chunks_sha256=chunk_digest.hexdigest(), + scalar_readout_normalization='Each exact numerator n/42 becomes signed42 chunks plus a signed remainder. Exact reconstruction and chunk magnitude<=1 checked; every same-frame shear is charged; reflection reverses chunk order.', + exact_chunk_reconstruction=True,bounded_chunk_coefficients=True, + old_readout_coefficients_over_42_sha256=coefficient_digest.hexdigest(), + literal_global_scalar_groups=G,conservative_local_G=safe, + forward_incidence_sha256=digest,reflected_incidence_sha256=reverse_digest, + rejected_controls=rejected, + scope='Exact finite source coefficients, dirty cancellation algebra and literal reflected frame/charge ledger. Copied-centre transforms, endpoint correction and residual-to-child/all-size transfer retain their stated inherited contracts.') + + +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--source',type=Path);ap.add_argument('--state',type=Path) + ap.add_argument('--output',type=Path);ap.add_argument('--check',type=Path);a=ap.parse_args() + assert bool(a.source)!=bool(a.state) + d=capture(a.source) if a.source else pickle.loads(a.state.read_bytes()) + result=audit(d);source=Path(d['source']) + result['source_sha256']=sha256(source.read_bytes()).hexdigest() + result['audit_sha256']=sha256(Path(__file__).read_bytes()).hexdigest() + result=json.loads(json.dumps(result));encoded=json.dumps(result,indent=2,sort_keys=True)+'\n' + if a.check:assert result==json.loads(a.check.read_text()) + if a.output:a.output.write_text(encoded) + else:print(encoded,end='') + print('PASS exact scalar and literal complement reflection audit',file=sys.stderr) + + +if __name__=='__main__':main() diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/replayed_producer.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/replayed_producer.py new file mode 100644 index 0000000000..673fbbba70 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/replayed_producer.py @@ -0,0 +1,179 @@ +"""Replayed h=24 complex producer with all centers disjoint (rational divisor 21). + +Copyright 2026 eumemic, Apache-2.0. AI-assisted (Claude). The DAG was found by an +automated search over producers of the retained paired-triple, pair-star and +center-disjoint interfaces. The checks below are adapted from +stopped_product/complex.py (copyright 2026 icekylinx, Apache-2.0, PR #104). + +The witness complex-dag.json.gz lists the ordinary +additions after the v triple inputs and the retained roots: the disjoint sums +D[t], the pair stars P(a,b,i) and the center-disjoint sums A_i. Every support, +core, cover, type and rank is recomputed here from the operands; nothing is +read from the witness except the operand pairs and the root indices. +""" +import gzip, json, struct, sys, array +from fractions import Fraction +from itertools import combinations +from pathlib import Path + + +def write_array(f, values): + """Little-endian array writer, as partial_swap.binary.write_array.""" + if sys.byteorder != 'little' and values.itemsize > 1: + values = array.array(values.typecode, values) + values.byteswap() + values.tofile(f) + + +def build(witness, prefix): + w = json.loads(gzip.decompress(Path(witness).read_bytes())) + h, v, d = w['h'], w['v'], w['central_disjoint'] + assert (h, d, w['center_denominator']) == (24, 24, 21) + triples = list(combinations(range(h), 3)) + assert v == len(triples) + args = [(0, 0)]; support = [0]; core = [0]; cover = [0]; types = [0]; ranks = [0] + for j, t in enumerate(triples): + mask = sum(1 << a for a in t) + args.append((0, 0)); support.append(1 << j); core.append(mask); cover.append(mask) + types.append(1); ranks.append(1) + flat = w['args'] + assert len(flat) % 2 == 0 + for k in range(0, len(flat), 2): + a, b, x = flat[k], flat[k+1], len(args) + assert 0 < a < x and 0 < b < x, 'Operands must precede their sum' + assert not support[a] & support[b], 'Ordinary additions must be cancellation-free' + args.append((a, b)); support.append(support[a] | support[b]) + core.append(core[a] & core[b]); cover.append(cover[a] | cover[b]) + if core[x].bit_count() >= 2: + types.append(1); ranks.append(support[x].bit_count()) + else: + types.append(2); ranks.append(cover[x].bit_count()) + n = len(args) + point_masks = [sum(1 << j for j, t in enumerate(triples) if a in t) for a in range(h)] + full_support = (1 << v) - 1 + roots, kind = [], [] + assert len(w['D']) == v + for t, node in zip(triples, w['D']): + assert 0 < node < n + assert support[node] == full_support & ~(point_masks[t[0]]|point_masks[t[1]]|point_masks[t[2]]) + target_mask = sum(1 << a for a in t) + if types[node] == 2: + assert not cover[node] & target_mask + else: + assert types[node] == 1 + assert not support[node] & (point_masks[t[0]]^point_masks[t[1]]^point_masks[t[2]]) + roots.append(node); kind.append(0) + stars = [(a, b, i) for a, b in combinations(range(h), 2) for i in range(h) if i not in (a, b)] + assert len(w['P']) == len(stars) + pair_outputs = {} + for (a, b, i), node in zip(stars, w['P']): + assert 0 < node < n + assert support[node] == point_masks[a] & point_masks[b] & ~point_masks[i] + assert types[node] == 1 + assert not support[node] & (point_masks[a]^point_masks[b]^point_masks[i]) + pair_outputs[a, b, i] = node + roots.append(node); kind.append(0) + assert len(w['A']) == d + for i, node in enumerate(w['A']): + assert 0 < node < n + assert support[node] == full_support & ~point_masks[i] + assert types[node] == 2 and cover[node] == ((1 << h)-1) ^ (1 << i) + assert ranks[node] == h-1 + roots.append(node); kind.append(1) + # Every A_i avoids i, so sum A_i = (h-3)T. The decoder is T=sum A_i/21 + # and the scatter is T-(1/2)sum_{i in target} A_i. + decoder = Fraction(1, h-3) + assert decoder == Fraction(1, 21) + scatter_coefficients = [decoder, decoder-Fraction(1, 2)] + for coefficient in scatter_coefficients: + odd_denominator = coefficient.denominator + while odd_denominator % 2 == 0: + odd_denominator //= 2 + assert 21 % odd_denominator == 0 and abs(coefficient) <= 1 + for source in triples: + assert sum(i not in source for i in range(h))*decoder == 1 + Dset = set(range(d)) + for triple in triples: + k = len(Dset.intersection(triple)) + assert 2*(3-k)-2*(d-k) == 2*(3-d) + patterns = {} + for target in triples: + chosen = len(Dset.intersection(target)) + if chosen not in patterns: + patterns[chosen] = target + for chosen, target in patterns.items(): + target_set = set(target) + for source in triples: + k = len(Dset.intersection(source)) + total_coefficient = Fraction(2*(3-k)-2*(d-k), 2*(3-d)) + scalar = Fraction(len((target_set-Dset).intersection(source)), 2) + scalar -= Fraction(len((target_set & Dset)-set(source)), 2) + scalar += Fraction(chosen-1, 2)*total_coefficient + assert scalar == Fraction(len(target_set.intersection(source))-1, 2) + for j, t in enumerate(triples): + masks = [point_masks[a] for a in t] + two = (masks[0]&masks[1]&~masks[2]) | (masks[0]&masks[2]&~masks[1]) | (masks[1]&masks[2]&~masks[0]) + actual = 0 + for a, b in combinations(t, 2): + excluded = next(i for i in t if i not in (a, b)) + actual |= support[pair_outputs[a, b, excluded]] + assert actual == two + assert masks[0]&masks[1]&masks[2] == 1 << j + assert [((k-1)+(k == 0)-(k == 2)) for k in range(4)] == [0, 0, 0, 2] + + def contained(x, y): + tx, ty = types[x], types[y] + if tx == 1 and ty == 1: return not(core[y]&~core[x] or cover[x]&~cover[y]) + if tx in (1, 2) and ty == 2: return not cover[x]&~cover[y] + return False + active = [0]*n; stack = list(roots) + while stack: + x = stack.pop() + if not x or active[x]: continue + active[x] = 1 + if args[x][0]: stack.extend(args[x]) + degree = [0]*n + for x in range(1, n): + if active[x]: + if types[x] == 1: + assert core[x].bit_count() >= 2 and ranks[x] == support[x].bit_count() + else: + assert types[x] == 2 and ranks[x] == cover[x].bit_count() + if active[x] and args[x][0]: + for y in args[x]: + assert y < x and contained(y, x), 'Binary frame nesting failed' + degree[y] += 1 + for x in roots: degree[x] += 1 + H = [0]*(h+1); c = 0; loss = 0 + for x in range(1, n): + if not active[x]: continue + r = ranks[x] + if args[x][0]: + c += 1; H[r] += degree[x]-1; H[h-r] += 1 + for y in args[x]: + assert r >= ranks[y] + H[r-ranks[y]] += 1 + else: H[1] += degree[x] + for x, k in zip(roots, kind): + r = ranks[x] + if k: H[r] += 1; H[h] += 1; loss += r + else: H[h-1-r] += 1; H[1] += 1 + q = len(roots); R = c+q + result = dict(h=h, v=v, c=c, q=q, R=R, loss=loss, central_disjoint=d, histogram=H, + rank_sum=sum(r*m for r, m in enumerate(H))) + assert loss == h*(h-1) and result['rank_sum'] == h*R+2*loss + result['center_denominator'] = 21 + result['scalar_validation'] = dict(ordinary_supports_exact=True, centers_exact=True, + center_decoder='sum A_i / 21', scatter_coefficients=list(map(str, scatter_coefficients)), + rational_scalar_identity_exact=True, mixed_center_scatter_exact=True, binary_frames_nested=True, + binary_frames_nondegenerate=True) + with open(str(prefix)+'.bin', 'wb') as f: + f.write(struct.pack('<4I', h, v, n, q)) + write_array(f, array.array('I', (a for pair in args for a in pair))) + write_array(f, array.array('Q', core)); write_array(f, array.array('Q', cover)) + write_array(f, array.array('I', roots)); write_array(f, array.array('I', kind)) + write_array(f, array.array('B', active)) + with open(str(prefix)+'.labels', 'wb') as f: + write_array(f, array.array('I', ranks)); write_array(f, array.array('B', types)) + Path(str(prefix)+'.json').write_text(json.dumps(result, indent=2)+'\n') + return result diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/test_controls.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/test_controls.py new file mode 100644 index 0000000000..fdeedf7d8d --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/test_controls.py @@ -0,0 +1,180 @@ +#!/usr/bin/env python3 +"""Negative controls for the shrunk-frame deferred finite witness. + +These controls target source omissions, altered inputs, paid rank accounting, +noncontracting children and invalid exact arithmetic. They do not substitute +for the full producer and literal reflection checks. Prepared for eumemic with +OpenAI Codex assistance; Apache-2.0, inherited notices retained. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Negative controls require assertions') + +import argparse +import copy +import gzip +import importlib.util +import json +from pathlib import Path +import shutil +import subprocess +import tempfile +import unittest + +from verify import check_sources, compare_json, digest, safe_file, validate_profile + +HERE = Path(__file__).resolve().parent +REPOSITORY = HERE.parents[1] + + +class FrozenControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.manifest = check_sources(HERE, REPOSITORY) + cls.profiles = {label: json.loads((HERE / (label + '-profile.json')).read_text()) + for label in ('bit', 'complex')} + sys.path.insert(0, str(REPOSITORY / 'scripts')) + spec = importlib.util.spec_from_file_location('checked_cyclic_certificate', HERE / 'certificate.py') + cls.certificate = importlib.util.module_from_spec(spec) + spec.loader.exec_module(cls.certificate) + cls.certificate.ROOT = REPOSITORY + + def test_all_frozen_profiles_satisfy_physical_ledgers(self): + for label, profile in self.profiles.items(): + validate_profile(profile, label) + + def test_frozen_exact_certificate_recomputed(self): + expected = json.loads((HERE / 'certificate.json').read_text()) + actual = self.certificate.js(self.certificate.exact()) + self.assertEqual(actual, expected) + + def test_omitted_endpoint_charge_rejected(self): + for label, original in self.profiles.items(): + changed = copy.deepcopy(original) + changed['child_multiplicities']['1'] -= changed['N'] + with self.assertRaisesRegex(ValueError, 'rank mass'): + validate_profile(changed, label) + + def test_nonshrinking_recursive_child_rejected(self): + for label, original in self.profiles.items(): + changed = copy.deepcopy(original) + changed['child_multiplicities'][str(changed['m'])] = 1 + with self.assertRaisesRegex(ValueError, 'recursive child'): + validate_profile(changed, label) + + def test_understated_role_count_rejected(self): + changed = copy.deepcopy(self.profiles['complex']) + changed['R'] -= 1 + with self.assertRaisesRegex(ValueError, 'physical ledger'): + validate_profile(changed, 'complex') + + def test_overstated_matching_rejected(self): + changed = copy.deepcopy(self.profiles['complex']) + changed['links'] += 1 + with self.assertRaisesRegex(ValueError, 'matching role ledger'): + validate_profile(changed, 'complex') + + def test_missing_transitive_dependency_rejected(self): + changed = copy.deepcopy(self.manifest) + del changed['repository_files']['scripts/exclusion_circuit.py'] + with self.assertRaisesRegex(ValueError, 'dependency closure'): + check_sources(HERE, REPOSITORY, changed) + + def test_omitted_physical_input_rejected(self): + changed = copy.deepcopy(self.manifest) + del changed['package_files']['inputs/deferred_23.json.gz'] + with self.assertRaisesRegex(ValueError, 'finite-input closure'): + check_sources(HERE, REPOSITORY, changed) + + def test_changed_input_digest_rejected(self): + changed = copy.deepcopy(self.manifest) + changed['package_files']['inputs/witness_23.json.gz'] = '0' * 64 + with self.assertRaisesRegex(ValueError, 'hash mismatch'): + check_sources(HERE, REPOSITORY, changed) + + def test_omitted_pinned_complex_dag_rejected(self): + changed = copy.deepcopy(self.manifest) + del changed['package_files']['inputs/complex-dag.json.gz'] + with self.assertRaisesRegex(ValueError, 'finite-input closure'): + check_sources(HERE, REPOSITORY, changed) + + def test_changed_complex_dag_digest_rejected(self): + with tempfile.TemporaryDirectory(prefix='shrunk-frames-altered-dag-') as directory: + package = Path(directory) + for name in self.manifest['package_files']: + target = package / name + target.parent.mkdir(parents=True, exist_ok=True) + shutil.copyfile(HERE / name, target) + name = 'inputs/complex-dag.json.gz' + path = package / name + graph = json.loads(gzip.decompress(path.read_bytes())) + graph['args'][0] = graph['args'][1] + path.write_bytes(gzip.compress(json.dumps(graph).encode(), mtime=0)) + with self.assertRaisesRegex(ValueError, 'hash mismatch'): + check_sources(package, REPOSITORY, self.manifest) + # Rehashing a substituted DAG must not erase its immutable provenance. + changed = copy.deepcopy(self.manifest) + changed['package_files'][name] = digest(path) + with self.assertRaisesRegex(ValueError, 'scalar-DAG provenance digest mismatch'): + check_sources(package, REPOSITORY, changed) + + def test_replayed_complex_dag_rejects_duplicated_operand(self): + from replayed_producer import build + with tempfile.TemporaryDirectory(prefix='shrunk-frames-invalid-dag-') as directory: + graph = json.loads(gzip.decompress((HERE / 'inputs/complex-dag.json.gz').read_bytes())) + graph['args'][0] = graph['args'][1] + path = Path(directory) / 'invalid.json.gz' + path.write_bytes(gzip.compress(json.dumps(graph).encode(), mtime=0)) + with self.assertRaisesRegex(AssertionError, 'cancellation-free'): + build(path, Path(directory) / 'invalid-producer') + + def test_manifest_parent_escape_rejected(self): + with self.assertRaisesRegex(ValueError, 'Unsafe manifest path'): + safe_file(HERE, '../certificate.json') + + def test_changed_regenerated_profile_rejected(self): + with tempfile.TemporaryDirectory(prefix='shrunk-frames-negative-') as directory: + changed = copy.deepcopy(self.profiles['complex']) + changed['child_multiplicities']['1'] += 1 + path = Path(directory) / 'changed.json' + path.write_text(json.dumps(changed)) + with self.assertRaisesRegex(ValueError, 'Frozen generated record mismatch'): + compare_json(path, HERE / 'complex-profile.json') + + def test_next_bit_and_complex_grid_points_rejected(self): + from fractions import Fraction as Q + module = self.certificate + self.assertFalse(module.contracts(module.profile('bit-profile.json'), module.COARSE + Q(1, 10**10))) + self.assertFalse(module.contracts(module.profile('complex-profile.json'), module.COMPLEX + Q(1, 10**12))) + + def test_unshrunk_pr114_profile_rejects_new_complex_saving(self): + module = self.certificate + previous = json.loads((HERE / 'controls/pr114-complex-profile.json').read_text()) + previous['child_multiplicities'] = {int(t): c for t, c in previous['child_multiplicities'].items()} + self.assertEqual((previous['R'], previous['deferred_roles']), (28705, 4706)) + self.assertTrue(module.contracts(previous, module.Q(109305097, 10**12))) + self.assertFalse(module.contracts(previous, module.COMPLEX)) + self.assertTrue(module.contracts(module.profile('complex-profile.json'), module.COMPLEX)) + + def test_optimized_verifier_rejected_before_any_regeneration(self): + result = subprocess.run([sys.executable, '-O', str(HERE / 'verify.py')], + capture_output=True, text=True) + self.assertNotEqual(result.returncode, 0) + self.assertIn('optimized Python is forbidden', result.stderr) + + +def main(): + global REPOSITORY + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--repository-root', type=Path, default=REPOSITORY) + args = parser.parse_args() + REPOSITORY = args.repository_root.resolve() + suite = unittest.defaultTestLoader.loadTestsFromTestCase(FrozenControls) + result = unittest.TextTestRunner(verbosity=2).run(suite) + if not result.wasSuccessful(): + raise SystemExit(1) + + +if __name__ == '__main__': + main() diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/verify.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/verify.py new file mode 100644 index 0000000000..b1a718029c --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/verify.py @@ -0,0 +1,254 @@ +#!/usr/bin/env python3 +"""Read-only verification of the frozen shrunk-frame deferred finite package. + +Regeneration occurs only in a temporary repository-shaped copy. Source hashes, +complete profile ledgers, the exact certificate, and the independent reflection +audit are required. General transfer proofs and the inherited round-seven bit +word/frame justification remain separate dependencies. Prepared for eumemic +with OpenAI Codex assistance; inherited authorship and licenses are retained. +""" +import sys +sys.dont_write_bytecode = True +if sys.flags.optimize: + raise ValueError('Verification requires assertions; optimized Python is forbidden') + +import argparse +import ast +from hashlib import sha256 +import json +from math import comb +import os +from pathlib import Path +import shutil +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +COMPLEX_DAG_PIN = '3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b' +BIT_PINS = { + 'witness_23.json.gz': 'b2486aa2bb222bacea6e52162a3920780e45dd8edc5d7cb03eabea336a1c6588', + 'deferred_23.json.gz': '8c38e947ff9e021e308000dd82bb5e2194eb265d8b75194e22ce783d3e75317c', +} +REQUIRED = { + 'verify.py', 'test_controls.py', 'producer.py', 'complex_deferred.py', + 'bit_round7.py', 'certificate.py', 'bit-profile.json', + 'complex-profile.json', 'certificate.json', 'replayed_producer.py', + 'inputs/complex-dag.json.gz', 'controls/pr114-complex-profile.json', + *('inputs/' + name for name in BIT_PINS), +} +DATA_DEPENDENCIES = {'certificates/copied-centers-network.json'} + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def safe_file(directory, name): + relative = Path(name) + require(not relative.is_absolute() and '..' not in relative.parts, + 'Unsafe manifest path: ' + name) + path = (directory / relative).resolve() + require(path.is_relative_to(directory.resolve()) and path.is_file(), + 'Missing or escaping manifest file: ' + name) + return path + + +def digest(path): + return sha256(path.read_bytes()).hexdigest() + + +def dependency_closure(package, repository, package_scripts): + """Include every local Python import, including package __init__ modules. + + All package scripts are roots, also covering explicit importlib loading of + the producer and audited source. Only stdlib imports may be unresolved. + The sole external data read used by exact assembly is listed separately. + """ + pending = [package / name for name in package_scripts] + seen, dependencies = set(), set(DATA_DEPENDENCIES) + while pending: + path = pending.pop().resolve() + if path in seen: + continue + seen.add(path) + imports = [] + for node in ast.walk(ast.parse(path.read_text(), filename=str(path))): + if isinstance(node, ast.Import): + imports.extend((alias.name, 0) for alias in node.names) + elif isinstance(node, ast.ImportFrom) and node.module: + imports.append((node.module, node.level)) + for name, level in imports: + parts = name.split('.') + if not level and parts[0] in sys.stdlib_module_names: + continue + found = None + bases = ((path.parent.parents[level-2] if level > 1 else path.parent),) if level else (package, repository / 'scripts') + for base in bases: + module = base.joinpath(*parts) + for candidate in (module.with_suffix('.py'), module / '__init__.py'): + if candidate.is_file(): + found = candidate.resolve() + break + if found is not None: + pending.append(found) + if found.is_relative_to((repository / 'scripts').resolve()): + dependencies.add(str(found.relative_to(repository.resolve()))) + parent = found.parent + while parent != (repository / 'scripts').resolve(): + initializer = parent / '__init__.py' + if initializer.is_file(): + pending.append(initializer) + dependencies.add(str(initializer.relative_to(repository))) + parent = parent.parent + break + require(found is not None, 'Unpinned non-stdlib Python import: ' + name) + return dependencies + + +def create_manifest(package, repository, reflection_script, reflection_receipt): + scripts = sorted(path.name for path in package.glob('*.py')) + names = REQUIRED | set(scripts) | {reflection_script, reflection_receipt} + dependencies = dependency_closure(package, repository, scripts) + return dict( + schema=1, + scope='Frozen finite producer, profiles, exact assembly and reflection audit; inherited all-size transfer remains conditional.', + package_files={name: digest(safe_file(package, name)) for name in sorted(names)}, + repository_files={name: digest(safe_file(repository, name)) for name in sorted(dependencies)}, + reflection=dict(script=reflection_script, receipt=reflection_receipt), + provenance=dict( + base='https://github.com/CrocSwap/integer-mult-bounds/pull/110', + cyclic_strips='https://github.com/CrocSwap/integer-mult-bounds/pull/111', + saturated_base=dict(pull_request='https://github.com/CrocSwap/integer-mult-bounds/pull/114', + commit='7dfa16edfa5d6452f2b10dadcbef20d26222827e'), + scalar_dag=dict(pull_request='https://github.com/CrocSwap/integer-mult-bounds/pull/117', + commit='cbb05ce504d571546d9b7794c186a613c659c3bf', + file='inputs/complex-dag.json.gz', sha256=COMPLEX_DAG_PIN), + round7_repository='https://github.com/Swapnil-jain/integer-mult-kappa', + round7_commit='741e7aa078392553815df7926ee17ac5e25a8c38', + round7_sha256=BIT_PINS), + attribution='Avi Eisenberg / ikeboy (PR62 and PR110, Anthropic Claude assistance); Rohan Arun (PR111, Anthropic Claude assistance); Swapnil Jain (round-seven bit word); icekylinx (retained stopped-product, copied-center and finite assembly interfaces); Zhihao Chen and RaD (retained assembly). PR117 scalar DAG is separate upstream work by eumemic with Anthropic Claude assistance, retained byte for byte with its original attribution. Saturated deferred-frame integration and verification for eumemic with OpenAI Codex assistance. Shrunk-frame step by Joel Pulikkan with Anthropic Claude assistance (PR114 base). Original source notices remain authoritative.') + + +def check_sources(package, repository, manifest=None): + manifest = manifest or json.loads((package / 'SOURCE.json').read_text()) + require(manifest['schema'] == 1, 'Unsupported source-manifest schema') + names = set(manifest['package_files']) + reflection = manifest['reflection'] + require(REQUIRED | {reflection['script'], reflection['receipt']} <= names, + 'Incomplete package source/finite-input closure') + for collection, base in ((manifest['package_files'], package), + (manifest['repository_files'], repository)): + for name, expected in collection.items(): + require(digest(safe_file(base, name)) == expected, 'Source hash mismatch: ' + name) + scripts = sorted(name for name in names if name.endswith('.py')) + expected = dependency_closure(package, repository, scripts) + require(set(manifest['repository_files']) == expected, + 'Incomplete or stale transitive repository dependency closure') + for name, expected in BIT_PINS.items(): + require(manifest['package_files']['inputs/' + name] == expected, + 'Round-seven provenance digest mismatch: ' + name) + require(manifest['package_files']['inputs/complex-dag.json.gz'] == COMPLEX_DAG_PIN, + 'PR117 scalar-DAG provenance digest mismatch') + return manifest + + +def validate_profile(profile, label): + fields = ('h', 'v', 'R', 'm', 'N', 'W', 'L', 'total_rank', 'deficit', 'maxchild') + require(all(type(profile[key]) is int and profile[key] > 0 for key in fields), + label + ': nonpositive or noninteger ledger value') + h, v, R, m, N, W, L = (profile[key] for key in fields[:7]) + require(v == comb(h, 3) and m == h*h and N == v*v, label + ': dimensions') + require(W == 2*N + 2*v*R and L == 2*v*h*(h-1), label + ': physical ledger') + rows = {int(t): count for t, count in profile['child_multiplicities'].items()} + require(len(rows) == len(profile['child_multiplicities']), label + ': duplicate child widths') + require(all(0 < t < m and type(count) is int and count > 0 for t, count in rows.items()), + label + ': invalid recursive child') + require(sum(t*count for t, count in rows.items()) == profile['total_rank'] == W*m-N+L, + label + ': rank mass') + require(profile['deficit'] == N-L and profile['maxchild'] == max(rows), + label + ': deficit or maximum child') + require(rows.get((h-1)**2) == 2*N and rows.get(1, 0) >= N, + label + ': omitted data projector or endpoint charge') + if label == 'complex': + require(R == profile['additions']+profile['roots']-profile['links'], + 'complex: addition/roots/matching role ledger') + require(sum(profile['deferred_dims'].values()) == profile['deferred_roles'], + 'complex: deferral inventory') + return rows + + +def compare_json(actual, expected): + require(json.loads(actual.read_text()) == json.loads(expected.read_text()), + 'Frozen generated record mismatch: ' + expected.name) + + +def snapshot(package, repository, manifest): + return { + **{'package:' + n: digest(package / n) for n in manifest['package_files']}, + **{'repository:' + n: digest(repository / n) for n in manifest['repository_files']}, + 'manifest': digest(package / 'SOURCE.json'), + } + + +def verify(package, repository): + manifest = check_sources(package, repository) + before = snapshot(package, repository, manifest) + for label in ('bit', 'complex'): + validate_profile(json.loads((package / (label + '-profile.json')).read_text()), label) + environment = dict(os.environ, PYTHONDONTWRITEBYTECODE='1') + environment.pop('PYTHONPATH', None) + with tempfile.TemporaryDirectory(prefix='shrunk-frames-verify-') as directory: + root = Path(directory) + target = root / 'research/shrunk-frames' + for collection, source, destination in ( + (manifest['package_files'], package, target), + (manifest['repository_files'], repository, root)): + for name in collection: + out = destination / name + out.parent.mkdir(parents=True, exist_ok=True) + shutil.copyfile(source / name, out) + shutil.copyfile(package / 'SOURCE.json', target / 'SOURCE.json') + + def run(script, *arguments): + subprocess.run([sys.executable, str(target / script), *map(str, arguments)], + cwd=root, env=environment, check=True) + + run('bit_round7.py', target / 'inputs') + compare_json(target / 'bit-profile.json', package / 'bit-profile.json') + print('PASS pinned round-seven bit ledger regenerated', flush=True) + run('complex_deferred.py') + compare_json(target / 'complex-profile.json', package / 'complex-profile.json') + print('PASS complete complex producer and deferred profile regenerated', flush=True) + run('certificate.py') + reflection = manifest['reflection'] + actual_reflection = root / 'actual-reflection.json' + run(reflection['script'], '--source', target / 'complex_deferred.py', + '--output', actual_reflection) + compare_json(actual_reflection, package / reflection['receipt']) + print('PASS independent literal reflection and scalar-charge audit', flush=True) + run('test_controls.py', '--repository-root', root) + require(snapshot(package, repository, manifest) == before, + 'Verification changed the frozen package or a dependency') + print('PASS read-only finite package verification; inherited transfer remains conditional', flush=True) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--repository-root', type=Path, default=HERE.parents[1]) + parser.add_argument('--freeze-manifest', action='store_true', + help='Explicit authoring operation: replace SOURCE.json from reviewed files') + parser.add_argument('--reflection-script', default='reflection_audit.py') + parser.add_argument('--reflection-receipt', default='reflection-audit.json') + args = parser.parse_args() + repository = args.repository_root.resolve() + if args.freeze_manifest: + manifest = create_manifest(HERE, repository, args.reflection_script, args.reflection_receipt) + (HERE / 'SOURCE.json').write_text(json.dumps(manifest, indent=2, sort_keys=True) + '\n') + print('Frozen source manifest; this operation does not certify the package') + else: + verify(HERE, repository) + + +if __name__ == '__main__': + main() diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/audit_short_guards.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/audit_short_guards.py new file mode 100644 index 0000000000..e5c52c8afe --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/audit_short_guards.py @@ -0,0 +1,183 @@ +#!/usr/bin/env python3 +"""Short working guards and an explicit, still-unproved gathering target. + +The packed gadget and address permutation are checked exactly. No fast tape +implementation of gathering is claimed; independent window moves are linear +in the number of windows and do not achieve the required saving. +""" +from fractions import Fraction as Q +from pathlib import Path +import json + +from certify import require, verify_sources +from prepare_layers import serializable, scenarios + +ROOT=Path(__file__).resolve().parents[1] +ROTATIONS=(('y',-1,0),('z',-1,0),('y',1,0),('z',1,0), + ('z',1,1),('y',1,1),('z',-1,1),('y',-1,1)) + + +def guard_width(p): + require(isinstance(p,int) and p>=2,'Integer p>=2 required') + return 4*(p-1).bit_length()+6 + + +def gather_order(f,K,rho,g): + """Input bit indices in output low-to-high order for one slot. + + Gather the first f-1 windows into the most significant contiguous field. + Keep the remaining coordinates in relative order in a spectator field. + The highest selected bit is omitted and handled separately after undo. + """ + require(f>=1 and K>=1 and 0<=rho>source)&1)<>target)&1)<>(j*g))&1)<<(j*g) for j in range(n)) + + +def rotate_gadget(x,y,z,n,g,*,inverse=False): + """Eight modular rotations on compact n*g-bit slots, omitting the top bit.""" + require(n>=1 and g>=1,'Nonempty compact slots required') + modulus=1<<(n*g) + state={'y':y,'z':z} + operations=reversed(ROTATIONS) if inverse else ROTATIONS + for target,sign,test in operations: + other=state['z' if target=='y' else 'y'] + offset=sum(1<<(j*g) for j in range(n-1) + if x>>(j*g)&1 and (other>>(j*g)&1)==test) + state[target]=(state[target]+(-sign if inverse else sign)*offset)%modulus + return x,state['y'],state['z'] + + +def exceptional(y,z,n,g): + mask=(1<>(j*g))&mask)//2<=maximum + for slot in (y,z) for j in range(n-1)) + + +def compact_add(x,y,z,n,g): + """Exact address map, including the existing exceptional-set correction. + + This simulates addresses, not a tape implementation or its running time. + For g<6 every guard may be exceptional; those cases are finite controls. + """ + out=rotate_gadget(x,y,z,n,g) + if exceptional(out[1],out[2],n,g): + original=rotate_gadget(*out,n,g,inverse=True) + out=(original[0],original[1]^active_mask(original[0],n-1,g),original[2]) + # Supply the most significant selected bit omitted by the rotations. + top=(n-1)*g + return out[0],out[1]^(((out[0]>>top)&1)<>rho)&1)<>spectator_width for v in packed] + updated=compact_add(*data,n,g) + result=[ungather((new<>top)&1)<= 64*p**4,'Short guard inequality failed') + # Before inserting A<=C*p and R superpolynomial, the bad fraction is + # bounded by 80*f*2^-g <= (5/4)*p^-3. This deliberately overcounts. + fraction=Q(80*f,1<0 and + 0=0,'Invalid exponent hypothesis') + gathering=r+theta*c+(1-beta)*max(sigma-r,Q(0)) + compact=tau+(1-beta)*max(sigma-tau,Q(0)) + leaf=sigma+beta*(1-sigma) + return dict(gathering=gathering,compact_gadget=compact,leaf=leaf, + layer=max(gathering,compact,leaf), + status='IMPLICATION OF AN UNPROVED GATHERING BOUND') + + +def monotone_lengths(permutation): + """Small exact LIS/LDS control; no inference about unrestricted tape time.""" + inc=[1]*len(permutation);dec=[1]*len(permutation) + for i,x in enumerate(permutation): + for j in range(i): + if permutation[j]x:dec[i]=max(dec[i],dec[j]+1) + return max(inc,default=0),max(dec,default=0) + + +def monotone_stream_obstruction(guard_bits,active_bits): + """A restricted transpose inside an extreme-field gathering permutation. + + For A guard values and B active values, any global monotone output stream + contains at most A+B-1 of the AB selected records. This only rules out a + bounded number of one-shot global monotone streams; nested local reversals + and coded tape algorithms are outside this model. + """ + require(guard_bits>=1 and active_bits>=1,'Need two nonempty variable fields') + A,B=1<= 20, "C1 must cover the upstream guard bound") + else: + # Caller must also certify m>=3 and 2<=s_c= 2 and p.beta >= Q(9, 10), + "Stopping guard requires C1>=2 and beta>=9/10") + slacks = constraints(p, layout_model=layout_model, assembly_model=assembly_model) + for name, slack in slacks.items(): + require(slack > 0, f"Failed strict constraint: {name} ({slack})") + gs = margins(p, layout_model=layout_model, assembly_model=assembly_model) + if strict_margin: + require(min(gs.values()) > p.kappa, "Need a positive absorption gap") + else: + require(min(gs.values()) >= 2*p.kappa, + "The proposed patch requires every g_i >= 2*kappa") + result = {"parameters": {k: str(v) for k, v in vars(p).items()}, + "constraint_slacks": {k: str(v) for k, v in slacks.items()}, + "margins": {k: str(v) for k, v in gs.items()}, + "minimum_margin": str(min(gs.values())), + "limiting_margins": [k for k, v in gs.items() if v == min(gs.values())], + "all_margins_at_least_twice_kappa": min(gs.values()) >= 2*p.kappa, + "absorption_gap": str(min(gs.values())-p.kappa), + "slack_rule": "strict" if strict_margin else "half", + "generalized_beta": generalized_beta} + if assembly_model != "original" or guard_model != "original": + result.update(assembly_model=assembly_model, guard_model=guard_model) + return result + + +def network(h): + """Generalized counts only; these do not prove the network interface.""" + require(h > 6 and h != 9, "Need spare coordinates and nondegenerate rational form") + v, m = comb(h, 3), h**3 + N, I = v**3, 3*v**2 + zb, zc = 3*comb(h-3, 2), comb(h-3, 3)+3*(h-3) + Wb, Wc = 2*N+I*(v*zb+h), 2*N+I*(v*zc+h+1) + Lb, Lc = I*h*h, I*(h+1)*h + sb, sc = Wb*m-N+2*Lb, Wc*m-2*N+2*Lc + eb, ec = Q(Wb*m-sb, Wb*m), Q(Wc*m-sc, Wc*m) + E = 64*(Wc+m+1)**3 + B = sc+E + nu = 1 + while m**nu < B: + nu += 1 + return dict(h=h, v=v, m=m, N=N, I=I, zb=zb, zc=zc, + Wb=Wb, Wc=Wc, Lb=Lb, Lc=Lc, sb=sb, sc=sc, + eta_b=eb, eta_c=ec, B=B, nu=nu, C1=max(20, nu+3)) + + +def certify_network(h, k, log_bound): + n = network(h) + # A positive Taylor partial sum below exp(log_bound) proves m n["m"], "Could not certify the logarithm bound") + for key in ("eta_b", "eta_c"): + require(n[key] > log_bound*dyadic(k), f"Insufficient deficit: {key}") + require(2*n["Lb"] < n["N"] and 2*n["Lc"] < n["N"], + "The generalized residual lemma requires L A*LOG_BOUND for key in ("eta_b", "eta_c")), + "Rank deficit does not support the requested rational saving") + certify_network(46, 36, 12) # Residual and guard conditions. + return {"h": 46, "saving": str(A), "log_bound": str(LOG_BOUND), + "log_lower": str(lo), "log_upper": str(hi), + "deficit_slacks": {k: str(n[k]-A*LOG_BOUND) for k in ("eta_b", "eta_c")}} + + +def certificates(): + return { + "upstream_commit": verify_sources(), + "scope": "Exact numerical certificates, conditional on the upstream proof interfaces", + "cases": {name: certify_parameters(p) for name, p in { + "baseline_182": BASELINE, "frozen_154": proposed(50), + "same_network_130": proposed(42), "h46_112": proposed(36), + "balanced_frozen_153": balanced(50), + "balanced_same_network_129": balanced(42), + "balanced_h46_111": balanced(36), + "near_supremum_frozen": near_supremum(50), + "near_supremum_same_network": near_supremum(42), + "near_supremum_h46": near_supremum(36), + }.items()} | { + f"pushed_{v}": certify_parameters(pushed(v), generalized_beta=v != "109", + strict_margin=True) + for v in ("109", "108", "rational") + }, + "networks": { + "baseline_h100": certify_network(100, 50, 20), + "improved_h100": certify_network(100, 42, 14), + "improved_h46": certify_network(46, 36, 12), + "rational_h46": certify_rational_network(), + }, + } + + +if __name__ == "__main__": + result = certificates() + out = ROOT / "certificates/parameters.json" + out.parent.mkdir(exist_ok=True) + out.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + for name, case in result["cases"].items(): + print(f"PASS {name}: minimum {case['minimum_margin']} ({', '.join(case['limiting_margins'])})") + print(f"Wrote {out.relative_to(ROOT)}") diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/compact_control_layer.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/compact_control_layer.py new file mode 100644 index 0000000000..11b2e751bf --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/compact_control_layer.py @@ -0,0 +1,156 @@ +#!/usr/bin/env python3 +"""Exact accounting for the written compact-control layer extension. + +Arithmetic checks accompany, and do not replace, the fixed-tape construction +and proof. Historical witnesses and pinned upstream files are unchanged. +""" +from fractions import Fraction as Q +from pathlib import Path +import hashlib +import json + +from certify import Parameters,constraints,margins,network,require,verify_sources +from paired_network import BIT_SAVING +from prepare_layers import guard,packed_exponents,complex_saving_bounds,serializable +from search_network import log_integer_bounds +from audit_short_guards import guard_width + +ROOT=Path(__file__).resolve().parents[1] +COMPLEX_H=25 +COMPLEX_SAVING=Q(418,10**12) +KAPPA=Q(83,10**12) + + +def ceil_log(n,base): + require(n>=1 and base>=2,'Invalid logarithm') + j=0;power=1 + while power=1 and min(m,W)>=2,'Invalid dimensions') + q0=ceil_log(W,2)*ceil_log(2*d,m) + k0=ceil_log(d,m) + H=d*G + front=(2*H+K-1)//K;back=(H+K-1)//K + reserved=q0+front+back + require(q0*K>=k0*ceil_log(W,2),'Insufficient row divisor capacity') + require(front*K>=2*H and back*K>=H,'Insufficient compact fields') + return dict(d=d,D=D,K=K,G=G,compact_capacity=H,row_chunks=q0, + front_chunks=front,back_chunks=back,reserved_chunks=reserved, + recursion_depth_cap=k0,row_bits=q0*K, + mode='individual' if D<=reserved else 'recursive', + active_chunks=max(0,D-reserved), + preprocessed_chunks=min(D,reserved), + front_slack_bits=front*K-2*H,back_slack_bits=back*K-H) + + +def repair_bound(p,n,K): + require(p>=2 and 0<=n<=p,'Invalid repair family') + G=guard_width(p);ell=(p-1).bit_length() + require(K>=G+4*ell+10,'Use the common eventual cutoff') + delta=Q(2*n,1<0,'Positive spacing growth required') + e=packed_exponents(tau,sigma,beta,c,theta=Q(0)) + return dict(internal=e['internal'],leaf=e['leaf'], + preprocessing=max(Q(0),1-c), + layer=max(e['internal'],e['leaf'],1-c,Q(0))) + + +def parameters(): + return Parameters(tau=1-BIT_SAVING,sigma=1-COMPLEX_SAVING, + epsilon=Q(1999,10000),c=Q(1,5), + lam=1-Q(1671,4*10**12),lamp=1-Q(167,4*10**11), + kappa=KAPPA,beta=Q(1,1000),delta=Q(1,10**6),C1=Q(49961,10000)) + + +def check(p,h=COMPLEX_H,zeta=Q(1,10000)): + require(0<1-p.tau<=BIT_SAVING,'Bit exponent exceeds retained witness') + n=network(h);lo,hi=complex_saving_bounds(h) + require(0<1-p.sigma0,'Compact-control constraint: '+name) + gs=margins(p,layout_model='nonadjacent',assembly_model='tight-gaussian') + require(min(gs.values())>p.kappa,'No final absorption gap') + require(Q(1,2**34)0 for v in cs.values()),'Milestone constraint failed') + gs=margins(p,layout_model='nonadjacent',assembly_model='tight-gaussian') + require(min(gs.values())>p.kappa,'Milestone has no absorption gap') + return dict(parameters=vars(p),guard=g,recurrence=e,constraint_slacks=cs, + minimum_margin=min(gs.values()),absorption_gap=min(gs.values())-p.kappa) + + +def certificate(): + from prepare_layers import scenarios + p=parameters();main=check(p);n=network(COMPLEX_H) + _,log_hi=log_integer_bounds(n['m']) + require(n['eta_c']>COMPLEX_SAVING*log_hi,'Simple exponential comparison failed') + targets={} + for key,h in (('hypothetical_39',50),('hypothetical_34',25)): + old=scenarios()[key] + targets[key.replace('hypothetical_','target_')]=milestone(Parameters(**old['parameters']),h) + hi=complex_saving_bounds(COMPLEX_H)[1] + # The Gaussian margin enforces epsilon<1/5; the leaf margin limits + # 1-lambda' to (1-beta)*a_c 2^-34; proof review required.') diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/complex_circuit.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/complex_circuit.py new file mode 100644 index 0000000000..9e83a1065c --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/complex_circuit.py @@ -0,0 +1,454 @@ +#!/usr/bin/env python3 +"""Compressed side correction for the complex network, with binary frames. + +Target S must receive (1/2) * sum{x_T : T disjoint from S} +minus (1/2) * sum{x_T : |S cap T| = 2}. Both sums are computed by +cancellation-free addition graphs and injected as pieces with those weights. + +Labels are subspaces of F2^h with the dot product. A disjoint-sum node carries +the coordinate space of its covered points; a pair-star node carries the span +of its triple indicators, which is orthonormal. An injected piece must leave a +point outside S uncovered: the residual up to t_S^perp then contains an odd +coordinate vector. A disjoint piece covering every point outside S would have +the alternating residual , so the disjoint sum is split. +""" +from fractions import Fraction as Q +from itertools import combinations + +EMPTY = frozenset() + + +def subsets(points, k): + return [frozenset(c) for j in range(min(k, len(points))+1) + for c in combinations(points, j)] + + +class ComplexSideCircuit: + def __init__(self, h): + assert h >= 8, 'Need at least four points outside every target' + self.h = h + self.triples = list(combinations(range(h), 3)) + self.index = {t: i for i, t in enumerate(self.triples)} + self.support = [0]; self.args = [None]; self.kind = [None] + self.lookup = {}; self.input = {} + for i, t in enumerate(self.triples): + self.input[t] = len(self.support) + self.support.append(1 << i); self.args.append(None); self.kind.append('in') + self.points = {} # covered point masks, filled lazily + self.pieces = [] # (target, node, coefficient) + self.build_disjoint() + self.build_pair_stars() + self.prune() + + # -- node store ------------------------------------------------------- + def x(self, *pts): + return self.input[tuple(sorted(pts))] + + def add(self, a, b, kind): + if not a: return b + if not b: return a + sa, sb = self.support[a], self.support[b] + assert not sa & sb, 'Cancellation is forbidden' + key = (kind, sa | sb) + node = self.lookup.get(key) + if node is None: + node = len(self.support) + self.lookup[key] = node + self.support.append(sa | sb); self.args.append((a, b)); self.kind.append(kind) + return node + + def total(self, nodes, kind): + nodes = [x for x in nodes if x] + while len(nodes) > 1: + nodes = [self.add(nodes[i], nodes[i+1], kind) if i+1 < len(nodes) else nodes[i] + for i in range(0, len(nodes), 2)] + return nodes[0] if nodes else 0 + + # -- disjoint sums ---------------------------------------------------- + def vec(self, items, k): + """{E: sum of item nodes whose points avoid E}, |E| <= k.""" + if not items: return {EMPTY: 0} + if len(items) == 1: + p, node = items[0] + return {EMPTY: node, frozenset([p]): 0} if k else {EMPTY: node} + half = len(items)//2 + A = self.vec(items[:half], k); B = self.vec(items[half:], k) + return {ea | eb: self.add(xa, xb, 'd0') for ea, xa in A.items() + for eb, xb in B.items() if len(ea)+len(eb) <= k} + + def pairs(self, pts, weight, k): + """{E: sum of weight(u,v) over pairs avoiding E}, |E| <= k.""" + if len(pts) < 2: return {E: 0 for E in subsets(pts, k)} + half = len(pts)//2; L, R = pts[:half], pts[half:] + PL = self.pairs(L, weight, k); PR = self.pairs(R, weight, k) + rows = {u: self.vec([(r, weight(u, r)) for r in R], k) for u in L} + cross = {} + for ER in subsets(R, k): + for EL, node in self.vec([(u, rows[u][ER]) for u in L], k-len(ER)).items(): + cross[EL, ER] = node + return {EL | ER: self.total([xl, xr, cross[EL, ER]], 'd0') + for EL, xl in PL.items() for ER, xr in PR.items() if len(EL)+len(ER) <= k} + + def tri_parts(self, pts, k): + """Recursive halves and the two mixed families, before combination.""" + half = len(pts)//2; L, R = pts[:half], pts[half:] + TL = self.tri(L, k); TR = self.tri(R, k) + PR = {r: self.pairs(L, lambda u, v, r=r: self.x(u, v, r), k) for r in R} + PL = {u: self.pairs(R, lambda a, b, u=u: self.x(u, a, b), k) for u in L} + return L, R, TL, TR, PR, PL + + def tri(self, pts, k): + """{E: sum of triples inside pts avoiding E}, |E| <= k.""" + if len(pts) < 3: return {E: 0 for E in subsets(pts, k)} + L, R, TL, TR, PR, PL = self.tri_parts(pts, k) + c21 = {}; c12 = {} + for EL in subsets(L, k): + for ER, node in self.vec([(r, PR[r][EL]) for r in R], k-len(EL)).items(): + c21[EL, ER] = node + for ER in subsets(R, k): + for EL, node in self.vec([(u, PL[u][ER]) for u in L], k-len(ER)).items(): + c12[EL, ER] = node + return {EL | ER: self.total([xl, xr, c21[EL, ER], c12[EL, ER]], 'd0') + for EL, xl in TL.items() for ER, xr in TR.items() if len(EL)+len(ER) <= k} + + def build_disjoint(self): + """Six pieces per target, each leaving an outside point uncovered.""" + pts = list(range(self.h)) + L, R, TL, TR, PR, PL = self.tri_parts(pts, 3) + R1, R2 = R[:len(R)//2], R[len(R)//2:] + L1, L2 = L[:len(L)//2], L[len(L)//2:] + for S in self.triples: + E = frozenset(S); EL = E & frozenset(L); ER = E & frozenset(R) + pieces = [TL[EL], TR[ER]] + for half in (R1, R2): + pieces.append(self.vec([(r, PR[r][EL]) for r in half], 3-len(EL))[ER & frozenset(half)]) + for half in (L1, L2): + pieces.append(self.vec([(u, PL[u][ER]) for u in half], 3-len(ER))[EL & frozenset(half)]) + for node in pieces: self.emit(S, node, Q(1, 2)) + + # -- pair stars ------------------------------------------------------- + def build_pair_stars(self): + """Prefix and suffix pair-star sums around each excluded third point.""" + h = self.h + for a, b in combinations(range(h), 2): + others = [u for u in range(h) if u not in (a, b)] + n = len(others) + pre = [0] + for u in others: pre.append(self.add(pre[-1], self.x(a, b, u), 'd2')) + suf = [0]*(n+1) + for i in range(n-1, -1, -1): suf[i] = self.add(self.x(a, b, others[i]), suf[i+1], 'd2') + for i, c in enumerate(others): + S = tuple(sorted((a, b, c))) + self.emit(S, pre[i], Q(-1, 2)); self.emit(S, suf[i+1], Q(-1, 2)) + + def emit(self, S, node, coef): + """Inject a piece, splitting it until it leaves a point outside S uncovered.""" + if not node: return + if self.cover(node) | sum(1 << p for p in S) == (1 << self.h)-1: + a, b = self.args[node] + self.emit(S, a, coef); self.emit(S, b, coef) + else: + self.pieces.append((S, node, coef)) + + # -- bookkeeping ------------------------------------------------------ + def prune(self): + self.active = set(); stack = [node for _, node, _ in self.pieces] + while stack: + node = stack.pop() + if node in self.active: continue + self.active.add(node) + if self.args[node]: stack.extend(self.args[node]) + self.additions = sum(self.args[n] is not None for n in self.active) + self.roles = self.additions + len(self.pieces) + + def cover(self, node): + """Mask of ground points covered by the node's source triples.""" + if node not in self.points: + s = self.support[node]; mask = 0 + while s: + low = s & -s; mask |= sum(1 << p for p in self.triples[low.bit_length()-1]); s ^= low + self.points[node] = mask + return self.points[node] + + def stats(self): + v = len(self.triples) + return dict(h=self.h, v=v, additions=self.additions, injections=len(self.pieces), + roles=self.roles, roles_per_target=round(self.roles/v, 3), + disjoint_additions=sum(self.kind[n] == 'd0' for n in self.active), + pair_star_additions=sum(self.kind[n] == 'd2' for n in self.active)) + + +# -- binary linear algebra on F2^h, vectors as integer masks --------------- +def echelon(vectors): + """Reduced basis {pivot bit: vector}; raises on dependence.""" + basis = {} + for x in vectors: + for bit, b in basis.items(): + if x & bit: x ^= b + assert x, 'Dependent label vectors' + bit = x & -x + for other in basis: + if basis[other] & bit: basis[other] ^= x + basis[bit] = x + return basis + + +def reduce(basis, x): + for bit, b in basis.items(): + if x & bit: x ^= b + return x + + +def dot(x, y): + return (x & y).bit_count() & 1 + + +def rank(rows): + rows = list(rows); r = 0 + for col in range(max((x.bit_length() for x in rows), default=0)): + bit = 1 << col + pivot = next((i for i in range(r, len(rows)) if rows[i] & bit), None) + if pivot is None: continue + rows[r], rows[pivot] = rows[pivot], rows[r] + for i in range(len(rows)): + if i != r and rows[i] & bit: rows[i] ^= rows[r] + r += 1 + return r + + +class Label: + """A binary subspace with a canonical basis.""" + def __init__(self, vectors): + self.basis = echelon(vectors); self.dim = len(self.basis) + self.key = tuple(sorted(self.basis.values())) + + def contains(self, other): + return all(not reduce(self.basis, x) for x in other.basis.values()) + + def nondegenerate(self): + vs = list(self.basis.values()) + return rank([sum(dot(a, b) << j for j, b in enumerate(vs)) for a in vs]) == len(vs) + + def complement_in(self, other): + """Basis of other ∩ self^perp, assuming self ⊆ other.""" + vs = list(other.basis.values()); us = list(self.basis.values()); k = len(us) + rows = [sum(dot(v, u) << j for j, u in enumerate(us)) | 1 << (k+i) + for i, v in enumerate(vs)] + r = 0 + for col in range(k): + bit = 1 << col + piv = next((i for i in range(r, len(rows)) if rows[i] & bit), None) + if piv is None: continue + rows[r], rows[piv] = rows[piv], rows[r] + for i in range(len(rows)): + if i != r and rows[i] & bit: rows[i] ^= rows[r] + r += 1 + out = [] + for row in rows[r:]: + assert not row & ((1 << k)-1) + x = 0 + for i, v in enumerate(vs): + if row >> (k+i) & 1: x ^= v + out.append(x) + return out + + +def odd(vectors): + return any(x.bit_count() & 1 for x in vectors) + + +# -- exact checks ----------------------------------------------------------- +def tmask(t): + return sum(1 << p for p in t) + + +class Checks: + """Exact verification of the side map, labels and compiled roles.""" + def __init__(self, c): + self.c = c; self.h = c.h; self.cache = {}; self.verdicts = {} + self.everything = Label([1 << p for p in range(c.h)]) + + def label(self, node): + if node in self.cache: return self.cache[node] + c = self.c; kind = c.kind[node] + if kind == 'in': + vectors = [tmask(c.triples[node-1])] + elif kind == 'd0': + m = c.cover(node); vectors = [1 << p for p in range(self.h) if m >> p & 1] + else: + s = c.support[node]; ts = [] + while s: + low = s & -s; ts.append(c.triples[low.bit_length()-1]); s ^= low + common = set(ts[0]).intersection(*ts) + assert len(common) >= 2, 'Pair-star node without a common pair' + vectors = [tmask(t) for t in ts] + lab = Label(vectors); self.cache[node] = lab + return lab + + def target_frame(self, S): + t = tmask(S) + key = ('perp', S) + if key not in self.cache: + self.cache[key] = Label([x for x in (1 << p for p in range(self.h)) + if not dot(x, t)] + [tmask((S[0], S[1])), tmask((S[1], S[2]))]) + return self.cache[key] + + def residual_ok(self, small, big): + """small ⊆ big and big ⊖ small is zero or has an odd vector.""" + key = (small.key, big.key) + if key not in self.verdicts: + res = small.complement_in(big) if big.contains(small) else None + self.verdicts[key] = res is not None and (not res or odd(res)) + return self.verdicts[key] + + def label_ok(self, lab): + """Nondegenerate, contains an odd vector, and its complement is zero or does.""" + key = ('label', lab.key) + if key not in self.verdicts: + perp = lab.complement_in(self.everything) + self.verdicts[key] = (lab.nondegenerate() and odd(lab.basis.values()) + and (not perp or odd(perp))) + return self.verdicts[key] + + def verify_map(self): + c = self.c + for node in c.active: + if c.args[node]: + a, b = c.args[node] + assert a < node and b < node and not c.support[a] & c.support[b] + assert c.support[node] == c.support[a] | c.support[b] + got = {} + for S, node, coef in c.pieces: + assert coef in (Q(1, 2), Q(-1, 2)) + key = (S, coef) + assert not got.get(key, 0) & c.support[node], 'Overlapping pieces' + got[key] = got.get(key, 0) | c.support[node] + nonzero = 0 + for S in c.triples: + zero = sum(1 << i for i, T in enumerate(c.triples) if not set(S) & set(T)) + two = sum(1 << i for i, T in enumerate(c.triples) if len(set(S) & set(T)) == 2) + assert got.get((S, Q(1, 2)), 0) == zero and got.get((S, Q(-1, 2)), 0) == two + nonzero += zero.bit_count()+two.bit_count() + return dict(targets=len(c.triples), nonzero_coefficients=nonzero, + side_map_exact=True, coefficients='+1/2 disjoint, -1/2 intersection two') + + def verify_labels(self): + c = self.c; checked = 0 + for node in sorted(c.active): + lab = self.label(node) + assert self.label_ok(lab), node # includes the exit to the full space + if c.args[node]: + for child in c.args[node]: + assert self.residual_ok(self.label(child), lab), (node, child) + checked += 1 + for S, node, coef in c.pieces: + assert self.residual_ok(self.label(node), self.target_frame(S)), (S, node) + checked += 1 + return dict(active_nodes=len(c.active), checked_inclusions=checked, + all_labels_nondegenerate=True, all_residuals_have_odd_vectors=True) + + +def compile_roles(c): + """Reversible roles: one per addition plus one per injected piece.""" + users = {x: [] for x in c.active} + for node in sorted(c.active): + if c.args[node]: + for pos, x in enumerate(c.args[node]): users[x].append(('gate', node, pos)) + for i, (_, node, _) in enumerate(c.pieces): users[node].append(('output', i)) + edge = {}; sources = {}; outputs = {}; gates = []; size = 0 + for node in sorted(c.active): + if c.args[node]: + ins = (edge[node, 0], edge[node, 1]); pivot = ins[0] + else: + pivot = size; size += 1; ins = (pivot,); sources[c.triples[node-1]] = pivot + assert users[node] + outs = (pivot,)+tuple(range(size, size+len(users[node])-1)) + size += len(users[node])-1 + assert len(set(ins)) == len(ins) and set(ins) & set(outs) == {pivot} + gates.append((node, ins, outs)) + for user, slot in zip(users[node], outs): + if user[0] == 'gate': edge[user[1], user[2]] = slot + else: outputs[user[1]] = slot + assert size == c.roles + return dict(roles=size, gates=gates, sources=sources, outputs=outputs) + + +def verify_role_frames(c, checks, code=None): + """Follow every physical role in both directions through its frames.""" + code = code or compile_roles(c) + def step(small, big): assert checks.residual_ok(small, big) + frames = [None]*code['roles'] + for T, slot in code['sources'].items(): frames[slot] = checks.label(c.input[T]) + for node, ins, outs in code['gates']: + lab = checks.label(node) + for slot in set(ins+outs): + if frames[slot] is None: assert checks.label_ok(lab) # entry from D0 + else: step(frames[slot], lab) + frames[slot] = lab + for i, slot in code['outputs'].items(): + S = c.pieces[i][0]; J = checks.target_frame(S) + step(frames[slot], J); frames[slot] = J + for lab in frames: + assert checks.label_ok(lab) # includes the exit residual to D1 + # Reverse stage: complements, traversed backward. U^perp grows iff U shrinks. + # Its entries and exits have the forward residuals U^perp and U, checked above. + back = [None]*code['roles'] + for i, slot in code['outputs'].items(): back[slot] = ('line', c.pieces[i][0]) + for node, ins, outs in reversed(code['gates']): + lab = checks.label(node) + for slot in set(ins+outs): + prev = back[slot] + if prev is None: + assert checks.label_ok(lab) # reverse entry residual is lab^perp + elif prev[0] == 'line': # ⊆ U^perp iff U ⊆ t_S^perp + step(lab, checks.target_frame(prev[1])) + else: + step(lab, prev[1]) # prev^perp ⊆ lab^perp iff lab ⊆ prev + back[slot] = ('node', lab) + for T, slot in code['sources'].items(): + assert back[slot][1].key == checks.label(c.input[T]).key # ends at t_T^perp + return dict(roles=code['roles'], forward_frames_nested=True, + reverse_complement_frames_nested=True) + + +def simulate_invocation(c, code, x, y, side, center, inverse=False): + """Scalar invocation over Q with arbitrary scratch; returns the new state. + + Forward: L,-J,L^-1,-R,V,G,R,L,J,L^-1,G^-1,V^-1 gives y <- y + x. + inverse=True runs the inverted schedule, giving x <- x - y. + """ + h = c.h; T = c.triples + side = list(side); center = dict(center); x = dict(x); y = dict(y) + def L(sign=1): + order = code['gates'] if sign > 0 else list(reversed(code['gates'])) + for node, ins, outs in order: + if sign > 0: + if len(ins) == 2: side[ins[0]] += side[ins[1]] + for o in outs[1:]: side[o] += side[outs[0]] + else: + for o in outs[1:]: side[o] -= side[outs[0]] + if len(ins) == 2: side[ins[0]] -= side[ins[1]] + def J(target, sign): + for i, slot in code['outputs'].items(): + S, _, coef = c.pieces[i]; target[S] += sign*coef*side[slot] + def V(source, sign): + for t, slot in code['sources'].items(): side[slot] += sign*source[t] + def G(source, sign): + for i in range(h): center[i] += sign*sum(source[t] for t in T if i in t) + center['*'] += sign*sum(source.values()) + def R(target, sign): + for t in T: target[t] += sign*(sum(center[i] for i in t)-center['*'])/2 + if not inverse: + L(); J(y, -1); L(-1); R(y, -1); V(x, 1); G(x, 1); R(y, 1) + L(); J(y, 1); L(-1); G(x, -1); V(x, -1) + else: # inverse schedule with logical source y and target x + V(y, 1); G(y, 1); L(); J(x, -1); L(-1); R(x, -1); G(y, -1); V(y, -1) + R(x, 1); L(); J(x, 1); L(-1) + return x, y, side, center + + +if __name__ == '__main__': + import sys, time + for h in map(int, sys.argv[1:] or ['10', '12', '16']): + t = time.time(); c = ComplexSideCircuit(h) + print(c.stats(), f'{time.time()-t:.1f}s', flush=True) diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/complex_network.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/complex_network.py new file mode 100644 index 0000000000..af9bb6d7b3 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/complex_network.py @@ -0,0 +1,120 @@ +#!/usr/bin/env python3 +"""Conditional 59/10^11 witness: a compressed complex side circuit. + +The compact-control witness was limited by the original complex motif, whose +v*z_c side wires per invocation dilute its rank deficit. The new side circuit +computes the same correction with shared sums, binary coordinate and pair-star +labels, and the bit network's transparent twelve-operation schedule. The bit +network, compact-control movement and assembly recipe are unchanged. +""" +from fractions import Fraction as Q +from math import comb +from pathlib import Path +import json + +from certify import Parameters, constraints, margins, require, verify_sources +from compact_control_layer import layer_exponents +from complex_circuit import ComplexSideCircuit, Checks, compile_roles, verify_role_frames +from paired_network import BIT_SAVING +from prepare_layers import serializable +from search_network import log_integer_bounds + +ROOT = Path(__file__).resolve().parents[1] +H = 25 +COMPLEX_SAVING = Q(14, 10**9) +LOG_BOUND = Q(966, 100) +KAPPA = Q(59, 10**11) + + +def counts(c): + h = c.h; v = comb(h, 3); m = h**3; N = v**3; I = 3*v*v + R = c.roles; W = 2*N+I*(R+h+1); L = I*(h+1)*h + s = W*m-2*N+2*L + require(L < N, 'Complex deficit is not positive') + return dict(h=h, v=v, m=m, N=N, I=I, side_roles_per_invocation=R, + central_roles=h+1, W=W, L=L, s=s, deficit=W*m-s, eta=Q(W*m-s, W*m), + original_side_wires_per_invocation=v*(comb(h-3, 3)+3*(h-3))) + + +def gate_count(c, n): + """Per invocation: four mixer passes, two copies, two injections, four central gates.""" + per = 4*len(c.active)+4*n['v']+4 + require(n['I']*per <= 12*n['W'], 'The 12W gate bound behind E=64(W+m+1)^3 failed') + return dict(gates_per_invocation=per, total_gates=n['I']*per, twelve_W=12*n['W']) + + +def guard(n, beta, zeta): + """Generalized stopped-depth guard with the new complex constants.""" + m, s, W = n['m'], n['s'], n['W'] + E = 64*(W+m+1)**3; B = s+E + require(m >= 3 and 2 <= s < m**5, 'Unverified coefficient-depth hypothesis') + require(s*(8+E) <= 9*B*B, 'One-piece constant failed') + C1 = 5-4*beta+zeta + raw = max(Q(128*m*B*B), 18*m*B*B*(1+1/zeta)) + C0 = -(-raw.numerator//raw.denominator) + require(9*m*B*B*(1+1/zeta)+18 <= C0, 'Whole-layer constant failed') + return dict(m=m, s=s, E=E, B=B, beta=beta, zeta=zeta, C0=C0, C1=C1) + + +def parameters(): + return Parameters(tau=1-BIT_SAVING, sigma=1-COMPLEX_SAVING, + epsilon=Q(19999, 100000), c=Q(999, 1000), + lam=1-Q(2958, 10**12), lamp=1-Q(2956, 10**12), + kappa=KAPPA, beta=Q(1, 1000), delta=Q(1, 10**6), + C1=Q(49961, 10000)) + + +def witness(p, n): + g = guard(n, p.beta, Q(1, 10000)) + require(p.C1 == g['C1'], 'Guard mismatch') + e = layer_exponents(p.tau, p.sigma, p.beta, p.c) + slacks = constraints(p, layout_model='nonadjacent', assembly_model='tight-gaussian') + slacks['packed_overhead'] = p.lam-e['internal'] # compact control: internal = max exponent + slacks['reserved_axes'] = p.lamp-e['preprocessing'] + for name, slack in slacks.items(): require(slack > 0, 'Constraint failed: '+name) + gs = margins(p, layout_model='nonadjacent', assembly_model='tight-gaussian') + require(min(gs.values()) > p.kappa, 'No final absorption gap') + return dict(parameters=vars(p), guard=g, recurrence=e, constraint_slacks=slacks, + margins=gs, minimum_margin=min(gs.values()), + limiting_margins=[k for k, v in gs.items() if v == min(gs.values())], + absorption_gap=min(gs.values())-p.kappa) + + +def witness_only(): + """Counts and parameter witness without the full finite checks (for the patch).""" + n = counts(ComplexSideCircuit(H)) + require(n['eta'] > COMPLEX_SAVING*LOG_BOUND, 'Complex saving failed') + return witness(parameters(), n) + + +def certificate(): + c = ComplexSideCircuit(H); checks = Checks(c); code = compile_roles(c) + side = checks.verify_map(); labels = checks.verify_labels() + roles = verify_role_frames(c, checks, code) + n = counts(c) + lo, hi = log_integer_bounds(n['m']) + require(hi < LOG_BOUND, 'Logarithm enclosure failed') + require(n['eta'] > COMPLEX_SAVING*LOG_BOUND, 'Complex saving failed') + p = parameters(); w = witness(p, n) + require(Q(1, 2**31) < KAPPA < Q(1, 2**30), 'Unexpected dyadic scale') + # With the bit exponent fixed, g3 <= epsilon*(1-lambda) < epsilon*a_b < a_b/5. + ceiling = BIT_SAVING/5 + require(ceiling < Q(1, 2**30), 'This bit network could cross 2^-30') + return dict(status='CONDITIONAL 59/10^11 WITNESS; COMPRESSED COMPLEX SIDE CIRCUIT; NOT FORMAL VERIFICATION', + upstream_commit=verify_sources(), circuit=c.stats(), side_map=side, + labels=labels, role_frames=roles, gates=gate_count(c, n), + complex_counts=n, complex_saving=COMPLEX_SAVING, log_m_upper=LOG_BOUND, + log_enclosure=(lo, hi), complex_deficit_slack=n['eta']-COMPLEX_SAVING*LOG_BOUND, + bit_saving=BIT_SAVING, witness=w, + improvement_over_compact_control=KAPPA/Q(83, 10**12), + scoped_ceiling=dict(upper=ceiling, below_2_to_minus_30=True, + scope='Published h=50 paired bit network and retained Gaussian margin; not a bound on other networks or algorithms.'), + scope='Conditional on the pinned upstream interfaces, the compact-control movement and guard proofs, the paired bit network, and the written binary-frame transfer for this complex side circuit. Exact arithmetic and finite checks are not formal verification.') + + +if __name__ == '__main__': + result = serializable(certificate()) + (ROOT/'certificates/complex-network.json').write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print('PASS conditional', KAPPA, '> 2^-31; minimum margin', result['witness']['minimum_margin']) + print('Side roles per invocation', result['complex_counts']['side_roles_per_invocation'], + 'vs original', result['complex_counts']['original_side_wires_per_invocation']) diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/__init__.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/__init__.py new file mode 100644 index 0000000000..e0758c53ca --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/__init__.py @@ -0,0 +1 @@ +"""Copied-center incremental certificates, copyright 2026 icekylinx.""" diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/corners.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/corners.py new file mode 100644 index 0000000000..80fc438270 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/corners.py @@ -0,0 +1,142 @@ +"""Exact selected PR31/PR33 corner witness and zero-minor verification. + +Original corner and incidence methods: Rohan Arun, PR31, commit +02f68f95369c39955c5ffcfddbd75cd83e26b305 (Apache-2.0; OpenAI Codex assistance). +Parameterization: Dominik Scholz, PR33, commit +a499a345c040aa15b68e984a0904eadc485c7a7e (Apache-2.0; recorded Anthropic +Claude Opus 5.5 and OpenAI GPT-6 Astra/Codex assistance). +Modification copyright 2026 icekylinx, Apache-2.0, with OpenAI GPT-6 Astra +and Codex assistance: verify the selected (25,23) saved partitions directly; +omit exploratory matroid search and unrelated historical dimensions. +See repository NOTICE, LICENSE and SOURCES.json for retained notices. +""" +from fractions import Fraction as Q +from functools import reduce +from math import gcd + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def integer_rank(matrix): + """PR31 exact rank by integer row operations and gcd reduction.""" + matrix = [row[:] for row in matrix] + height = len(matrix) + width = len(matrix[0]) if height else 0 + rank = 0 + for col in range(width): + pivot = next((r for r in range(rank,height) if matrix[r][col]),None) + if pivot is None: + continue + matrix[rank],matrix[pivot] = matrix[pivot],matrix[rank] + for row in range(rank+1,height): + if not matrix[row][col]: + continue + d = gcd(matrix[rank][col],matrix[row][col]) + u,v = matrix[rank][col]//d,matrix[row][col]//d + matrix[row] = [u*x-v*y for x,y in zip(matrix[row],matrix[rank])] + common = reduce(gcd,matrix[row],0) + if common: + matrix[row] = [x//common for x in matrix[row]] + rank += 1 + if rank == height: + break + return rank + + +def incidence(edges, mask, constant): + bits = [] + while mask: + bit = mask & -mask + bits.append(bit) + mask ^= bit + return [[int(bit == constant or bit == 1 << u or bit == 1 << v) + for bit in bits] for u,v in edges] + + +def verify(certificate): + a,b = 25,23 + m,d = a*b,a+b-1 + rows = (list(range(a))+list(range(1,a))+[0])[:d] + cols = ([a-1]+list(range(a-1))+list(range(a)))[-d:] + require(certificate['dimensions'] == [a,b] and certificate['m'] == m + and certificate['d'] == d, 'Wrong selected corner dimensions') + require(certificate['R'] == rows and certificate['C'] == cols, + 'Wrong controlled boundary prescription') + require(certificate['gamma_offset'] == (m-d)%b, 'Wrong column residue offset') + left = [Q((r+1)**2,sum(s*s for s in range(1,a+1))) for r in range(a)] + right = [Q((t+1)**3,sum(s**3 for s in range(1,b+1))) for t in range(b)] + witness = certificate['witness'] + require(list(map(Q,witness['left_weights'])) == left and + list(map(Q,witness['right_weights'])) == right, + 'Wrong rational witness weights') + require(sum(left) == sum(right) == 1 and all(left) and all(right), + 'Degenerate normalized witness') + matrix = [[Q(rows[i]==cols[j])/left[rows[i]] + +Q(i%b==(m-d+j)%b)/right[i%b]-1 + for j in range(d)] for i in range(d)] + available = list(range(d)) + pivots = [] + require(len(witness['pivots']) == d, 'Incomplete rational pivot certificate') + for row,(saved_row,saved_col,saved_value) in enumerate(witness['pivots']): + col = next((j for j in reversed(available) if matrix[row][j]),None) + require(saved_row == row and col == saved_col and col is not None, + 'Wrong rightmost rational pivot') + value = matrix[row][col] + require(value == Q(saved_value) and value != 0, 'Wrong rational pivot value') + pivots.append((row,col)) + available.remove(col) + for r in range(row+1,d): + if matrix[r][col]: + ratio = matrix[r][col]/value + for c in available: + matrix[r][c] -= ratio*matrix[row][c] + matrix[r][col] = 0 + runs = [] + for row,col in pivots: + if runs and row == runs[-1][-1][0]+1 and col == runs[-1][-1][1]+1: + runs[-1].append([row,col]) + else: + runs.append([[row,col]]) + require(certificate['runs'] == runs, 'Wrong contiguous pivot runs') + profile = dict(singletons=sum(len(run)==1 for run in runs), + blocks=[len(run) for run in runs if len(run)>1]+[m-2*d], + rank=m-d) + require(profile == certificate['data_profile'] == + dict(singletons=11,blocks=[21,15,481],rank=528), + 'Wrong selected data profile') + constant = 1 << (a+b) + full = (constant << 1)-1 + zero_records = certificate['zero_minor_certificates'] + require(len(zero_records) == 315, 'Wrong number of zero-minor certificates') + selected_rows,selected_cols = [],[] + position = 0 + for row,pivot in pivots: + for col in range(pivot+1,d): + if col in selected_cols: + continue + require(position < len(zero_records), 'Missing rightmost-zero minor') + record = zero_records[position] + position += 1 + require((record['row'],record['col'],record['size']) == + (row,col,row+1), 'Wrong zero-minor coverage/order') + partition = record['partition'] + require(isinstance(partition,int) and 0 <= partition <= full, + 'Invalid incidence partition') + row_edges = [(rows[i],a+i%b) for i in selected_rows+[row]] + col_edges = [(cols[j],a+(m-d+j)%b) for j in selected_cols+[col]] + r1 = integer_rank(incidence(row_edges,partition,constant)) + r2 = integer_rank(incidence(col_edges,full^partition,constant)) + require(r1 == record['row_rank'] and r2 == record['column_rank'], + 'Wrong exact partition ranks') + require(r1+r2 < row+1, 'Partition fails to force zero minor') + require(record['common_independent_size'] == r1+r2, + 'Inconsistent archived intersection rank') + selected_rows.append(row) + selected_cols.append(pivot) + require(position == len(zero_records), 'Unused or duplicated minor certificate') + return dict(dimensions=[a,b], rational_pivots=d, zero_minors=position, + integer_rank_checks=2*position, data_profile=profile, + exact=True, matroid_search_repeated=False) diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/physical.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/physical.py new file mode 100644 index 0000000000..31d0083382 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/physical.py @@ -0,0 +1,31 @@ +"""Exact copied-retained-total physical histogram replacement. + +Copyright 2026 icekylinx, Apache-2.0; developed with OpenAI GPT-6 Astra and +Codex assistance. The copied-stream interface is credited to Aurel Prosz +(Paureel); this application to retained-total reads is icekylinx's work. +""" +from .corners import require + + +def copied_histogram(record): + """Return H' from the unchanged selected scalar/matching record.""" + h, roles = record['h'], record['R'] + old = record['histogram'] + loss = h*(h-1) + require(record['loss'] == loss, 'Every selected retained center must have rank h-1') + require(len(old) == h+1 and all(isinstance(n,int) and n>=0 for n in old), + 'Invalid original physical histogram') + require(sum(r*n for r,n in enumerate(old)) == h*roles+2*loss, + 'Original producer rank identity failed') + require(old[h] >= h, 'Missing retained-total rank-h cleanup children') + changed = list(old) + changed[1] += h + changed[h] -= h + require(sum(changed) == sum(old), 'Copied reads changed the charged call count') + require(changed[h-1] == old[h-1], 'Copied rank-(h-1) transforms were removed') + require(all(changed[r] == old[r] for r in range(h+1) if r not in (1,h)), + 'Copied read modified an unrelated residual') + mass = sum(r*n for r,n in enumerate(changed)) + require(mass == h*roles+loss, 'Copied-total rank mass failed') + return dict(histogram=changed, rank_sum=mass, saved_rank=loss, + retained_total_uses=h, roles_unchanged=roles) diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers_network.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers_network.py new file mode 100644 index 0000000000..74796d6e15 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers_network.py @@ -0,0 +1,196 @@ +#!/usr/bin/env python3 +"""Exact selected copied-center moments and semantic assembly. + +Copyright 2026 icekylinx. Apache-2.0. +Prepared with substantial OpenAI GPT-6 Astra and Codex assistance. +Two-stage topology: Aurel Prosz (Paureel), through PR29 (Zhihao Chen). +Corner method: Rohan Arun PR31, parameterized by Dominik Scholz PR33. +Semantic assembly: Zhihao Chen PR23, building on RaD (hipotures). +See SOURCES.json and references/copied-centers for pinned contributions. +""" +import argparse +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import json +import sys + +from certify import require +from copied_centers.physical import copied_histogram as physical_histogram +from partial_swap_network import moment +from structured_bulk_assembly import assembly, halving, js + +ROOT = Path(__file__).resolve().parents[1] +AB = Q(384599, 10**10) +AC = Q(717, 10**7) +KAPPA = Q(384569, 10**10) +GRID = 1 << 100 + + +def copied_histogram(row): + require(row['v'] == comb(row['h'], 3), 'Triple count') + return physical_histogram(row)['histogram'] + + +def profile(rows, corner=None): + a, b = (row['h'] for row in rows) + m, N = a*b, rows[0]['v']*rows[1]['v'] + B1, B2 = (N//row['v']*row['R'] for row in rows) + W = 2*N+B1+B2 + L = sum(N//row['v']*row['loss'] for row in rows) + z = Counter() + + def ordinary(h, r, n): + if 2*r > h: + z[2*r-h] += n + z[1] += (h-r)*n + else: + z[1] += r*n + + if corner is not None: + require((a, b) == (25, 23), 'Selected bit dimensions') + require(corner['dimensions'] == [a, b] and corner['m'] == m, 'Corner dimensions') + cp = corner['data_profile'] + require(cp['singletons'] == 11 and cp['blocks'] == [21, 15, 481], 'Selected data profile') + for h, count in ((a, B1), (b, B2)): + z[h] += count + z[m-2*h] += count + z[1] += cp['singletons']*2*N + for t in cp['blocks']: + z[t] += 2*N + else: + require((a, b) == (28, 28), 'Selected complex dimensions') + z[m-a] += B1 + z[m-b] += B2 + z[(a-1)*(b-1)] += 2*N + + copied = [] + for row in rows: + h, copies = row['h'], N//row['v'] + hist = copied_histogram(row) + copied.append(dict(h=h, center_ranks=[h-1]*h, histogram=hist)) + for r, n in enumerate(hist): + if corner is not None: + ordinary(h, r, copies*n) + elif r: + z[r] += copies*n + if corner is not None: + ordinary(h, h-1, 2*N) + else: + z[h-1] += 2*N + z[1] += N # Paid endpoint transform on the copied first output. + z = dict(sorted((t, n) for t, n in z.items() if t and n)) + require(all(0 < t < m and n > 0 for t, n in z.items()), 'Child domains') + s = W*m-N+L + require(sum(t*n for t, n in z.items()) == s, 'Complete two-stage rank') + return dict(dimensions=[a,b], m=m, N=N, B1=B1, B2=B2, W=W, L=L, + total_rank=s, deficit=N-L, maxchild=max(z), + copied_center_circuits=copied, child_multiplicities=z) + + +def grid_upper(x): + return Q((x.numerator*GRID+x.denominator-1)//x.denominator, GRID) + + +def bit_moment(p): + def log_upper(x): + k = 0 + while x >= 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + return 2*sum((z**(2*j+1)/(2*j+1) for j in range(24)), Q(0)) + 2*z**49/(49*(1-z*z)) + return grid_upper(k*small(Q(2))+small(x)) + total = Q(0) + logs = {} + for t, n in p['child_multiplicities'].items(): + logs[t] = log_upper(Q(p['m'], t)) + u = AB*logs[t] + require(0 < u < 3, 'Bit exponential enclosure') + total += n*t*grid_upper(1+u+u*u/(2*(1-u/3))) + upper = total/(p['W']*p['m']) + require(upper < 1, 'Strict bit moment') + return dict(saving=AB, exponent=1-AB, moment_upper=upper, strict_gap=1-upper, + logarithm_upper_bounds=logs, rounding_denominator=GRID, + enclosure='24-term atanh log with geometric tail; exp upper 1+u+u^2/(2(1-u/3)); upward 2^-100 rounding') + + +def finite_bridge(bit, phase, rows): + m, W, s, N = (phase[k] for k in ('m', 'W', 'total_rank', 'N')) + terms = [] + for row in rows: + h, v, c = (row[k] for k in ('h', 'v', 'c')) + local = 4*(c+v)+10*v+4*h*v+4*h*h+8*h+8 + terms.append(dict(h=h, v=v, c=c, invocations=N//v, + local_group_upper=local, copied_center_extra_groups=2*h)) + G = N+sum(t['invocations']*(t['local_group_upper']+t['copied_center_extra_groups']) for t in terms) + E = 64*(W+m+G+1)**3 + charge = 2*G*W*W+8*s+4*W+4+32*m + B, r = s+E, phase['maxchild'] + C0 = 32*m*B*B + require(charge < E and 2*B*(m-r) >= s+E and 2*B+18 < C0, 'Semantic induction') + db, dc = halving(bit['m'], bit['maxchild']), halving(m, r) + wb, wc = bit['W'].bit_length(), W.bit_length() + coeff = wb*db+wc*dc + degree = 1000*((coeff*51)//25000+1) + return dict(bit=dict(m=bit['m'], W=bit['W'], maxchild=bit['maxchild'], halving_degree=db, wire_bits=wb), + complex=dict(m=m, W=W, s=s, maxchild=r, halving_degree=dc, wire_bits=wc, + scalar_terms=terms, scalar_group_upper=G), + semantic=dict(E=E, literal_charge=charge, strict_literal_gap=E-charge, B=B, + C0=C0, C1=1, induction_gap=2*B*(m-r)-s-E), + rows=dict(coefficient=coeff, degree=degree, suffix_slope=4*degree, + degree_gap=Q(degree)-Q(coeff*51,25), + contract='W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential')) + + +def certificate(): + require(not sys.flags.optimize, 'Run without -O') + def read(name): + return json.loads((ROOT/'certificates'/('copied-centers-'+name+'.json')).read_text()) + axes, row, corner, expected = map(read, ('bit-axes', 'complex-input', 'corner-25-23', 'input')) + bit, phase = profile(axes, corner), profile([row, row]) + for label, p in (('bit', bit), ('complex', phase)): + for key, value in expected[label].items(): + require(js(p[key]) == value, label+' saved '+key) + bm = bit_moment(bit) + cm = moment(phase['m'], phase['W'], phase['child_multiplicities'], AC, True) + require(bm['strict_gap'] == Q(expected['bit_moment_gap']), 'Saved bit moment') + require(cm['strict_gap'] == Q(expected['complex_moment_gap']), 'Saved complex moment') + bridge = finite_bridge(bit, phase, [row, row]) + assembled = assembly(AB, AC, bridge, KAPPA) + require(js(bridge) == expected['finite_bridge'], 'Saved finite bridge') + require(js(assembled) == expected['assembly'], 'Saved assembly') + require(len(assembled['strict_constraints']) == 47 and len(assembled['margins']) == 7, 'Complete assembly') + sources = sorted(p for p in (ROOT/'certificates').glob('copied-centers-*.json') if p.name != 'copied-centers-network.json') + sources += sorted((ROOT/'scripts').glob('copied_centers*.py')) + sources += sorted(p for p in (ROOT/'scripts/copied_centers').rglob('*') if p.is_file() and '__pycache__' not in p.parts) + sources += sorted((ROOT/'notes').glob('copied-centers-*.tex')) + sources += [ROOT/'scripts/structured_bulk_assembly.py', ROOT/'scripts/partial_swap_network.py'] + manifest = json.loads((ROOT/'references/copied-centers/MANIFEST.json').read_text()) + for name, digest in manifest['files'].items(): + require(sha256((ROOT/'references/copied-centers'/name).read_bytes()).hexdigest() == digest, 'Adopted source hash: '+name) + sources += [ROOT/'references/copied-centers/MANIFEST.json'] + return dict(status='Conditional copied-center multiplication witness', kappa=KAPPA, + bit=dict(counts=bit, **bm), complex=dict(counts=phase, **cm), + finite_bridge=bridge, assembly=assembled, + inherited_commit='0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52', adopted_sources=manifest, + source_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in sources}, + scope='Exact finite moments and assembly; producer and corner certificates checked separately. ' + 'Copied-stream scheduling, simultaneous basis existence, analytic and tape interfaces remain written proof dependencies.') + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--output', type=Path, default=ROOT/'certificates/copied-centers-network.json') + args = parser.parse_args() + result = certificate() + args.output.write_text(json.dumps(js(result), indent=2, sort_keys=True)+'\n') + print('PASS kappa=384569/10000000000 = 3.84569e-5') + print('Both exact moments; copied-center rank budgets; C1=1; p^2000 row stock; 47 strict constraints') + + +if __name__ == '__main__': + main() diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/exclusion_circuit.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/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<=1 holds eventually because 2eps<1. + """ + s = constraints(p, layout_model='nonadjacent', assembly_model='tight-gaussian') + for key in ('gaussian_cost', 'dimension_upper_bound', 'alpha_below_sqrt_p', 'gamma_sublinear'): + del s[key] + s['gaussian_cost'] = 1-p.delta-2*p.epsilon + s['alpha_squared_theta_growth'] = 1-2*p.epsilon + return s + + +def fast_margins(p): + g = margins(p, layout_model='nonadjacent', assembly_model='tight-gaussian') + g['g5'] = 1-p.delta-2*p.epsilon + return g + + +def witness(p, n): + g = guard(n, p.beta, ZETA) + require(p.C1 == g['C1'], 'Guard mismatch') + e = layer_exponents(p.tau, p.sigma, p.beta, p.c) + slacks = fast_constraints(p) + slacks['packed_overhead'] = p.lam-e['internal'] + slacks['reserved_axes'] = p.lamp-e['preprocessing'] + for name, slack in slacks.items(): require(slack > 0, 'Constraint failed: '+name) + gs = fast_margins(p) + require(min(gs.values()) > p.kappa, 'No final absorption gap') + return dict(parameters=vars(p), guard=g, recurrence=e, constraint_slacks=slacks, + margins=gs, minimum_margin=min(gs.values()), + limiting_margins=[k for k, v in gs.items() if v == min(gs.values())], + absorption_gap=min(gs.values())-p.kappa) + + +def witness_only(): + """Counts and parameter witness without the finite checks (for the patch).""" + n = counts(ComplexSideCircuit(H)) + require(n['eta'] > COMPLEX_SAVING*Q(966, 100), 'Complex saving failed') + return witness(parameters(), n) + + +def nearest(x): + """Nearest integer with ties rounded up, as for q_j=floor(tj/s+1/2).""" + return floor(x+Q(1, 2)) + + +def step_inequality(s, t, H): + """Exact check of c(j,h) >= Phi(j+h)-Phi(j)+sigma h^2 for 0<=j= 0, 'Step inequality failed') + require(abs(beta(j+h)) <= Q(1, 2), 'Phase outside the half interval') + worst = excess if worst is None else min(worst, excess) + return worst + + +def neumann_count(p_bits, alpha, theta): + """n_new=ceil((p+1)/(4 alpha^2)+1/theta) and the original count ceil(p/(alpha^2 theta)). + + With L=log2(2.01)<101/100 and pi log2(e) > KAPPA0_LO, each extra power of E + gains at least KAPPA0_LO*alpha^2-L >= 4 alpha^2 bits, and the burn-in costs at + most KAPPA0_HI*alpha^2*(1/(4 theta)+1/2) bits. + """ + a2 = alpha*alpha + require(alpha >= 2 and a2*theta >= 1 and theta < 1, 'Need alpha>=2, alpha^2 theta>=1, theta<1') + require(Q(201, 100)**100 < 2**101, 'log2(2.01)<101/100 failed') + require(KAPPA0_LO*a2-Q(101, 100) >= 4*a2, 'Per-step decay constant failed') + n_new = ceil(Q(p_bits+1, 4*a2)+1/theta) + require(4*a2*n_new >= p_bits+1+KAPPA0_HI*a2*(1/(4*theta)+Q(1, 2)), 'Neumann count failed') + n_hvdh = ceil(Q(p_bits)/(a2*theta)) + return dict(n_new=n_new, n_hvdh=n_hvdh, n=min(n_new, n_hvdh)) + + +def application_counts(d, b): + """Counts at given (d,b): alpha=floor(sqrt(b/(8d))), theta>1/(4d).""" + from math import isqrt + alpha = isqrt(b//(8*d)) + while 8*d*(alpha+1)**2 <= b: alpha += 1 + while 8*d*alpha**2 > b: alpha -= 1 + gamma = 2*d*alpha*alpha + theta = Q(1, 4*d) + require(gamma*4 <= b, 'gamma exceeds b/4') + return dict(d=d, b=b, alpha=alpha, gamma=gamma, **neumann_count(6*b, alpha, theta)) + + +def certificate(): + c = ComplexSideCircuit(H); n = counts(c) + require(n['eta'] > COMPLEX_SAVING*Q(966, 100), 'Complex saving failed') + p = parameters(); w = witness(p, n) + require(Q(1, 2**30) < KAPPA < Q(1, 2**29), 'Unexpected dyadic scale') + steps = {f'{s}/{t}': str(step_inequality(s, t, 6)) for s, t in ((7, 8), (31, 32), (61, 64), (97, 101), (251, 256))} + samples = [application_counts(d, b) for d, b in ((8, 2**20), (64, 2**30), (1000, 2**40))] + for x in samples: require(x['n_new'] <= 30*x['d'], 'Neumann count exceeds 30d') + # Under the retained Gaussian margin the same networks are capped below a_b/5. + return dict(status='CONDITIONAL 1479/10^12 WITNESS; FAST GAUSSIAN RESAMPLING; NOT FORMAL VERIFICATION', + upstream_commit=verify_sources(), complex_counts=dict(h=n['h'], W=n['W'], s=n['s'], eta=n['eta']), + bit_saving=BIT_SAVING, complex_saving=COMPLEX_SAVING, witness=w, + step_inequality_minimum_excess=steps, neumann_samples=samples, + gaussian_cost_power='2*epsilon+delta (was 3/4+delta+5*epsilon/4)', + improvement_over_compressed_complex=KAPPA/Q(59, 10**11), + improvement_over_compact_control=KAPPA/Q(83, 10**12), + scoped_ceiling=dict(upper=BIT_SAVING/2, below_2_to_minus_29=BIT_SAVING/2 < Q(1, 2**29), + scope='g2,g3,g4 <= a_b*min(eps,1-eps); published h=50 paired bit network only.'), + scope='Conditional on the pinned upstream interfaces, the compact-control movement and guard, ' + 'the compressed complex network, and the written fast resampling lemmas. ' + 'Exact arithmetic and finite checks are not formal verification.') + + +if __name__ == '__main__': + result = serializable(certificate()) + (ROOT/'certificates/fast-gaussian.json').write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print('PASS conditional', KAPPA, '> 2^-30; minimum margin', result['witness']['minimum_margin'], + 'limiting', result['witness']['limiting_margins']) diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/paired_exclusion_circuit.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/paired_exclusion_circuit.py new file mode 100644 index 0000000000..36d1fa2c02 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/paired_exclusion_circuit.py @@ -0,0 +1,41 @@ +#!/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): + 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)<=4: + 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/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/paired_network.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/paired_network.py new file mode 100644 index 0000000000..910449dd51 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/paired_network.py @@ -0,0 +1,91 @@ +#!/usr/bin/env python3 +"""Conditional 2^-59 certificate: paired sums, stopped guard, tighter Gaussian width.""" +from fractions import Fraction as Q +from pathlib import Path +import json + +from certify import Parameters,certify_parameters,network,require,verify_sources +from shared_point_circuit import SharedPointCircuit +from shared_point_network import counts +from paired_exclusion_circuit import PairedExclusionCircuit +from search_network import log_integer_bounds + +ROOT=Path(__file__).resolve().parents[1] +H=50 +BIT_SAVING=Q(296,10**11) +COMPLEX_SAVING=Q(1,10**11) +LOG_BOUND=Q(11737,1000) +KAPPA=Q(1,2**59) + + +def circuit(h=H):return SharedPointCircuit(h,PairedExclusionCircuit(h-1)) + + +def parameters(): + a=BIT_SAVING;b=Q(999,1000) + return Parameters(1-a,1-COMPLEX_SAVING,Q(199,1000),b*a, + 1-(1+b)*a*a/2,1-b*a*a,KAPPA,beta=b, + delta=Q(1,10000),C1=2) + + +def guard_certificate(h=H,beta=Q(999,1000)): + n=network(h);m=n['m'];s=n['sc'];E=n['B']-s;B=n['B'] + require(m>=3 and 2<=sBIT_SAVING*LOG_BOUND,'Bit saving failed') + require(old['eta_c']>COMPLEX_SAVING*LOG_BOUND,'Complex saving failed') + require(2*old['Lc']=2^40 cutoff failed') + witness=certify_parameters(p,generalized_beta=True,strict_margin=True, + layout_model='nonadjacent',guard_model='stopping',assembly_model='tight-gaussian') + require(Q(witness['minimum_margin'])==p.epsilon*p.beta*BIT_SAVING**2,'Wrong limiting margin') + a_upper=n['eta']/((1-n['eta'])*lo) + ceiling=a_upper*a_upper/(5*(1-a_upper)) + require(ceiling= 1, 'Log argument below one') + power = 0 + while value > 2: + value /= 2 + power += 1 + def series(x): + z = (x-1)/(x+1) + return 2*sum((z**(2*j+1)/(2*j+1) for j in range(24)), Q(0)) + 2*z**49/(49*(1-z*z)) + scaled = (power*series(Q(2)) + series(value))*10**12 + return Q(-(-scaled.numerator//scaled.denominator), 10**12) + + +def moment(m, W, rows, saving, sharp): + upper = Q(0) + logs = {} + for t, count in sorted(rows.items()): + require(0 < t < m and count >= 0, 'Invalid recursive child') + ell = log_upper(Q(m, t)) + u = saving*ell + require(0 <= u < 1, 'Exponential enclosure outside range') + bound = 1+u+u*u/(2*(1-u/3)) if sharp else 1/(1-u) + upper += Q(count*t, W*m)*bound + logs[str(t)] = ell + require(upper < 1, 'Characteristic moment does not contract') + return dict(saving=saving, exponent=1-saving, moment_upper=upper, + strict_gap=1-upper, logarithm_upper_bounds=logs, + child_width_multiplicities=sorted(rows.items()), + enclosure='1+u+u^2/(2(1-u/3))' if sharp else '1/(1-u)') + + +def bit_counts(d): + dims = (25, 23, 57) + ps = d['producers'] + v = [comb(h, 3) for h in dims] + N, m = prod(v), prod(dims) + banks = [N//vi*ps[str(h)]['roles'] for h, vi in zip(dims, v)] + B1, B2, B3 = banks + E = B3-B1 + require(E >= 0, 'Stage-three bank must accommodate stage one') + W = 2*N+B2+B3 + L = N*sum((Q(6, h-2) for h in dims), Q(0)) + require(L.denominator == 1, 'Nonintegral retained loss') + L = int(L) + s = W*m-2*N+2*L + rows = Counter() + profiles = [(B1, (25,7,25,25,32611)), (E,(57,32661)), + (B2,(575,31625)), (B2,(23,529)), + (2*N,(55,463,31513)), (2*N,(481,)), + (2*N,(1,23)), (2*N,(1,21)), (2*N,(1,55))] + rows[1] += 2*N*(113+47) + for count, profile in profiles: + for t in profile: + rows[t] += count + for h, vi in zip(dims, v): + p = ps[str(h)] + require(p['v'] == vi and p['outputs'] == 3*vi+h, 'Producer dimensions') + require(p['roles'] == p['additions']+p['outputs']-p['matches'], 'Role count') + require(p['loss'] == h*(h-1), 'Producer retained loss') + hist = p['histogram'] + require(len(hist) == h+1 and all(n >= 0 for n in hist), 'Histogram range') + require(sum(r*n for r,n in enumerate(hist)) == h*p['roles']+2*h*(h-1), 'Internal rank mass') + for r,n in enumerate(hist): + copies = N//vi*n + block = max(0, 2*r-h) + rows[1] += copies*(r-block) + if block: + rows[block] += copies + computed = dict(m=m,N=N,B1=B1,B2=B2,B3=B3,E=E,W=W,L=L,s=s, + deficit=W*m-s,eta=Q(W*m-s,W*m),singletons=rows[1]) + for name,value in computed.items(): + require(value == Q(d['parameters'][name]), 'Recorded bit count differs: '+name) + require(sorted((t,n) for t,n in rows.items() if t>1) == [tuple(x) for x in d['bit_bulk_width_multiplicities']], 'Recorded bit multiset differs') + require(sum(t*n for t,n in rows.items()) == s, 'Complete bit rank mass') + return computed, rows + + +def complex_counts(d): + p = d['complex'] + h=28; v=comb(h,3); m=h**3; N=v**3 + B=v*v*(93838+h+1); W=2*N+2*B + s=W*m-2*N+6*v*v*h*(h+1) + macros=[(m-2*h,B),(m-h*h,B),((h*h-1)*(h-1),2*N), + (h*(h-1),B-N),((h-1)**2,3*N)] + require(macros == [tuple(x) for x in p['macro_width_multiplicities']], 'Complex macro profiles') + hist=p['histogram'] + require(sum(r*n for r,n in enumerate(hist)) == h*(93838+h+1)+2*h*(h+1), 'Complex internal rank mass') + rows=Counter(dict(macros)) + for r,n in enumerate(hist): + if r>=2: + rows[r] += 3*v*v*n + # The remaining physical and macro singleton transitions are fixed by the + # retained full rank budget; the internal histogram is regenerated separately. + rows[1]=s-sum(t*n for t,n in rows.items()) + counts=dict(h=h,v=v,m=m,N=N,B=B,W=W,s=s,singletons=rows[1]) + for name,value in counts.items(): + require(value == int(p[name]), 'Recorded complex count differs: '+name) + return counts, rows + + +def guard(n): + m=n['m']; W=n['W']; h=n['h']; q=m+6*h + rho=Q(6,5); gamma=Q(4999,5000); lower=160000 + require(lower**5 < m**6 and 28 < 2**5 and 756 < 4**5, 'Guard power bounds') + t=Q(56,m) + # Taylor integral remainder: (1-t)^(6/5) <= 1-6t/5+3t²/[25(1-t)]. + power=1-Q(6,5)*t+Q(3,25)*t*t/(1-t) + bounds=dict(largest=power+Q(2*(q-(m-56)),lower), + other_large=Q(27,28)+Q(4*979,lower), + no_large=Q(4*q,lower)) + require(all(2*r>q for r in (21896,21168,21141)), 'Two large edges on a path') + require(q-21896 < 729, 'Largest-edge remainder admits medium edge') + require(max(bounds.values()) < gamma, 'Precision path does not contract') + E=64*(W+m+1)**3 + require(36*W**3+4*n['s']+4*W+8*m+4 < E, 'Local coefficient allowance') + dep=5000*(E+16*m+1) + beta=Q(1,1000); zeta=Q(1,10000) + raw=128*m*(1+1/zeta)*dep + C0=-(-raw.numerator//raw.denominator) + require(dep*(1-gamma)>=E and dep>=16*m, 'Depth induction allowance') + require(m*(1+1/zeta)*dep+18<=C0, 'Layer allowance') + return dict(q=q,rho=rho,gamma=gamma,path_moment_upper=bounds, + strict_gap=gamma-max(bounds.values()),E=E,dependency_constant=dep, + C0=C0,C1=rho-(rho-1)*beta+zeta) + + +def parameters(): + tau=1-BIT_SAVING + return Parameters(tau=tau,sigma=1-COMPLEX_SAVING, + epsilon=1/(2+BIT_SAVING),c=Q(1),beta=Q(1,1000),delta=Q(1,10**16), + lam=tau+Q(1,10**20),lamp=tau+Q(2,10**20),C1=Q(11999,10000),kappa=KAPPA) + + +def assembly(p=None): + p=parameters() if p is None else p + ex=layer_exponents(p.tau,p.sigma,p.beta,p.c) + cs=fast_constraints(p) + cs['packed_overhead']=p.lam-ex['internal'] + cs['reserved_axes']=p.lamp-ex['preprocessing'] + require(len(cs)==29 and all(v>0 for v in cs.values()), 'Strict assembly constraint') + margins=fast_margins(p) + require(len(margins)==7 and min(margins.values())>p.kappa, 'Strict assembly absorption') + return dict(parameters=asdict(p),recurrence=ex,constraints=cs,margins=margins, + minimum_margin=min(margins.values()),absorption_gap=min(margins.values())-p.kappa) + + +def basis_combinatorics(): + a,b,k=25,23,57; H=a*b; size=k+a + R=list(range(a))+list(range(7))+list(range(a))*2 + C=list(range(a))*2+list(range(7))+list(range(a)) + completions=[] + for beta in range(b): + prescribed={} + def set_entry(row,col): + require(row not in prescribed or prescribed[row]==col, 'Conflicting prescribed row') + require(col not in prescribed.values() or prescribed.get(row)==col, 'Conflicting prescribed column') + prescribed[row]=col + for i,label in enumerate(R): + if i%b==beta: set_entry(i//b,label) + for j,label in enumerate(C): + i=H-size+j + if i%b==beta: set_entry(i//b,label) + unused=iter(c for c in range(a) if c not in prescribed.values()) + completions.append([prescribed[r] if r in prescribed else next(unused) for r in range(a)]) + forward=[(0,23),(1,24)]+[((j+2)%23,j) for j in range(7)]+[((j+9)%23,j) for j in range(15)] + dual=[(23,0),(24,1)]+[(2+((-9+j)%23),j) for j in range(7)]+[(2+((-11+j)%23),j) for j in range(10,25)] + for edges in (forward,dual): + require(len(edges)==24, 'Tree edge count') + seen={0} + while True: + expanded=seen|{y for x,y in edges if x in seen}|{x for x,y in edges if y in seen} + if expanded==seen:break + seen=expanded + require(seen==set(range(25)), 'A5 incidence graph disconnected') + return dict(row_labels=R,inverse_column_labels=C,permutation_completions=completions, + A5_forward_tree=forward,A5_dual_tree=dual, + scope='Prescription compatibility and A5 trees; remaining generic minors are proved in the note.') + + +def certificate(): + d=json.loads(INPUT.read_text()) + bn,br=bit_counts(d); cn,cr=complex_counts(d) + bit=moment(bn['m'],bn['W'],br,BIT_SAVING,True) + comp=moment(cn['m'],cn['W'],cr,COMPLEX_SAVING,False) + require(bit['strict_gap']>Q(617,10**16), 'Bit gap lower bound') + require(comp['strict_gap']>Q(23982,10**15), 'Complex gap lower bound') + a=assembly(); g=guard(cn) + require(g['C1']==a['parameters']['C1'], 'Guard exponent mismatch') + require(a['absorption_gap']>Q(44822,10**17), 'Assembly gap lower bound') + sources=[INPUT,Path(__file__).resolve(),ROOT/'scripts/partial_swap_producer.py'] + sources += sorted(p for p in (ROOT/'scripts/partial_swap').iterdir() if p.is_file()) + sources += sorted((ROOT/'notes').glob('partial-swap-*.tex')) + return dict(status='Conditional partial-swap integer-multiplication witness', + kappa=KAPPA,bit=dict(counts=bn,**bit),complex=dict(counts=cn,**comp), + basis_combinatorics=basis_combinatorics(),guard=g,assembly=a, + source_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in sources}, + inherited_PR10_commit='62691e395a0458ce089a1c7b5d89e74291e95e29', + scope='Exact finite arithmetic and basis combinatorics. Producer regeneration is separate. ' + 'The common-basis, recursion, and retained analytic/tape arguments remain written proofs.') + + +def main(): + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('--output',type=Path,default=ROOT/'certificates/partial-swap-network.json') + args=parser.parse_args() + result=certificate() + args.output.write_text(json.dumps(serializable(result),indent=2,sort_keys=True)+'\n') + print('PASS partial-swap kappa='+str(KAPPA)+' = 1.884586e-6') + print('29 strict constraints; 7 strict assembly margins; bit/complex moments and precision guard') + +if __name__=='__main__': + main() diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/prepare_layers.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/prepare_layers.py new file mode 100644 index 0000000000..8e17b52f95 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/prepare_layers.py @@ -0,0 +1,163 @@ +#!/usr/bin/env python3 +"""Reusable layer estimates and complex-family screen, not a new headline bound. + +The sparse-cost examples are implications of an UNPROVED primitive. They are +kept explicitly separate from estimates for the existing machine routine. +""" +from fractions import Fraction as Q +from pathlib import Path +import json + +from certify import Parameters, constraints, margins, network, require, verify_sources +from search_network import log_integer_bounds, log_ratio_bounds + +ROOT = Path(__file__).resolve().parents[1] +BIT_SAVING = Q(296, 10**11) + + +def guard(beta, zeta=Q(1, 100), h=50): + """Explicit guard for any fixed rational beta in (0,1); see the proof note.""" + require(0 < beta < 1 and zeta > 0, 'Need 00') + n = network(h) + m, s, B = n['m'], n['sc'], n['B'] + E = B-s + require(m >= 3 and 2 <= s < m**5, 'Unverified coefficient-depth hypothesis') + require(s*(8+E) <= 9*B*B, 'One-piece constant failed') + C1 = 5-4*beta+zeta + raw_C0 = max(Q(128*m*B*B), 18*m*B*B*(1+1/zeta)) + C0 = -(-raw_C0.numerator//raw_C0.denominator) + require(9*m*B*B*(1+1/zeta)+18 <= C0, 'Whole-layer constant failed') + return dict(h=h, m=m, s=s, E=E, B=B, beta=beta, zeta=zeta, + C0=C0, C1=C1, one_piece_exponent=5-4*beta) + + +def packed_exponents(tau, sigma, beta, c, *, theta=None): + """Sum the recurrence for either exponent ordering. + + theta=tau is the EXISTING packed bound. Any other theta is only a + hypothetical O(V e^tau K^theta) primitive with the same remaining contract. + """ + require(0 < tau < 1 and 0 <= sigma < 1 and 0 < beta < 1 and c > 0, + 'Invalid recurrence parameters') + theta = tau if theta is None else theta + require(theta >= 0, 'Negative spacing exponent is not supported') + internal = tau+(1-beta)*max(sigma-tau, Q(0))+theta*c + leaf = sigma+beta*(1-sigma) + return dict(internal=internal, leaf=leaf, layer=max(internal, leaf), + theta=theta, hypothetical=theta != tau) + + +def check_parameters(p, g, *, hypothetical_theta=None): + """Check the stated extensions, without relaxing the published checker.""" + require(g == guard(g['beta'],g['zeta'],g['h']), 'Guard certificate was altered') + require(p.beta == g['beta'] and p.C1 == g['C1'], 'Guard/parameter mismatch') + require(1-p.tau <= BIT_SAVING, 'Preparation retains the published bit saving') + require(1-p.sigma < complex_saving_bounds(g['h'])[0], + 'Complex exponent is not supported by the chosen motif') + exp = packed_exponents(p.tau, p.sigma, p.beta, p.c, theta=hypothetical_theta) + slacks = constraints(p, layout_model='nonadjacent', assembly_model='tight-gaussian') + slacks['packed_overhead'] = p.lam-exp['internal'] + for name, slack in slacks.items(): + require(slack > 0, 'Failed preparation constraint: '+name) + gs = margins(p, layout_model='nonadjacent', assembly_model='tight-gaussian') + require(min(gs.values()) > p.kappa, 'No strict final margin') + return dict(status=('HYPOTHETICAL SPARSE PRIMITIVE; NOT A MULTIPLICATION RESULT' + if exp['hypothetical'] else + 'Existing packed routine; conditional preparation estimates'), + parameters=vars(p), guard=g, recurrence=exp, + constraint_slacks=slacks, margins=gs, minimum_margin=min(gs.values())) + + +def complex_saving_bounds(h): + n = network(h) + eta = n['eta_c'] + require(0 < eta < Q(1, 2), 'Complex deficit must be positive') + lo, hi = log_ratio_bounds(1/(1-eta), terms=3) + dlo, dhi = log_integer_bounds(n['m']) + return lo/dhi, hi/dlo + + +def complex_search(): + # L_c3h(h+1) iff h^2-21h-16>0, hence integer h>=22. + bounds = {h: complex_saving_bounds(h) for h in range(22, 200)} + winner = max(bounds, key=lambda h: bounds[h][0]) + lo, hi = bounds[winner] + require(all(lo > b[1] for h, b in bounds.items() if h != winner), + 'Finite winner not separated') + n200 = network(200) + # eta_c<2/(3*z_c*m), log(m)>1; every factor increases for h>=200. + tail = Q(2, 3*n200['zc']*n200['m']-2) + require(log_integer_bounds(n200['m'])[0] > 1, 'Tail log denominator failed') + require(lo > tail, 'Tail could improve the result') + n = network(winner) + certified = Q(418, 10**12) + _, log_hi = log_integer_bounds(n['m']) + require(n['eta_c'] > certified*log_hi, 'Chosen simple complex saving failed') + require(n['Lc'] < n['N'] and 2*n['Lc'] >= n['N'], + 'Expected the complex-only admissibility range') + require(n['sc'] < n['m']**5, 'Guard requires a different depth bound') + fixed50 = Q(169, 10**13) + require(network(50)['eta_c'] > fixed50*log_integer_bounds(50**3)[1], + 'Fixed-h=50 saving failed') + return dict(status='Conditional complex interface; separate-arity integration not patched', + winner_h=winner, admissible_integer_h_minimum=22, + saving_lower=lo, saving_upper=hi, certified_saving=certified, + counts={k:n[k] for k in ('h','m','v','N','Wc','sc','Lc','eta_c')}, + fixed_h50_saving=fixed50, tail_start=200, tail_upper=tail, + finite_enclosures={str(h):dict(lower=b[0],upper=b[1]) for h,b in bounds.items()}, + scope='Original complex motif only, all integer h>=22; no shared bit positivity requirement. Written interface audit required, not a formal proof.') + + +def scenarios(): + a = BIT_SAVING + epsilon = Q(199,1000) + # The published numerical choice remains valid under the generalized proof. + beta = Q(999,1000) + g = guard(beta) + existing = Parameters(1-a, 1-Q(1,10**11), epsilon, beta*a, + 1-(1+beta)*a*a/2, 1-beta*a*a, Q(1,2**59), + beta=beta, delta=Q(1,10000), C1=g['C1']) + result = {'existing_59_control':check_parameters(existing,g)} + # These two rows assume theta=a instead of theta=tau. No such primitive + # is supplied here. They expose exact research targets and guard budgets. + for name,h,ac,beta,c,q,k in ( + ('hypothetical_39',50,Q(1,10**11),Q(1,100),Q(1,200),Q(95,10**13),39), + ('hypothetical_34',25,Q(418,10**12),Q(1,5),Q(1,10),Q(3,10**10),34)): + g = guard(beta,h=h) + exp = packed_exponents(1-a,1-ac,beta,c,theta=a) + lamp = 1-q + lam = (max(1-a,1-ac,exp['internal'])+lamp)/2 + p = Parameters(1-a,1-ac,epsilon,c,lam,lamp,Q(1,2**k), + beta=beta,delta=Q(1,10000),C1=g['C1']) + result[name] = check_parameters(p,g,hypothetical_theta=a) + actual = packed_exponents(p.tau,p.sigma,p.beta,p.c) + require(actual['internal'] > 1, 'Hypothetical target accidentally uses an existing bound') + result[name]['existing_primitive_internal_exponent'] = actual['internal'] + result[name]['missing_hypothesis'] = 'Uniform fixed-tape O(V f^(1-a) K^a) selected-bit primitive, up to fixed powers of log(p) only, including descriptors, exceptional repair, and dirty-scratch restoration.' + return result + + +def certificate(): + return dict(status='PREPARATION PASS; published headline remains conditional 2^-59', + upstream_commit=verify_sources(), complex_family=complex_search(), + scenarios=scenarios(), + verification_boundary='Exact arithmetic and finite recurrence checks accompany written proofs. Sparse scenarios are unproved design targets, not certificates of new algorithms.') + + +def serializable(value): + if isinstance(value,Q): + return str(value) + if isinstance(value,dict): + return {k:serializable(v) for k,v in value.items()} + if isinstance(value,(list,tuple)): + return [serializable(v) for v in value] + return value + + +if __name__ == '__main__': + result = certificate() + (ROOT/'certificates/layer-preparation.json').write_text( + json.dumps(serializable(result),indent=2,sort_keys=True)+'\n') + print('PASS preparation estimates; complex-family optimum h='+str(result['complex_family']['winner_h'])) + print('Published result remains 2^-59. Sparse targets 2^-39 and 2^-34 remain hypothetical.') diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/search_network.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/search_network.py new file mode 100644 index 0000000000..f03d5c1b2c --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/search_network.py @@ -0,0 +1,105 @@ +#!/usr/bin/env python3 +"""Certify the best shared recurrence exponent within the generalized h family. + +Uses rational enclosures of logarithms, plus a tail bound for all h>=200. +The result concerns the counting formulas, conditional on the network proof. +""" +from fractions import Fraction as Q +import json +from pathlib import Path +from certify import network, require + +ROOT = Path(__file__).resolve().parents[1] + + +def log_ratio_bounds(x, terms=24): + """Bounds for log(x), 1 <= x <= 2, by the atanh series.""" + require(1 <= x <= 2, "Log series expects 1<=x<=2") + z = (x-1)/(x+1) + lower = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(terms)), Q(0)) + tail = 2*z**(2*terms+1)/((2*terms+1)*(1-z*z)) + return lower, lower+tail + + +def log_integer_bounds(m): + k = m.bit_length()-1 + lo2, hi2 = log_ratio_bounds(Q(2)) + lo, hi = log_ratio_bounds(Q(m, 2**k)) + return k*lo2+lo, k*hi2+hi + + +def saving_bounds(n, bit_only=False): + eta = n["eta_b"] if bit_only else min(n["eta_b"], n["eta_c"]) + require(0 < eta < Q(1, 2), "Need a positive small rank deficit") + # Shared exponent saving is min(-log(1-eta_b),-log(1-eta_c))/log(m). + lo_num, hi_num = log_ratio_bounds(1/(1-eta), terms=3) + lo_den, hi_den = log_integer_bounds(n["m"]) + return lo_num/hi_den, hi_num/lo_den + + +def search(bit_only=False): + bounds = {} + rejected = [] + for h in range(7, 200): + if h == 9: + rejected.append(h) + continue + n = network(h) + if 2*n["Lb"] >= n["N"] or 2*n["Lc"] >= n["N"]: + rejected.append(h) + continue + bounds[h] = saving_bounds(n, bit_only=bit_only) + winner = max(bounds, key=lambda h: bounds[h][0]) + lo, hi = bounds[winner] + require(all(lo > b[1] for h, b in bounds.items() if h != winner), + "Enclosures do not separate a unique winner") + # eta_b < 1/(3*z_b*m), and -log(1-eta_b) < eta_b/(1-eta_b). + # For h>=200, z_b and m increase and log(m)>1. This bounds ALL the tail. + n200 = network(200) + tail_upper = Q(1, 3*n200["zb"]*n200["m"]-1) + require(lo > tail_upper, "Tail could contain a better network") + dyadic_power = 1 + while Q(1, 2**dyadic_power) >= lo: + dyadic_power += 1 + require(hi < Q(1, 2**(dyadic_power-1)), "Cannot certify optimal dyadic saving") + return { + "scope": ("Bit-network saving alone" if bit_only else "Common tau=sigma saving") + + "; generalized counting formulas, construction conditional", + "winner_h": winner, + "saving_lower": str(lo), "saving_upper": str(hi), + "largest_certified_dyadic_saving": f"2^-{dyadic_power}", + "tail_start": 200, "tail_saving_upper": str(tail_upper), + "excluded_h": rejected, + "finite_enclosures": {str(h): {"lower": str(b[0]), "upper": str(b[1])} + for h, b in bounds.items()}, + } + + +def parameter_ceiling(): + """Upper bound for kappa even with variable beta and separate sigma. + + Put a=1-tau. The final g4>0 gives epsilon Q(99, 100)*upper, "Witness below 99% of ceiling") + return {"bit_network_search": result, "kappa_upper": str(upper), + "simple_kappa_upper": str(Q(5838, 10**36)), + "witness": str(witness), "witness_fraction_of_upper": str(witness/upper), + "next_dyadic_excluded": "2^-107", + "scope": "Seven-margin accounting and stated network rank bounds; not all algorithms"} + + +if __name__ == "__main__": + result = search() + result["parameter_ceiling"] = parameter_ceiling() + path = ROOT / "certificates/network-search.json" + path.parent.mkdir(exist_ok=True) + path.write_text(json.dumps(result, indent=2, sort_keys=True)+"\n") + print(f"Certified h={result['winner_h']} best within the stated counting family,") + print(f"including all h>=200 by a tail bound; dyadic saving {result['largest_certified_dyadic_saving']}") diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/shared_point_circuit.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/shared_point_circuit.py new file mode 100644 index 0000000000..8347a0bda6 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/shared_point_circuit.py @@ -0,0 +1,149 @@ +#!/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): + 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<=6 and h%2==0,'Even ground size required') + c=circuit or SharedPointCircuit(h) + require(c.h==h,'Mismatched circuit') + v=comb(h,3);N=v**3;m=h**3;R=c.additions+len(c.outputs) + W=2*N+2*v*v*(R+h);L=3*v*v*h*h;D=N-2*L + return dict(h=h,v=v,N=N,m=m,side_roles_per_invocation=R, + W=W,L=L,D=D,s=W*m-D,eta=Q(D,W*m)) + + +def parameters(): + a=BIT_SAVING + return Parameters(1-a,1-A,Q(1,21),9*a/10,1-19*a*a/20, + 1-9*a*a/10,KAPPA,beta=Q(9,10)) + + +def certificate(): + c=SharedPointCircuit(46);n=counts(circuit=c) + symbolic=c.verify();frames=c.verify_frames() + _,log_hi=log_integer_bounds(n['m']) + require(log_hiBIT_SAVING*LOG_BOUND,'Insufficient saving') + witness=certify_parameters(parameters(),generalized_beta=True,strict_margin=True, + layout_model='nonadjacent') + require(Q(witness['minimum_margin'])==3*BIT_SAVING**2/70,'Wrong minimum') + # Necessary bound for this particular circuit and downstream constraints. + log_lo,_=log_integer_bounds(n['m']) + a_upper=n['eta']/((1-n['eta'])*log_lo) + ceiling=a_upper*a_upper/(20*(1-a_upper)) + require(ceilingQ(1,2**59),'Invalid target saving') + budget=n['D']/(2*n['v']**2*n['m']*target_a*LOG_BOUND)-n['v']-n['h'] + return dict(status='CONDITIONAL 13*2^-66 WITNESS; frame-transfer proof supplied separately', + upstream_commit=verify_sources(),bit_counts={k:str(v) for k,v in n.items()}, + circuit=symbolic,frames=frames,bit_saving=str(BIT_SAVING), + complex_saving_unchanged=str(A),log_m_upper=str(LOG_BOUND), + deficit_slack=str(n['eta']-BIT_SAVING*LOG_BOUND),witness=witness, + exact_circuit_kappa_upper=str(ceiling), + target_59=dict(bit_saving=str(target_a), + sufficient_maximum_integer_side_roles=(budget.numerator-1)//budget.denominator), + scope='Conditional on the written source-span/complement-frame transfer and unchanged upstream interfaces; no general optimality claim.') + + +if __name__=='__main__': + result=certificate() + (ROOT/'certificates/shared-point-network.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + print('PASS conditional shared-point witness 13*2^-66; minimum',result['witness']['minimum_margin']) + print(result['bit_counts']) + print('Target 59:',result['target_59']) diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/structured_bulk_assembly.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/structured_bulk_assembly.py new file mode 100644 index 0000000000..b76f9cb5a4 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/structured_bulk_assembly.py @@ -0,0 +1,103 @@ +#!/usr/bin/env python3 +"""Copyright 2026 icekylinx. Apache-2.0. +Substantial OpenAI GPT-6 Astra and Codex assistance. + +Exact finite bridge and assembly for the round-three networks. + +Adapted parameter calculation and semantic/product-row proof from PR23, +Zhihao Chen (jacklightChen), which attributes routing, phase-cell inverse +and bulk resampling to the RaD project (hipotures), commit +45d9b60355872041f9275f77c057514def0d45bc. This file does not regenerate, +audit, or substitute for the finite-network or analytic source proofs. +""" +from fractions import Fraction as Q + +def js(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):js(v) for k,v in x.items()} + if isinstance(x,(tuple,list)):return [js(v) for v in x] + return x + +def halving(m,r): + assert 0=s+E and 2*B+18Q(coeff*51,25) + return dict(bit=dict(m=bit_m,W=bit_W,maxchild=bit_maxchild, + halving_degree=db,wire_bits=wb), + complex=dict(m=m,W=W,s=s,maxchild=r,halving_degree=dc, + wire_bits=wc,scalar_terms=scalar_terms,scalar_group_upper=G), + semantic=dict(E=E,literal_charge=charge,strict_literal_gap=E-charge, + B=B,C0=C0,C1=1,induction_gap=2*B*(m-r)-s-E), + rows=dict(coefficient=coeff,degree=degree,suffix_slope=4*degree, + degree_gap=Q(degree)-Q(coeff*51,25), + contract='W_complex^D_complex * W_bit^D_bit; preceding row prefix, single complete-row padding, nested bit stock restored')) + +def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)): + a,b=bit_saving,complex_saving + tau,sigma=1-a,1-b + q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2 + c=q*(1+eta); eps=(1-eta)/(1+c+q) + minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8 + internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma) + margins=dict(original_prefix=1-eps*(1+c),coordinate_movement=a, + compact_phase_layer=minimum,bulk_exposure=a, + Gaussian_arithmetic=min(1-eps-delta,r-delta), + scalar_work=1-eps-delta,dimension=eps) + slacks=dict(bit_positive=a,complex_above_bit=b-a, + complex_below_one_over32=Q(1,32)-b,beta_positive=beta, + beta_below_one=1-beta,leaf_saving_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,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-minimum, + artificial_boundary=8-eps+r-delta-minimum, + literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']), + row_product_gap=bridge['rows']['degree_gap']) + slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()}) + assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0} + assert min(margins.values())==minimum + assert margins['original_prefix']-minimum==eta + return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma, + eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam, + lambda_prime=lp,alpha_squared_power=r,delta=delta, + C0=bridge['semantic']['C0'],C1=1,kappa=kappa), + strict_constraints=slacks,margins=margins,minimum_margin=minimum, + absorption_gap=minimum-kappa, + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c)) diff --git a/research/shrunk-birth-terminal/search/original-runtime/verify_candidate.py b/research/shrunk-birth-terminal/search/original-runtime/verify_candidate.py new file mode 100644 index 0000000000..fb23464023 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/verify_candidate.py @@ -0,0 +1,17 @@ +from pathlib import Path +from hashlib import sha256 +import datetime,importlib.util,json,os,sys,time,pickle +W=Path(__file__).resolve().parent;P=W/'repo/research/r12-logical-frames' +name=sys.argv[1];O=W/name;O.mkdir(exist_ok=True) +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 +config={k:os.environ[k] for k in ('R12_FRAME_MODE','R12_FRAME_ROUNDS','R12_DEFER_MODE')};sources={str(p.relative_to(P)):sha256(p.read_bytes()).hexdigest() for p in P.glob('*.py')};start=time.monotonic() +(O/'process.json').write_text(json.dumps(dict(started_utc=datetime.datetime.now(datetime.timezone.utc).isoformat(),config=config,sources=sources),indent=2)+'\n') +sys.path.insert(0,str(P));ref=load('r12_reflection',P/'reflection_audit.py');d=ref.capture(P/'complex_deferred.py') +(O/'complex-profile.json').write_text(json.dumps(d['out'],indent=2,sort_keys=True)+'\n') +adapter=load('r12_birth_checkpoint',W/'references/birth_checkpoint.py');adapter.export_checkpoint(d,O) 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0000000000..261eeb9e9f --- /dev/null +++ b/research/shrunk-birth-terminal/search/references/pr124/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 + + 1. 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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. + +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. + +Stopped product-ring extension, 9 October 2026 +Copyright 2026 icekylinx + +The opposite-bank generic projector factorization, componentwise atom-ring +adapters, stopped recurrence and outer ordinary-interchange conversion, +aligned pair-star producer with rational centers, exact denominator-21 +grid and selected (23,23)/(24,24) composition are contributed by icekylinx +with substantial OpenAI GPT-6 Astra and Codex assistance. This extension +builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is +integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37. + +The retained ordinary leaf uses the preceding projector, corner and +copied-center proofs. The selected two-stage topology retains Aurel Prosz +(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly +retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching, +original source notices and each imported license remain unchanged. diff --git a/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/BASE_INPUTS.json b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/BASE_INPUTS.json new file mode 100644 index 0000000000..36c46849a3 --- /dev/null +++ b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/BASE_INPUTS.json @@ -0,0 +1,9 @@ +{ + "head": "6ec868e8568ca9a74b7245494de1b187c7be78fe", + "files": { + "research/deferred-replayed-117/complex-dag.json.gz": "3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b", + "research/deferred-replayed-117/complex-profile.json": "ff5e9bbc1a3794d8dd3f75e194ea002cef8439c40a5d434c4a84e46967edc98e", + "research/deferred-replayed-117/certificate.json": "f1d77d26036cf2b01bc630a572b2cdea0027e0faa2e4899b5b907b9d455ff916", + "certificates/copied-centers-network.json": "7dbd675e42e22ac076280360f8750031851564bb7a56079e66236fee5d0a6cdf" + } +} diff --git a/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/PROOF.md b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/PROOF.md new file mode 100644 index 0000000000..2f65bed9a8 --- /dev/null +++ b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/PROOF.md @@ -0,0 +1,45 @@ +# Dirty readouts permit physical slot reuse + +Base: rohanarun/integer-mult-bounds at6ec868e8568ca9a74b7245494de1b187c7be78fe (corrected PR118). The operand/root DAG and virtual role/frame profile are unchanged fromec862a5af51537495c745d9f2323e8a5736ee265. Under its retained analytic, exact-recovery, prime, whole-residual, complete-row and fixed-tape hypotheses, this construction gives + + T(n)=O(n(log n)^(1−kappa)), + kappa=5519166047173/50000000000000000=0.00011038332094346. + +This is an author-checked conditional draft; independent review remains pending. No upstream program is executed by the supplied checks. + +## The new operation + +In a linear virtual program, regard the initial value of each newly born register as an independent symbol g_a. Let D_a be its exact future contribution to output accumulators, cutting propagation at each subsequent birth on that storage. Then the output is Fx+sum(D_a g_a). A physical birth may leave any old value in its slot: read that value and add −D_a g_a to the output. The corrections cancel identically even if birth values contain source signals or are correlated with earlier dirt. Reverse every actual workspace/source gate chronologically to restore all original workspace. + +Sources, workspace and output banks must be disjoint. Outputs are never later controls, sources, guards or addresses. Every correction is paid and must occur at a legal common frame. There is no physical dirty reset and no assumption that a fresh-signal relation is equality of dirty contents. + +PR118 already reads each untouched deferred register B negatively at sigma_B after center phase one. Choose an old role A whose last forward gate and every terminal read are already finished, with final frame E contained in sigma_B. Raise A to sigma_B; use its actual value in B's existing negative readout; route B's future virtual life through A. The virtual program and D_B are unchanged. The new offset is canceled by the same readout. Selected pairs are disjoint, and all selected recipients have no source injection. The implementation nevertheless uses true reverse chronology for every inverse source gate. + +Per matched local role, put e=dim E and s=dim sigma_B. Remove children24−e and552+s; add child s−e (record zero rank explicitly); remove one original physical role. Weighted rank drops by576. All target read frames, copied centers and response coefficients remain unchanged. Added positive residuals are checked nonalternating. For0v for s in removed),'Selected deferred source injection requires explicit inverse insertion review' +for b,a in merge.items():assert a not in g['placed']and b in g['placed']and b not in g['touched']and g['last'][a]in g['phase']and a not in g['terminal'] +frames=[()];ids={():0} +def fid(F): + if F not in ids:ids[F]=len(frames);frames.append(F) + return ids[F] +FULL=fid(fulltuple);tm=[fid((m,))for m in g['tm']];U=[fid(F)for F in g['U']] +def basis(rows): + piv={} + for x in rows: + for p in sorted(piv,reverse=True): + if x>>p&1:x^=piv[p] + if x: + p=x.bit_length()-1 + for q in piv: + if piv[q]>>p&1:piv[q]^=x + piv[p]=x + return tuple(piv[p]for p in sorted(piv,reverse=True)) +@lru_cache(None) +def dual(i): + A=frames[i];piv={r.bit_length()-1 for r in A};out=[] + for j in range(24): + if j not in piv: + x=1<>j&1:x|=1<<(r.bit_length()-1) + out.append(x) + return fid(basis(out)) +@lru_cache(131072) +def nested(i,j): + for x in frames[i]: + for r in frames[j]: + if x>>(r.bit_length()-1)&1:x^=r + if x:return False + return True +word=[];forward_workspace=[] +def gate(d,s,c,F,remember=False): + assert d!=s;word.append(('g',d,s,c,F)) + if remember:forward_workspace.append((d,s,c,F)) +def oldread(s,F): + mask=ALL if g['reach_all'][s]else g['reach'][s] + word.append(('r',physical(s),v,mask,-1,F,('old',s))) +def source(s): + x=g['first'][s];assert 1<=x<=v;gate(physical(s),x-1,1,U[x],True) +def mix(i): + op,s,t,x=g['ops'][i] + if op==1:gate(physical(s),physical(t),1,U[x],True) + elif op==2:gate(physical(t),physical(s),1,U[x],True) +for s in range(R): + if s not in g['placed']:oldread(s,0) +for s,x in enumerate(g['first']): + if x<=v and s not in g['placed']:source(s) +for i in sorted(g['phase']):mix(i) +for s in g['center_roles']: + j=g['terminal'][s];F=fid(g['U'][g['roots'][j]]);assert len(frames[F])==23 + word.append(('c',physical(s),v,ALL,1,F,0,('center',j-(len(g['roots'])-24)))) +for s,F in sorted(g['placed'].items(),key=lambda item:(len(item[1]),item[0])):oldread(s,fid(F)) +for s,x in enumerate(g['first']): + if x<=v and s in g['placed']:source(s) +for i in range(len(g['ops'])): + if i not in g['phase']:mix(i) +for s,j in sorted(g['terminal'].items(),key=lambda item:item[1]): + if j0 + hist[r]+=1;current[s]=F;incidences+=1 + if s<2*v: + bank=s//v;counts[bank][old]-=1 + if not counts[bank][old]:del counts[bank][old] + counts[bank][F]+=1 + def targets(bank,mask,F): + if len(counts[bank//v])==1 and counts[bank//v].get(F)==v:return + while mask: + b=mask&-mask;mask-=b;promote(bank+b.bit_length()-1,F) + for e in events: + digest.update(repr(e).encode()) + if e[0]=='g':_,d,s,c,F=e;assert c in(-1,1);promote(d,F);promote(s,F) + elif e[0]=='r':_,s,bank,mask,sign,F,key=e;assert mask>=0 and not(mask&~ALL);promote(s,F);targets(bank,mask,F) + else: + _,s,bank,mask,sign,F,T,key=e;promote(s,F);targets(bank,mask,T) + assert (F==FULL and T==0)or nested(F,T)or nested(T,F) + r=abs(len(frames[F])-len(frames[T]));assert r==23;hist[r]+=1;copies+=1 + for s in active:promote(s,end[s]) + assert current==end + return hist,copies,incidences,digest.hexdigest() +active_set=set(active);forward=scan(word,initial,finish) +def swap(s):return s+v if s>p&1:x^=piv[p] + if x: + p=x.bit_length()-1 + for q in piv: + if piv[q]>>p&1:piv[q]^=x + piv[p]=x + return tuple(piv[p]for p in sorted(piv,reverse=True)) +@lru_cache(65536) +def contained(A,B): + for x in A: + for r in B: + if x>>(r.bit_length()-1)&1:x^=r + if x:return False + return True +@lru_cache(65536) +def perpendicular(A): + piv={r.bit_length()-1 for r in A};out=[] + for j in range(H): + if j not in piv: + x=1<>j&1:x|=1<<(r.bit_length()-1) + out.append(x) + return basis(out) +@lru_cache(65536) +def intersection(A,B):return perpendicular(basis(perpendicular(A)+perpendicular(B))) +@lru_cache(65536) +def nondeg(A):return len(basis(sum(((x&y).bit_count()%2)<=0 else 1<<(j-(len(roots)-H))for j,t in enumerate(g['targets'])] + succ=[set()for _ in range(n)];rootf=[[]for _ in range(n)] + def connect(x,uid): + _,typ,dest,_=use[uid] + if typ:rootf[x].append(fun[dest]) + else:succ[x].add(dest) + for x in active: + for uid in uses[x]: + if matched[uid]<0:connect(x,uid) + for x,uid in links.items():connect(x,uid) + order=sorted(active,key=lambda x:(rank[x],x),reverse=True);demand=[()]*n + for x in order:demand[x]=basis(rootf[x]+[r for y in sorted(succ[x])for r in demand[y]]) + def envelope(x): + if not args[x]:return (tm[x-1],) + if kind[x]==2:return basis(1<=len(roots)-H:dense[s]=True + else:reach[s]=1<rank[x]for x in active)) + assert g['lifted']==39989,g['lifted'];save('LIFTED.pkl',g) + print('Lifted checkpoint',len(cand),'candidates',round(time.monotonic()-start,2),flush=True) +# Only this saturating placement is repeated if a previous cap ended after LIFTED. +U=g['U'];reach=g['reach'];cand=g['candidates'];bytarget=defaultdict(list);placed={};order=sorted(cand,key=lambda s:(-len(cand[s]),s)) +for step,s in enumerate(order): + X=cand[s];changed=True + while changed and X: + changed=False + for t in bits(reach[s]): + for prior in bytarget[t]: + B=placed[prior] + if (len(B)>=len(X)and not contained(X,B))or(len(B)=len(g['roots'])-H else perpendicular((g['tm'][g['targets'][j]],)) + actual.append(terminal_frame) + assert all(contained(a,b)for a,b in zip(actual,actual[1:]))and all(nondeg(A)for A in actual) + ds=[len(A)for A in actual];chains[s]=ds + for a,b in zip(ds,ds[1:]): + if b>a:hist[b-a]+=2*v + if s in g['terminal']and g['terminal'][s]>=len(g['roots'])-H:hist[H-1]+=2*v + if H>ds[-1]:hist[H-ds[-1]]+=2*v + hist[576-H+ds[0]]+=2*v +for t in range(v): + levels=sorted({0,H-1}|{len(placed[s])for s in bytarget[t]}) + for a,b in zip(levels,levels[1:]):hist[b-a]+=2*v +hist[H-1]+=2*N;hist[(H-1)**2]+=2*N;hist[1]+=N +expected=json.loads((REPO/'research/deferred-replayed-117/complex-profile.json').read_text()) +assert dict(hist)=={int(k):v for k,v in expected['child_multiplicities'].items()},('Histogram mismatch',hist) +assert Counter(len(A)for A in placed.values())==Counter({int(k):v for k,v in expected['deferred_dims'].items()}) +g.update(placed=placed,bytarget=dict(bytarget),histogram=dict(hist),chain_dims=chains);digest=save('FRAMES.pkl',g) +result=dict(status='PASS original118 full frame/profile reconstruction',roles=roles,deferred=len(placed),maxchild=max(hist),weighted_rank=sum(t*n for t,n in hist.items()),all_bins_match=True,frame_sha256=digest,seconds=time.monotonic()-start,rss_KiB=resource.getrusage(resource.RUSAGE_SELF).ru_maxrss) +(ROOT/'FRAMES_CHECK.json').write_text(json.dumps(result,indent=2)+'\n');print(json.dumps(result,indent=2)) diff --git a/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/build_roles.py b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/build_roles.py new file mode 100644 index 0000000000..427d518e8f --- /dev/null +++ b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/build_roles.py @@ -0,0 +1,109 @@ +"""Original exact carrier matching/role reconstruction, no upstream imports.""" +import sys,os +if sys.flags.optimize or os.environ.get('PYTHONOPTIMIZE'):raise RuntimeError('Assertions required') +from pathlib import Path +from collections import deque +import pickle,json,time,resource,hashlib +ROOT=Path(__file__).resolve().parent;REPO=Path(os.environ.get('BIRTH_REPO',ROOT.parents[1]));start=time.monotonic() +resource.setrlimit(resource.RLIMIT_AS,(512*1024**2,512*1024**2));resource.setrlimit(resource.RLIMIT_CPU,(30,30));sys.setrecursionlimit(5000) +g=pickle.loads((ROOT/'GRAPH.pkl').read_bytes());h,v=g['h'],g['v'];args,core,cover,rank,kind=[g[k]for k in ('args','core','cover','rank','kind')];active=g['active'];roots=g['roots'];n=len(args);full=(1<=shortest:continue + for uid in adj[x]: + y=R[uid] + if y<0:shortest=dist[x]+1 + elif dist[y]==INF:dist[y]=dist[x]+1;queue.append(y) + if shortest==INF:break + def augment(x): + for uid in adj[x]: + y=R[uid] + if (y<0 and dist[x]+1==shortest)or(y>=0 and dist[y]==dist[x]+1 and augment(y)): + L[x]=uid;R[uid]=x;return True + dist[x]=INF;return False + gained=sum(augment(x)for x in left if L[x]<0);assert gained;rounds.append((shortest,gained)) +links={x:L[x]for x in left if L[x]>=0};assert len(links)==71185,len(links) +# Every matched edge is an actual unchanged input continuation into a later use. +assert len(set(links.values()))==len(links) +for x,uid in links.items():assert use[uid][0]in args[x]and uid in adj[x] +held=[];first=[];ops=[];role_of={};terminal={} +def alloc(x): + s=len(first);first.append(x);held.append([x]);return s +for x in sorted(active,key=lambda x:(rank[x],x)): + free=[uid for uid in uses[x]if R[uid]<0] + if not args[x]: + for uid in free: + s=alloc(x);ops.append((0,s,x,-1));role_of[uid]=s + continue + a,b=args[x];sa,sb=role_of.pop(edge[x,0]),role_of.pop(edge[x,1]);assert sa!=sb + if x in links and use[links[x]][0]==a:sa,sb=sb,sa + ops.append((1,sa,sb,x));held[sa].append(x);held[sb].append(x) + if x in links:role_of[links[x]]=sb + assert free;role_of[free[0]]=sa + for uid in free[1:]: + s=alloc(x);ops.append((2,sa,s,x));role_of[uid]=s +for uid,row in enumerate(use): + if row[1]:terminal[role_of.pop(uid)]=row[2] +assert not role_of and len(first)==28705 and len(terminal)==len(roots) +# All original-role fresh signals, not sampled values. +values=[0]*len(first) +for op,s,t,x in ops: + if op==0:values[s]=1<<(t-1) + elif op==1: + assert not(values[s]&values[t]);values[s]|=values[t];assert values[s]==g['support'][x] + else:assert values[t]==0;values[t]=values[s];assert values[t]==g['support'][x] +for s,j in terminal.items():assert values[s]==g['support'][roots[j]] +for chain in held: + for a,b in zip(chain,chain[1:]):assert contains(a,b) +# Dependencies in the exact selected chronological program. +previous=[-1]*len(first);pred=[[]for _ in ops];last=[-1]*len(first) +for i,(op,s,t,x)in enumerate(ops): + if op: + for r in(s,t): + if previous[r]>=0:pred[i].append(previous[r]) + previous[r]=i;last[r]=i +centers=[s for s,j in terminal.items()if j>=len(roots)-h] +phase=set();todo=[last[s]for s in centers] +while todo: + i=todo.pop() + if i not in phase:phase.add(i);todo.extend(pred[i]) +touched=set(centers) +for i in phase: + _,s,t,_=ops[i];touched.update((s,t)) +expected=json.loads((REPO/'research/deferred-replayed-117/complex-profile.json').read_text());assert (len(phase),len(touched))==(expected['phase_one_ops'],expected['phase_one_roles']),(len(phase),len(touched)) +g.update(uses=uses,use=use,links=links,matched_use=R,holds=held,first=first,ops=ops,terminal=terminal,last=last,phase=phase,touched=touched,center_roles=centers) +raw=pickle.dumps(g,protocol=4);(ROOT/'ROLES.pkl').write_bytes(raw) +receipt=dict(status='PASS original exact118 matching/role/source reconstruction',links=len(links),roles=len(first),ops=len(ops),phase_one_ops=len(phase),phase_one_roles=len(touched),augmenting_rounds=rounds,checkpoint_sha256=hashlib.sha256(raw).hexdigest(),seconds=time.monotonic()-start,rss_KiB=resource.getrusage(resource.RUSAGE_SELF).ru_maxrss) +(ROOT/'ROLES_CHECK.json').write_text(json.dumps(receipt,indent=2)+'\n');print(json.dumps(receipt,indent=2)) diff --git a/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/check_assembly.py b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/check_assembly.py new file mode 100644 index 0000000000..088f44ee93 --- /dev/null +++ b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/check_assembly.py @@ -0,0 +1,71 @@ +"""Original exact assembly for paid birth-read slot reuse. No upstream imports.""" +import sys,os,gzip +if sys.flags.optimize or os.environ.get('PYTHONOPTIMIZE'):raise RuntimeError('Assertions required') +from pathlib import Path +from fractions import Fraction as Q +from math import factorial +import json,hashlib,time,resource +root=Path(__file__).resolve().parent;repo=Path(os.environ.get('BIRTH_REPO',root.parents[1]));start=time.monotonic() +profile=json.loads(gzip.decompress((root/'BIRTH_MATCHES.json.gz').read_bytes()));bill=json.loads((root/'READOUT_COST.json').read_text()) +source=repo/'research/deferred-replayed-117/certificate.json' +oldpath=repo/'certificates/copied-centers-network.json' +cert=json.loads(source.read_text());old_leaf=json.loads(oldpath.read_text()) +logcache={} +def smalllog(x): + z=(x-1)/(x+1);N=40;lo=2*sum((z**(2*j+1)/Q(2*j+1)for j in range(N)),Q(0));tail=2*z**(2*N+1)/(Q(2*N+1)*(1-z*z));return lo,lo+tail +ln2=smalllog(Q(2)) +def logbound(x): + if x in logcache:return logcache[x] + k=0;y=x + while y>=2:y/=2;k+=1 + lo,hi=smalllog(y);out=(k*ln2[0]+lo,k*ln2[1]+hi);logcache[x]=out;return out + +def expbound(lo,hi): + n=8;assert 0<=lo<=hi<1 + a=sum((lo**j/Q(factorial(j))for j in range(n+1)),Q(0));b=sum((hi**j/Q(factorial(j))for j in range(n+1)),Q(0));b+=hi**(n+1)/Q(factorial(n+1))/(1-hi/Q(n+2));return a,b + +def moment(label,m,W,children,saving): + rows={int(t):int(n)for t,n in children.items()};assert rows and all(00 for t,n in rows.items());lo=Q(0);hi=Q(0) + for t,n in sorted(rows.items()): + ll,lh=logbound(Q(m,t));a,b=expbound(saving*ll,saving*lh);weight=Q(n*t,m*W);lo+=weight*a;hi+=weight*b + scale=1<<192 + lo=Q((lo*scale).numerator//(lo*scale).denominator,scale) + u=hi*scale;hi=Q((u.numerator+u.denominator-1)//u.denominator,scale) + assert hi<1,label + return dict(label=label,m=m,W=W,saving=saving,rank=sum(t*n for t,n in rows.items()),lower=lo,upper=hi,strict_gap=1-hi,enclosure_grid_bits=192,log_terms=40,exponential_degree=8) + + +coarse=cert['bit_profile'];old=old_leaf['bit']['counts'];alpha=Q(1,1000);a0=Q(620523,5000000000);old_a=Q(384599,10**10) +aactual=(1-alpha)*a0+alpha*old_a;b=Q(11040781,10**11);beta=Q(1,10**6);buffer=Q(1,10**12);a=min(aactual,(1-beta)*b-buffer) +assert aactual==Q(1240189553,10**13)==Q(cert['actual_bit_saving'])and aactual>a>0 +moments=[moment('coarse_bit',529,coarse['W'],coarse['child_multiplicities'],a0),moment('old_ordinary',old['m'],old['W'],old['child_multiplicities'],old_a),moment('birth_reused_complex',576,profile['W'],profile['child_histogram'],b)] +m,W,s,rmax,R=576,profile['W'],profile['rank'],max(map(int,profile['child_histogram'])),profile['R'];G=bill['global_scalar_group_upper'] +assert (W,s,R,rmax)==(115865904,66736898624,26599,574) +E=64*(W+m+G+1)**3;charge=2*G*W*W+8*s+4*W+4+32*m;B=s+E;C0=32*m*B*B +assert charge=s+E and 2*B+182*r**t) +stock=[dict(m=mm,W=ww,maxchild=rr,depth=halving(mm,rr),wire_bits=ww.bit_length())for mm,ww,rr in [(529,coarse['W'],528),(575,old['W'],529),(576,W,rmax)]] +rows=sum(x['depth']*x['wire_bits']for x in stock);rowgap=Q(32000)-Q(51,25)*rows +assert rows==15561 and rowgap==Q(6389,25) +bridge=dict(m=m,W=W,rank=s,R=R,maxchild=rmax,G=G,E=E,literal_charge=charge,B=B,C0=C0,C1=1,stock=stock,rows=rows,row_degree=32000,row_gap=rowgap,suffix_slope=128000,odd_grid='2^-P21^-K; K=G*(D_complex+1), with completed child preserving incoming odd exponent') +# Exact retained assembly formulas, written independently and never imported. +eta=Q(1,10**8);beta=Q(1,10**6);tau=1-a;sigma=1-b;q=a*(1-2*eta);c=q*(1+eta);eps=(1-eta)/(1+c+q);lp=1-q;lam=(tau+lp)/2;g=eps*q;rr=(g+1-eps)/2;delta=eta/8 +internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma) +grid=10**17;kappa=Q((g*grid).numerator//(g*grid).denominator,grid) +if kappa==g:kappa-=Q(1,grid) +margins=dict(original_prefix=1-eps*(1+c),coordinate_movement=a,compact_phase_layer=g,bulk_exposure=a,Gaussian_arithmetic=min(1-eps-delta,rr-delta),scalar_work=1-eps-delta,dimension=eps) +slacks=dict(bit_positive=a,complex_above_bit=b-a,complex_below_one_over32=Q(1,32)-b,beta_positive=beta,beta_below_one=1-beta,leaf_saving_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,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=rr-delta,gamma_sublinear=1-eps-rr,cell_above_band=eps-(1-rr)/2,prime_interval_packing=1-eps,alpha_positive=rr,alpha_below_one=1-rr,alpha_below_one_fourth=Q(1,4)-rr,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+rr-delta-g,literal_scalar_guard=Q(E-charge),row_product_gap=rowgap) +slacks.update({name+'_above_kappa':v-kappa for name,v in margins.items()}) +assert len(slacks)==47 and len(margins)==7 and all(v>0 for v in slacks.values());assert min(margins.values())==g and margins['original_prefix']-g==eta +next_kappa=kappa+Q(1,grid);assert g-next_kappa<=0 + + +inputfiles=[root/'BIRTH_MATCHES.json.gz',root/'READOUT_COST.json',source,oldpath] +pins={('new/'+p.name)if p.parent==root else('base/'+str(p.relative_to(repo))):hashlib.sha256(p.read_bytes()).hexdigest()for p in inputfiles} +out=dict(status='AUTHOR_CHECKED_CONDITIONAL_ASSEMBLY; independent review pending',source_head='6ec868e8568ca9a74b7245494de1b187c7be78fe',profile_source_head='ec862a5af51537495c745d9f2323e8a5736ee265',pins=pins,kappa=kappa,complex_saving=b,actual_bit_saving=aactual,supported_bit_parameter=a,moments=moments,finite_bridge=bridge,assembly=dict(parameters=dict(a=a,b=b,beta=beta,eta=eta,q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,r=rr,delta=delta,C0=C0,C1=1),constraints=slacks,margins=margins,minimum_margin=g,absorption_gap=g-kappa),next_grid=next_kappa,next_grid_gap=g-next_kappa) +def js(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):js(v)for k,v in x.items()} + if isinstance(x,(list,tuple)):return [js(v)for v in x] + return x +(root/'CANDIDATE.json').write_text(json.dumps(js(out),indent=2)+'\n');print(json.dumps(dict(kappa=str(kappa),decimal=float(kappa),complex_saving=str(b),G=G,W=W,R=R,constraints=len(slacks),margins=len(margins),seconds=time.monotonic()-start),indent=2)) diff --git a/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/check_birth_lemma.py b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/check_birth_lemma.py new file mode 100644 index 0000000000..67f9e2c1e9 --- /dev/null +++ b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/check_birth_lemma.py @@ -0,0 +1,87 @@ +"""Original exact adversarial check of reset compensation; no upstream imports.""" +import sys,os +if sys.flags.optimize or os.environ.get('PYTHONOPTIMIZE'):raise RuntimeError('Assertions required') +from fractions import Fraction as F +from random import Random +from pathlib import Path +import json,time,resource +T0=time.monotonic() +def add(a,b,c=F(1)): + for i,x in enumerate(b):a[i]+=c*x + +def response(events,R,X,Y,cut=True): + B=[[F(0)for _ in range(Y)]for _ in range(R)];M=[[F(0)for _ in range(Y)]for _ in range(X)];D={} + for k in range(len(events)-1,-1,-1): + e=events[k];kind,r=e[:2] + if kind=='read':_,r,t,c=e;B[r][t]+=c + elif kind=='gate':_,r,s,c=e;add(B[s],B[r],c) + elif kind=='source':_,r,j,c=e;add(M[j],B[r],c) + elif kind=='birth': + D[k]=B[r][:] + if cut:B[r]=[F(0)for _ in range(Y)] + else:raise AssertionError(e) + return B,M,D + +def run(events,R,X,Y,x,z,D=None,uncompute=True,omit=None,fresh_only=False): + a=z[:];out=[F(0)for _ in range(Y)];gates=[];births=[] + for k,e in enumerate(events): + kind,r=e[:2] + if kind=='birth': + if D is None:a[r]=F(0) + else: + g=a[r];births.append((k,g)) + if k!=omit: + for t,d in enumerate(D[k]):out[t]-=d*g + elif kind=='gate':_,r,s,c=e;a[r]+=c*a[s];gates.append(e) + elif kind=='source':_,r,j,c=e;a[r]+=c*x[j];gates.append(e) + elif kind=='read':_,r,t,c=e;out[t]+=c*a[r] + if D is not None and uncompute: + for e in reversed(gates): + kind,r,j,c=e;a[r]-=c*(a[j]if kind=='gate'else x[j]) + return out,a,births +rng=Random(114113);basis_checks=0;dependent_nonzero_births=0;coefficient_max=F(0) +for case in range(96): + R=1+case%5;X=1+(case//5)%4;Y=1+(case//20)%4 + events=[('birth',r)for r in range(R)] + for step in range(24): + kind=rng.choice(['birth','source','read','gate']if R>1 else['birth','source','read']) + r=rng.randrange(R);c=rng.choice([F(1),F(-1),F(2),F(-2),F(1,2),F(-1,3)]) + if kind=='birth':events.append((kind,r)) + elif kind=='source':events.append((kind,r,rng.randrange(X),c)) + elif kind=='read':events.append((kind,r,rng.randrange(Y),c)) + else: + s=rng.choice([i for i in range(R)if i!=r]);events.append((kind,r,s,c)) + # Force a genuinely used reuse with a nonzero old-source offset. + events += [('source',0,0,F(1)),('read',0,0,F(1)),('birth',0),('source',0,0,F(2)),('read',0,Y-1,F(1))] + B,M,D=response(events,R,X,Y);assert all(not any(row)for row in B) + coefficient_max=max(coefficient_max,max((abs(c)for row in D.values()for c in row),default=F(0))) + for b in range(X+R): + x=[F(i==b)for i in range(X)];z=[F(X+i==b)for i in range(R)] + expected=run(events,R,X,Y,x,[F(0)]*R)[0] + actual,restored,births=run(events,R,X,Y,x,z,D) + assert actual==expected and restored==z + assert expected==[sum(M[i][t]*x[i]for i in range(X))for t in range(Y)] + basis_checks+=1;dependent_nonzero_births+=sum(bool(g)for _,g in births) + # Dense signed rational source/dirty inputs exercise dependent birth values. + x=[F(rng.randrange(-7,8),rng.randrange(1,5))for _ in range(X)];z=[F(rng.randrange(-7,8),rng.randrange(1,5))for _ in range(R)] + assert run(events,R,X,Y,x,z,D)[:2]==(run(events,R,X,Y,x,[F(0)]*R)[0],z) +# A one-slot two-life example: x0 is still in the slot at its second birth. +e=[('birth',0),('source',0,0,F(1)),('read',0,0,F(1)),('birth',0),('source',0,1,F(1)),('read',0,1,F(1))] +B,M,D=response(e,1,2,2);x=[F(3),F(5)];z=[F(7)] +out,restored,births=run(e,1,2,2,x,z,D);assert out==x and restored==z and births==[(0,F(7)),(3,F(10))] +controls={} +controls['omit_reuse_readout']=run(e,1,2,2,x,z,D,omit=3)[0]!=x +controls['do_not_cut_next_birth']=run(e,1,2,2,x,z,response(e,1,2,2,cut=False)[2])[0]!=x +controls['omit_inverse_workspace']=run(e,1,2,2,x,z,D,uncompute=False)[1]!=z +# Grouping negative source injections at the end fails after role aliasing. +e2=[('birth',0),('birth',1),('source',0,0,F(1)),('gate',1,0,F(1)),('read',1,0,F(1)),('birth',0),('source',0,1,F(1)),('read',0,1,F(1))] +_,_,D2=response(e2,2,2,2);z2=[F(7),F(11)] +assert run(e2,2,2,2,x,z2,D2)[:2]==(x,z2) +a=run(e2,2,2,2,x,z2,D2,uncompute=False)[1] +for kind,r,s,c in reversed([v for v in e2 if v[0]=='gate']):a[r]-=c*a[s] +for kind,r,j,c in reversed([v for v in e2 if v[0]=='source']):a[r]-=c*x[j] +controls['group_negative_sources_at_end']=a!=z2 +# The gate/readout model forbids source-target-workspace aliasing by construction. +assert all(controls.values()) +result=dict(status='PASS exact scalar lemma controls; no actual114 word or bound yet',cases=96,complete_source_dirty_basis_vectors=basis_checks,dense_rational_cases=96,nonzero_dependent_birth_values=dependent_nonzero_births,largest_test_response_coefficient=str(coefficient_max),rejected_controls=controls,one_slot_example=dict(source=['3','5'],dirty='7',birth_values=['7','10'],output=['3','5'],restored='7'),seconds=time.monotonic()-T0,rss_KiB=resource.getrusage(resource.RUSAGE_SELF).ru_maxrss) +Path(__file__).with_name('CHECKS.json').write_text(json.dumps(result,indent=2)+'\n');print(json.dumps(result,indent=2)) diff --git a/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/load_graph.py b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/load_graph.py new file mode 100644 index 0000000000..72118a4c86 --- /dev/null +++ b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/load_graph.py @@ -0,0 +1,31 @@ +"""Original exact reconstruction from PR117's passive operand/root witness.""" +import sys,os +if sys.flags.optimize or os.environ.get('PYTHONOPTIMIZE'):raise RuntimeError('Assertions required') +from pathlib import Path +from itertools import combinations +import json,gzip,pickle,time,resource,hashlib +ROOT=Path(__file__).resolve().parent;REPO=Path(os.environ.get('BIRTH_REPO',ROOT.parents[1]));start=time.monotonic();resource.setrlimit(resource.RLIMIT_AS,(512*1024**2,512*1024**2));resource.setrlimit(resource.RLIMIT_CPU,(30,30)) +p=REPO/'research/deferred-replayed-117/complex-dag.json.gz';raw=p.read_bytes();assert hashlib.sha256(raw).hexdigest()=='3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b';w=json.loads(gzip.decompress(raw));h=24;tr=list(combinations(range(h),3));v=len(tr);assert (w['h'],w['v'],w['central_disjoint'],w['center_denominator'])==(24,v,24,21) +args=[None]*(v+1);support=[0]+[1<=2 else 2;kind.append(ty);rank.append(support[x].bit_count()if ty==1 else cover[x].bit_count()) +point=[sum(1<>p&1:x^=piv[p] + if x: + p=x.bit_length()-1 + for q in piv: + if piv[q]>>p&1:piv[q]^=x + piv[p]=x + return tuple(piv[p]for p in sorted(piv,reverse=True)) +def perp(A): + piv={x.bit_length()-1 for x in A};out=[] + for j in range(24): + if j not in piv: + x=1<>j&1:x|=1<<(r.bit_length()-1) + out.append(x) + return basis(out) +def contained(A,B):return all(not any((a&b).bit_count()%2 for a in A)for b in perp(B)) +@lru_cache(None) +def characteristic(A): + k=len(A);rows=[sum(((a&b).bit_count()%2)<>j&1);rows[j],rows[p]=rows[p],rows[j] + for i in range(k): + if i!=j and rows[i]>>j&1:rows[i]^=rows[j] + result=0 + for j in range(k): + if rows[j]>>k&1:result^=A[j] + return result +DG=defaultdict(list) +for s,last in enumerate(g['last']): + if last in g['phase']and(s not in g['terminal']or s in g['center_roles']):DG[g['U'][g['holds'][s][-1]]].append(s) +frames=sorted(DG,key=lambda F:(-len(F),F));pool=[DG[F][:]for F in frames];byB=defaultdict(list) +for b,F in g['placed'].items():byB[F].append(b) +allgroups=(1<25:raise RuntimeError('Bounded eligibility screen capped before matching; no partial claim') +# Deterministic most-constrained frame classes, highest-rank legal donor first. +available=allgroups;pairs=[] +for F in sorted(byB,key=lambda F:(capacity[F],len(F),F)): + for b in sorted(byB[F]): + mask=eligible[F]&available + if not mask:break + i=(mask&-mask).bit_length()-1;a=pool[i].pop();A=frames[i] + if not pool[i]:available^=1<e:H[s-e]+=2*v +assert min(H.values())>=0 +roles=len(g['first'])-len(pairs);W=2*v*v+2*v*roles;mass=sum(r*n for r,n in H.items());assert mass==576*W-1862080 +assert len({p['donor']for p in pairs})==len(pairs)==len({p['recipient']for p in pairs}) +def moment(a):return math.fsum(n*r*math.exp(a*math.log(576/r))for r,n in H.items()if n)/(576*W) +lo,hi=0.,.001 +for _ in range(65): + mid=(lo+hi)/2 + if moment(mid)<1:lo=mid + else:hi=mid +res=dict(status='Author exact liveness/containment/paid-profile birth-reuse screen; scalar expansion and full reflected word still to check',source_head='ec862a5af51537495c745d9f2323e8a5736ee265',base_roles=len(g['first']),donors=sum(len(v)for v in DG.values()),donor_frame_classes=len(frames),births=len(g['placed']),matched=len(pairs),R=roles,W=W,rank=mass,deficit=1862080,child_histogram=dict(sorted((r,n)for r,n in H.items()if n)),match_ranks=dict(Counter(f"{r['e']}->{r['s']}"for r in pairs)),new_positive_residuals_nonalternating=True,root_float_screen=(lo+hi)/2,zero_rank_merge_records=sum(r['e']==r['s']for r in pairs),pairs=pairs,source_frame_checkpoint_sha256=hashlib.sha256((ROOT/'FRAMES.pkl').read_bytes()).hexdigest(),seconds=time.monotonic()-start,rss_KiB=resource.getrusage(resource.RUSAGE_SELF).ru_maxrss) +(ROOT/'BIRTH_MATCHES.json.gz').write_bytes(gzip.compress((json.dumps(res,indent=2)+'\n').encode(),mtime=0));print(json.dumps({k:v for k,v in res.items()if k not in('pairs','child_histogram','match_ranks')},indent=2)) diff --git a/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/readout_cost.py b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/readout_cost.py new file mode 100644 index 0000000000..a5b3bc5075 --- /dev/null +++ b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/readout_cost.py @@ -0,0 +1,70 @@ +"""Original exact signed integer dirty-readout responses and literal unit bill. +All coefficients are represented over42 by unsigned bitplanes; no modular test. +""" +import sys,os +if sys.flags.optimize or os.environ.get('PYTHONOPTIMIZE'):raise RuntimeError('Assertions required') +from pathlib import Path +from functools import reduce +from operator import or_ +from itertools import combinations +import pickle,json,time,resource,hashlib +ROOT=Path(__file__).resolve().parent;start=time.monotonic();resource.setrlimit(resource.RLIMIT_AS,(512*1024**2,512*1024**2));resource.setrlimit(resource.RLIMIT_CPU,(30,30)) +g=pickle.loads((ROOT/'FRAMES.pkl').read_bytes());R=len(g['first']);v=g['v'];N=v*v;allbits=(1<>i&1 else 0 for i in range(n.bit_length())) +def plus(a,b): + out=[];carry=0 + for i in range(max(len(a),len(b))): + x=a[i]if i=len(g['roots'])-24: + i=j-(len(g['roots'])-24);P[s]=scaled(allbits^point[i],2);M[s]=scaled(point[i],19) + elif jmaximum:maximum=maxhere;max_role=s + # Pin full exact responses, including zero coefficients and signs. + digest.update(s.to_bytes(4,'little'));digest.update(len(z).to_bytes(4,'little'));digest.update(neg.to_bytes((v+7)//8,'little')) + for w in z:digest.update(w.to_bytes((v+7)//8,'little')) + if s in g['placed']: + # Deferred origin has no center contribution; every actual target is in the conservative reach set. + assert not(nonzero&~g['reach'][s]);dense_reached+=nonzero.bit_count() +terminal_weight=0;terminal_count=0 +for a,b in zip(*seeds): + z,_=absdiff(a,b);terminal_weight+=sum(w.bit_count()*(1<a:H[b-a]+=2*v + if s in g['terminal']and g['terminal'][s]>=len(g['roots'])-h:H[h-1]+=2*v + H[h-ds[-1]]+=2*v;H[ext+ds[0]]+=2*v + for t in range(v): + ds=sorted(levels[t]|{0,h-1}) + for a,b in zip(ds,ds[1:]):H[b-a]+=2*v + N=v*v;H[h-1]+=2*N;H[(h-1)**2]+=2*N;H[1]+=N;H.pop(0,None) + g['histogram']=dict(sorted((r,n)for r,n in H.items()if n));p=g['base_profile'] + assert sum(r*n for r,n in H.items())==p['total_rank']==m*p['W']-p['deficit'] + p.update(child_multiplicities=g['histogram'],deferred_roles=len(g['placed']), + deferred_dims=dict(Counter(map(len,g['placed'].values())))) + +phase_inputs=[('prune','recipe/prune.json','recipe/protected-birth-matches.json.gz'), + ('coordinates','recipe/coordinates.json','evidence/protected-prune/BIRTH_MATCHES.json.gz'), + ('expansion','recipe/expansion.json','evidence/protected-coordinates/BIRTH_MATCHES.json.gz')] +for phase,recipe_path,match_path in phase_inputs: + recipe=read(HERE/recipe_path) + matches=json.loads(gzip.decompress((HERE/match_path).read_bytes())) + protected={r['recipient']:tuple(r['birth_frame'])for r in matches['pairs']} + assert all(g['placed'][s]==F for s,F in protected.items()) + if phase=='prune': + for row in recipe['removed']: + s=row['role'];assert s not in protected and len(g['placed'][s])==row['dimension'] + del g['placed'][s] + else: + for row in recipe['moves']: + s=row['role'];assert s not in protected + assert tuple(row['before'])==g['placed'].get(s,()) + if row['after']:g['placed'][s]=tuple(row['after']) + else:g['placed'].pop(s,None) + rebuild();assert all(g['placed'][s]==F for s,F in protected.items());mark(phase+'_recorded_moves_and_complete_frame_checks') +expected=read(HERE/'recipe/expected-geometry.json') +digest=sha256(canonical_geometry(g)).hexdigest();assert digest==expected['canonical_geometry_sha256'],'Entire selected geometry mismatch' +assert sha256(source.read_bytes()).hexdigest()==source_unchanged +(OUT/'FRAMES.pkl').write_bytes(pickle.dumps(g,protocol=4)) +record=dict(status='PASS from-source graph and exact selected geometry regeneration', + canonical_geometry_sha256=digest,selected_fixture_sha256=expected['selected_pickle_sha256'], + reproduced_pickle_sha256=sha256((OUT/'FRAMES.pkl').read_bytes()).hexdigest(), + original_runtime_imports_sha256=sha256((HERE/'IMPORTS.json').read_bytes()).hexdigest(), + wrapper_sha256=sha256(Path(__file__).read_bytes()).hexdigest(), + stage_seconds=timings,total_seconds=time.monotonic()-start, + scalar_dirty_word_replay='Not repeated here; enclosing selected physical word has separate full exact rational source/dirty and reflection audits.', + scope='All geometric keys regenerated and compared, excluding descriptive base_profile metadata. Pickle bytes may differ. Explicit recorded legal moves reproduce a selected witness; no heuristic-search or global-optimality claim.') +(OUT/'REPRODUCTION.json').write_text(json.dumps(record,indent=2,sort_keys=True)+'\n');print(json.dumps(record,indent=2)) diff --git a/research/shrunk-birth-terminal/selected/INPUTS.json b/research/shrunk-birth-terminal/selected/INPUTS.json new file mode 100644 index 0000000000..99d03c09b4 --- /dev/null +++ b/research/shrunk-birth-terminal/selected/INPUTS.json @@ -0,0 +1,42 @@ +{ + "BIRTH_MATCHES.json.gz": { + "bytes": 38343, + "encoding": "identity", + "sha256": "1cc40ab44413de0953dfa039fa7446008f3f480062560e9e7833dd48dced5de5", + "stored_bytes": 38343, + "stored_name": "BIRTH_MATCHES.json.gz", + "stored_sha256": "1cc40ab44413de0953dfa039fa7446008f3f480062560e9e7833dd48dced5de5" + }, + "FRAMES.pkl": { + "bytes": 30960758, + "encoding": "gzip", + "sha256": "3e3b2158ebad61910433735562de52d51c2bf803474662e90b7c478f90112a83", + "stored_bytes": 4159341, + "stored_name": "FRAMES.pkl.gz", + "stored_sha256": "c213d6ea7302ea4dd2a63eea54d9459289c1ab363f750fcdc37f109fd5c5c16a" + }, + "READOUTS.pkl": { + "bytes": 30742405, + "encoding": "gzip", + "sha256": "3fc2db8947189be57880cb55a5cb028592431f2c4175ea85827af53829c0dedb", + "stored_bytes": 2337744, + "stored_name": "READOUTS.pkl.gz", + "stored_sha256": "7db47c7dcb0cc508f414ff3c43e799e0de4924e1fda81dfe33cc2b04456c3fcd" + }, + "READOUT_COST.json": { + "bytes": 1252, + "encoding": "identity", + "sha256": "12c38cecf8c154f3c365cadafc68a73a60abb2368bc0387c820a08a33c110c10", + "stored_bytes": 1252, + "stored_name": "READOUT_COST.json", + "stored_sha256": "12c38cecf8c154f3c365cadafc68a73a60abb2368bc0387c820a08a33c110c10" + }, + "TERMINAL_ROLES.json": { + "bytes": 3432, + "encoding": "identity", + "sha256": "17c0132f5b7e1aea34313173fc8059f5199cc281ee582c843ea7650af5e6bd19", + "stored_bytes": 3432, + "stored_name": "TERMINAL_ROLES.json", + "stored_sha256": "17c0132f5b7e1aea34313173fc8059f5199cc281ee582c843ea7650af5e6bd19" + } +} diff --git a/research/shrunk-birth-terminal/selected/READOUT_COST.json b/research/shrunk-birth-terminal/selected/READOUT_COST.json new file mode 100644 index 0000000000..87a498b5bc --- /dev/null +++ b/research/shrunk-birth-terminal/selected/READOUT_COST.json @@ -0,0 +1,29 @@ +{ + "checkpoint_sha256": "3fc2db8947189be57880cb55a5cb028592431f2c4175ea85827af53829c0dedb", + "deferred_readout_count_scope": "The inherited count describes the input billing snapshot. 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"integer_gain_on_removal": 55171907, + "role": 24025 + } + ], + "seconds": 0.27302141598192975, + "source_sha256": "a3ffb97dbbc1062f157b21cabbc13a506b48e539025312da1d73e1b83647bd28", + "status": "SCREEN ONLY complete histogram and protected birth frames preserved; scalar word not replayed" + }, + "birth_reuses": 2108, + "child_multiplicities": { + "1": 435042608, + "2": 266771296, + "3": 29060592, + "4": 60639040, + "5": 26643936, + "6": 15333824, + "7": 11743248, + "8": 22069696, + "9": 3938704, + "10": 7735728, + "11": 6658960, + "12": 33578160, + "13": 13184336, + "14": 1821600, + "15": 3238400, + "16": 631488, + "17": 404800, + "18": 202400, + "19": 311696, + "20": 550528, + "21": 1222496, + "22": 64768, + "23": 8383408, + "529": 8193152, + "552": 97071040, + "554": 3456992, + "556": 1481568, + "558": 2384272, + "560": 445280, + "562": 48576, + "571": 740784, + "572": 101200, + "573": 28336, + "574": 364320 + }, + "deferral_optimization": { + "mode": "original" + }, + "deferred_dims": { + "2": 854, + "4": 368, + "6": 589, + "8": 142, + "10": 25, + "12": 323, + "14": 241, + "16": 337, + "17": 1, + "18": 885, + "19": 456, + "20": 26, + "21": 7, + "22": 90 + }, + "deferred_roles": 4344, + "deficit": 1862080, + "frame_optimization": { + "changed_frames": 16029, + "mode": "both_endpoints", + "passes": [ + { + "grow": 0, + "integer_score_gain": 49871856783307, + "moves": 16031, + "pass_index": 0, + "radical_completions": 0, + "shrink": 16031 + }, + { + "grow": 2, + "integer_score_gain": 5545177444, + "moves": 2, + "pass_index": 1, + "radical_completions": 0, + "shrink": 0 + }, + { + "grow": 0, + "integer_score_gain": 0, + "moves": 0, + "pass_index": 2, + "radical_completions": 0, + "shrink": 0 + } + ], + "requested_rounds": 8, + "scope": "Heuristic integer rank-moment score; fresh complete physical word and exact arithmetic remain required.", + "shrunk_frames": 16029 + }, + "h": 24, + "lifted_additions": 24794, + "links": 71185, + "m": 576, + "maxchild": 574, + "phase_one_ops": 18844, + "phase_one_roles": 13555, + "pre_terminal_physical_roles": 26597, + "replay": { + "dirty_columns": 26216, + "forward_signed_identity": 1, + "method": "Exact signed bit-plane all-column responses over Q, both orientations", + "reflected_signed_identity": -1, + "scratch_restored": true, + "source_columns": 2024, + "target_columns": 2024 + }, + "role_count_scope": "Explicit physical birth-reused and terminal-elided word; DAG role formula is the pre-composition virtual count.", + "roots": 8120, + "terminal_direct_updates": 1167, + "terminal_eliminations": 381, + "total_rank": 65843877440, + "v": 2024, + "virtual_roles": 28705 +} diff --git a/research/shrunk-birth-terminal/selected/construction-sources/compose_terminal.py b/research/shrunk-birth-terminal/selected/construction-sources/compose_terminal.py new file mode 100644 index 0000000000..a3b0826651 --- /dev/null +++ b/research/shrunk-birth-terminal/selected/construction-sources/compose_terminal.py @@ -0,0 +1,328 @@ +#!/usr/bin/env python3 +"""Compose disjoint terminal elimination with an exact shrunk/birth word. + +Original terminal-elision identity: SovereignSteak, PR122. +Shrunk frames: Joel Pulikkan, PR125. Birth reuse: James Chang, PR124. +PR117 DAG: eumemic; deferred compiler: Avi Eisenberg and Rohan Arun. +This explicit composition, complete word/profile checks and all-column +response audit were prepared with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter +from functools import lru_cache +from hashlib import sha256 +import argparse, gzip, json, pickle, resource, subprocess, sys, time + +assert not sys.flags.optimize, 'Assertions must remain enabled' +W=Path(__file__).resolve().parent +p=argparse.ArgumentParser(description=__doc__) +p.add_argument('--frames',type=Path,required=True) +p.add_argument('--matches',type=Path,required=True) +p.add_argument('--readouts',type=Path,required=True) +p.add_argument('--scalar-bill',type=Path,required=True) +p.add_argument('--out',type=Path,required=True) +p.add_argument('--terminal-roles',type=Path,help='JSON list of exact terminal IDs; validated after supplied real birth matches.') +a=p.parse_args();start=time.monotonic();O=a.out.resolve();O.mkdir(parents=True,exist_ok=False) +source_directory=O/'construction-sources';source_directory.mkdir() +source_bytes={q.name:q.read_bytes() for q in [Path(__file__),W/'terminal_inventory.py']} +for name,data in source_bytes.items():(source_directory/name).write_bytes(data) +inputs=O/'inputs';inputs.mkdir();pins={} +for source,name in [(a.frames,'FRAMES.pkl'),(a.matches,'BIRTH_MATCHES.json.gz'),(a.readouts,'READOUTS.pkl'),(a.scalar_bill,'READOUT_COST.json')]: + data=source.read_bytes();(inputs/name).write_bytes(data);assert source.read_bytes()==data + pins[name]={'source_path':str(source.resolve()),'sha256':sha256(data).hexdigest(),'bytes':len(data)} +selection_args=[] +if a.terminal_roles: + data=a.terminal_roles.read_bytes();(inputs/'TERMINAL_ROLES.json').write_bytes(data);assert a.terminal_roles.read_bytes()==data + pins['TERMINAL_ROLES.json']={'source_path':str(a.terminal_roles.resolve()),'sha256':sha256(data).hexdigest(),'bytes':len(data)} + selection_args=['--terminal-roles',str(inputs/'TERMINAL_ROLES.json')] +subprocess.run([sys.executable,str(source_directory/'terminal_inventory.py'),'--frames',str(inputs/'FRAMES.pkl'),'--matches',str(inputs/'BIRTH_MATCHES.json.gz'),'--readouts',str(inputs/'READOUTS.pkl'),'--out',str(O/'inventory.json'),*selection_args],check=True,stdout=subprocess.DEVNULL) +inventory=json.loads((O/'inventory.json').read_text()) +g=pickle.loads((inputs/'FRAMES.pkl').read_bytes());readouts=pickle.loads((inputs/'READOUTS.pkl').read_bytes()) +choice=json.loads(gzip.decompress((inputs/'BIRTH_MATCHES.json.gz').read_bytes())) +bill=json.loads((inputs/'READOUT_COST.json').read_text()) +R=len(g['first']);v=g['v'];h=g['h'];m=h*h;N=v*v +merge={r['recipient']:r['donor'] for r in choice['pairs']} +removed={r['role'] for r in inventory['selected']};selected={r['role']:r for r in inventory['selected']} +assert removed and not removed & (set(merge)|set(merge.values())) +live=set(range(R))-set(merge)-removed +assert len(live)==choice['R']-len(removed) +physical=lambda s:2*v+merge.get(s,s) + +frames=[()];ids={():0} +def fid(F): + F=tuple(F) + if F not in ids:ids[F]=len(frames);frames.append(F) + return ids[F] +def basis(rows): + piv={} + for x in rows: + for q in sorted(piv,reverse=True): + if x>>q&1:x^=piv[q] + if x: + q=x.bit_length()-1 + for r in piv: + if piv[r]>>q&1:piv[r]^=x + piv[q]=x + return tuple(piv[q] for q in sorted(piv,reverse=True)) +FULL=fid(tuple(1<>j&1:x|=1<<(r.bit_length()-1) + out.append(x) + return fid(basis(out)) +@lru_cache(None) +def nested(i,j): + for x in frames[i]: + for r in frames[j]: + if x>>(r.bit_length()-1)&1:x^=r + if x:return False + return True +@lru_cache(None) +def nondeg(i): + A=frames[i] + return len(basis(sum(((x&y).bit_count()&1)<=2*v and d-2*v in live + e=('g',d,s,sign,F);word.append(e) + if remember:forward_workspace.append(e) +def oldread(s,F): + mask=ALL if g['reach_all'][s] else g['reach'][s] + if s in removed: + assert mask==1<0 + hist[r]+=1;current[s]=F;incidences+=1 + if s<2*v: + bank=s//v;counts[bank][old]-=1 + if not counts[bank][old]:del counts[bank][old] + counts[bank][F]+=1 + def targets(bank,mask,F): + assert bank in (0,v) and mask>=0 and not(mask&~ALL) + if len(counts[bank//v])==1 and counts[bank//v].get(F)==v:return + while mask: + b=mask&-mask;mask-=b;promote(bank+b.bit_length()-1,F) + for e in events: + digest.update(repr(e).encode()) + if e[0]=='g': + _,d,s,c,F=e;assert c in (-1,1);promote(d,F);promote(s,F) + elif e[0]=='d': + _,d,s,c,F,idx,role=e;assert c in (-21,21);promote(d,F);promote(s,F) + elif e[0]=='r': + _,s,bank,mask,sign,F,key=e;promote(s,F);targets(bank,mask,F) + elif e[0]=='f': + _,bank,mask,F,key=e;targets(bank,mask,F) + else: + _,s,bank,mask,sign,F,T,key=e;promote(s,F);targets(bank,mask,T) + assert (F==FULL and T==0) or nested(F,T) or nested(T,F) + rank=abs(len(frames[F])-len(frames[T]));assert rank==h-1;hist[rank]+=1;copies+=1 + for s in active:promote(s,end[s]) + assert current==end + return {'histogram':dict(hist),'copies':copies,'transitions':incidences,'word_sha256':digest.hexdigest()} + +forward=scan(word,initial,finish) +def swap(s):return s+v if s=sum(before_sorted[:k]) for k in range(1,5)) + assert before_sorted!=after_sorted + for width in before: + if width:delta[width]-=2*v + # The width-m term is only the padding used to compare changing W. + if F0>M:delta[F0-M]+=2*v + packets.append({'role':row['role'],'target':row['target'],'old':before,'new_with_dummy_m':after}) +expected=Counter(oldH) +expected.update(delta);expected=Counter({r:n for r,n in expected.items() if n}) +assert all(n>=0 for n in expected.values()) and H==expected,('Full profile != exact complete packet sum',H-expected,expected-H) +newR=len(live);newW=2*v*v+2*v*newR;rank=sum(r*n for r,n in H.items()) +assert m*newW-rank==choice['deficit']==g['base_profile']['deficit'] +hinges={k:sum(min(r,k)*n for r,n in H.items())+2*v*len(removed)*min(m,k)-sum(min(r,k)*n for r,n in oldH.items()) for k in range(1,m+1)} +assert all(x<=0 for x in hinges.values()) and min(hinges.values())<0 + +def plus(a,b): + out=[];carry=0 + for i in range(max(len(a),len(b))): + x=a[i] if i>i&1 else 0 for i in range(n.bit_length())) + +def responses(events,inputbank,outputbank,expected_sign): + P,M=[()]*R,[()]*R;XP,XM=[()]*v,[()]*v + def accumulate(aux,positive,negative): + assert aux>=2*v and aux-2*v in live + r=aux-2*v;P[r],M[r]=plus(P[r],positive),plus(M[r],negative) + for e in reversed(events): + kind=e[0] + if kind=='f':continue + if kind in ('r','c'): + aux,bank,sign=e[1],e[2],e[4];assert bank==outputbank + key=e[-1] + if key[0]=='old':s=key[1];seed=False + elif key[0]=='side':s=key[2];seed=True + else:s=next(s for s in g['center_roles'] if g['terminal'][s]==len(g['roots'])-h+key[1]);seed=True + aa=readouts['terminal_positive' if seed else 'positive'][s] + bb=readouts['terminal_negative' if seed else 'negative'][s] + if sign<0:aa,bb=bb,aa + accumulate(aux,aa,bb) + elif kind=='d': + _,dst,src,num,F,idx,role=e + assert outputbank<=dst=2*v + aa,bb=P[dst-2*v],M[dst-2*v] + if sign<0:aa,bb=bb,aa + if src>=2*v:accumulate(src,aa,bb) + else: + assert inputbank<=src0:source_ok=all(aa==plus(bb,scaled(1<=bill['global_scalar_group_upper'] +profile=dict(g['base_profile']);profile.update(R=newR,W=newW,total_rank=rank,maxchild=max(H),child_multiplicities=dict(sorted(H.items())),pre_terminal_physical_roles=choice['R'],virtual_roles=R,birth_reuses=len(merge),terminal_eliminations=len(removed),terminal_direct_updates=len(direct_origins),deferred_roles=len(g['placed'])-len(removed),role_count_scope='Explicit physical birth-reused and terminal-elided word; DAG role formula is the pre-composition virtual count.',replay={'method':'Exact signed bit-plane all-column responses over Q, both orientations','source_columns':v,'dirty_columns':newR,'target_columns':v,'forward_signed_identity':1,'reflected_signed_identity':-1,'scratch_restored':True}) +dd=Counter({int(k):n for k,n in profile['deferred_dims'].items()}) +for row in inventory['selected']:dd[row['sigma']]-=1 +profile['deferred_dims']=dict(sorted((k,n) for k,n in dd.items() if n)) +scalar_bill={**{k:value for k,value in bill.items() if k not in {'rss_KiB','rss_bytes','seconds'}},'status':'PASS conservative scalar upper bound for new terminal composition','inherited_local_scalar_upper':bill['local_scalar_upper'],'terminal_direct_updates':len(direct_origins),'terminal_extra_scalar_charge':extra_scalar,'local_scalar_upper':newlocal,'global_scalar_group_upper':newG,'terminal_charge_rule':'Keep the entire inherited scalar bill and add 29 groups per direct output update: 21 same-frame shears of coefficient +/-1/42, plus eight conservative bookkeeping groups. No new role, source copy or frame incidence is introduced; denominator42 and odd21 grid are unchanged.','expansion':'Each numerator n/42 is |n| same-frame shears of coefficient sign(n)/42, with no new roles, source copies or frame transitions. Reverse all workspace/source gates chronologically. The retained eight-scan allowance, factor16 and explicit endpoint groups conservatively bound scalar bookkeeping/wrappers. Direct terminal updates use the same expansion, with eight additional bookkeeping groups per update.','original_bill_sha256':pins['READOUT_COST.json']['sha256']} +# The inherited bill is a conservative charge for the full virtual graph. +# Its descriptive deferred support count may belong to another placement. +def old_readout_support(role): + positive=readouts['positive'][role];negative=readouts['negative'][role];mask=0 + for i in range(max(len(positive),len(negative))): + mask|=(positive[i] if i>(r.bit_length()-1)&1:x^=r + if x:return False + return True + +incoming=defaultdict(list);outgoing=Counter() +for i,(op,s,t,x) in enumerate(g['ops']): + if op==1:dst,src=s,t + elif op==2:dst,src=t,s + else:continue + incoming[dst].append((i,src,x));outgoing[src]+=1 + +target_front=[() for _ in range(v)] +for s,F in sorted(g['placed'].items(),key=lambda z:(len(z[1]),z[0])): + targets=g['reach'][s] + while targets: + b=targets&-targets;targets-=b;t=b.bit_length()-1 + assert contains(target_front[t],F) + target_front[t]=F + +def scaled(mask,n):return tuple(mask if n>>i&1 else 0 for i in range(n.bit_length())) + +blocked=Counter();eligible=[] +for s,j in sorted(g['terminal'].items()): + if j>=len(g['roots'])-h:blocked['center_root']+=1;continue + if outgoing[s]:blocked['controls_auxiliary']+=1;continue + if s in merge and not a.include_birth_recipients:blocked['physical_slot_shared_as_birth_recipient']+=1;continue + assert s not in set(merge.values()) + if s not in g['placed']:blocked['not_deferred']+=1;continue + if g['first'][s]<=v:blocked['source_injection_excluded_from_this_bounded_pass']+=1;continue + if not incoming[s]:blocked['no_incoming_update']+=1;continue + if any(i in g['phase'] for i,_,_ in incoming[s]):blocked['early_update']+=1;continue + assert s not in g['touched'] + t=g['targets'][j];sign=1 if j0 else ()) + assert readouts['negative'][s]==(expected if sign<0 else ()) + F0=g['U'][incoming[s][0][2]];M=target_front[t];sigma=g['placed'][s] + if not contains(M,F0):blocked['target_front_past_first_update']+=1;continue + fs=[M]+[g['U'][x] for _,_,x in incoming[s]] + assert all(contains(a,b) for a,b in zip(fs,fs[1:])),s + assert contains(sigma,M) and len(fs[-1])<=h-1 + if a.include_birth_recipients and not len(sigma)==len(M)==len(F0):blocked['unequal_packet_dimensions_excluded_from_joint_options']+=1;continue + eligible.append({'role':s,'target':t,'root_index':j,'coefficient_numerator':21*sign,'sigma':len(sigma),'M':len(M),'F0':len(F0),'incoming_operations':[i for i,_,_ in incoming[s]],'incoming_count':len(incoming[s]),'frames':[list(F) for F in fs],'current_birth_donor':merge.get(s),'terminal_local_scalar_charge':29*len(incoming[s]),'packet_replication':2*v,'old_packet':[m-h+len(sigma),1,len(F0)-len(sigma),h-1-len(M)],'padded_new_packet':[m,len(F0)-len(M),0,0]}) + +# One terminal per target gives disjoint target-front packets; this avoids +# treating individually legal but interleaved output paths as simultaneous. +bytarget=defaultdict(list) +for row in eligible:bytarget[row['target']].append(row) +selected=[min(group,key=lambda x:x['role']) for _,group in sorted(bytarget.items())] +if a.terminal_roles: + requested=json.loads(a.terminal_roles.read_text()) + assert isinstance(requested,list) and all(type(s) is int for s in requested), 'Selection must be a JSON list of integer role IDs' + assert len(requested)==len(set(requested)), 'Duplicate terminal role ID' + rows={row['role']:row for row in eligible} + assert set(requested)<=rows.keys(), f'Ineligible requested terminal roles: {sorted(set(requested)-rows.keys())}' + selected=[rows[s] for s in sorted(requested)] + assert len({row['target'] for row in selected})==len(selected), 'Selected terminals must have distinct targets' + assert not set(requested)&(set(merge)|set(merge.values())), 'Selected terminals must have no birth aliases' +record={'status':'PASS exact local eligibility and disjoint-target selection on new composition inputs','base_virtual_roles':R,'base_physical_roles':choice['R'],'birth_merges_preserved':len(merge),'eligible_unshared_terminal_roles':len(eligible),'selected_terminal_roles':len(selected),'selected_targets':len(bytarget),'blocked':dict(blocked),'selection_rule':'Lowest eligible role id per target; no frame, deferral or birth matching changes.','selected':selected,'eligible':eligible,'expected_physical_roles':choice['R']-len(selected),'input_sha256':{str(p):sha256(p.read_bytes()).hexdigest() for p in [a.frames,a.readouts,a.matches]}} +if a.terminal_roles: + record.update(selection_rule='Exact requested role-ID subset, validated against ordinary unshared eligibility and distinct targets',selected_targets=len(selected),selection_sha256=sha256(a.terminal_roles.read_bytes()).hexdigest()) +if a.include_birth_recipients: + record.update(status='PASS virtual eligibility options for joint birth/terminal optimization; not a legal simultaneous elimination selection',joint_optimization_options=True,eligible_virtual_terminal_roles=len(eligible),currently_birth_matched_options=sum(row['current_birth_donor'] is not None for row in eligible),selection_rule='All eligible options retained in eligible; selected is only the lowest role per target and may conflict with existing births. Choose at most one option per target and never choose both a terminal edge and a birth donor edge for the same role. After changing the birth matching, rerun the default inventory and full builder.') + record.pop('eligible_unshared_terminal_roles');record.pop('expected_physical_roles') +a.out.parent.mkdir(parents=True,exist_ok=True) +a.out.write_text(json.dumps(record,indent=2,sort_keys=True)+'\n') +print(json.dumps({k:v for k,v in record.items() if k not in ['selected','eligible','input_sha256']},indent=2)) diff --git a/research/shrunk-birth-terminal/selected/inputs/BIRTH_MATCHES.json.gz b/research/shrunk-birth-terminal/selected/inputs/BIRTH_MATCHES.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..f6bf701f10ccbe4bb871624719956407c754d4d9 GIT binary patch literal 38343 zcmV)kK%l=LiwFP!00002|LncZt|Uj2rMaJ{AZlHO)*li5nE?vuSLn?w1_L6R8Cl70 z7MUQK)icxRcOSc#j0n3Paju)2n;uhD6Xv3dm+|9n`kAVz$dM!e^MCv9yMOxa_Yc4S z4#r_{{6#`KmYs3pMU>P zfB*2~U;gFqzy9*qAAkDz-GBY@*Wds4FTZ~L$8R6M`|XEcKYslA|5*O-ho3&Y{1Jcu z@bhm!{_^v8AAbJJcYpoIPd|P4>&L(T^znz^KmO&r|MAPOfBEjW-+x?w`1>#4{qVPs 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After changing the birth matching, rerun the default inventory and full builder.", + "status": "PASS virtual eligibility options for joint birth/terminal optimization; not a legal simultaneous elimination selection" +} diff --git a/research/shrunk-birth-terminal/search/evidence/joint-terminal/TERMINAL_ROLES.json b/research/shrunk-birth-terminal/search/evidence/joint-terminal/TERMINAL_ROLES.json new file mode 100644 index 0000000000..1a89950939 --- /dev/null +++ b/research/shrunk-birth-terminal/search/evidence/joint-terminal/TERMINAL_ROLES.json @@ -0,0 +1,383 @@ +[ + 24058, + 24074, + 24588, + 26827, + 26887, + 26900, + 26909, + 26995, + 27092, + 27140, + 27149, + 27198, + 27220, + 27258, + 27344, + 27348, + 27375, + 27386, + 27389, + 27413, + 27460, + 27463, + 27470, + 27472, + 27477, + 27489, + 27532, + 27534, + 27537, + 27543, + 27547, + 27556, + 27560, + 27562, + 27574, + 27576, + 27581, + 27585, + 27601, + 27602, + 27603, + 27605, + 27608, + 27609, + 27617, + 27625, + 27631, + 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28690 +] diff --git a/research/shrunk-birth-terminal/search/evidence/joint-terminal/TRANSPORT.json b/research/shrunk-birth-terminal/search/evidence/joint-terminal/TRANSPORT.json new file mode 100644 index 0000000000..f105371e96 --- /dev/null +++ b/research/shrunk-birth-terminal/search/evidence/joint-terminal/TRANSPORT.json @@ -0,0 +1,10 @@ +{ + "flow": 2489, + "integer_surrogate_gain": 78714009339017904, + "augmentations": 1900, + "classes": [ + 1732, + 1429 + ], + "eligible_class_edges": 470173 +} diff --git a/research/shrunk-birth-terminal/search/evidence/metadata-resolution.json b/research/shrunk-birth-terminal/search/evidence/metadata-resolution.json new file mode 100644 index 0000000000..4d85cc965e --- /dev/null +++ b/research/shrunk-birth-terminal/search/evidence/metadata-resolution.json @@ -0,0 +1,9 @@ +{ + "correct_interpretation": "Inherited diagnostic from prior cost-filtered placement, not used by the conservative scalar upper bill", + "historical_field": "deferred_readout_terms=9732", + "mathematical_effect": "None: physical word, complete profile, conservative scalar bill G and selected kappa remain identical. Portable rerun is owned by certificate_package.", + "portable_fix": "The portable composer independently counts signed bit-plane response support, preserves9732 as inherited_deferred_readout_terms and emits current virtual/retained counts separately.", + "retained_after_terminal": 11503, + "selected_virtual": 11884, + "status": "Metadata observation acknowledged and corrected by enclosing portable composer; original discovery records stay immutable" +} diff --git a/research/shrunk-birth-terminal/search/evidence/mutation-provenance.json b/research/shrunk-birth-terminal/search/evidence/mutation-provenance.json new file mode 100644 index 0000000000..fd0f6f21c1 --- /dev/null +++ b/research/shrunk-birth-terminal/search/evidence/mutation-provenance.json @@ -0,0 +1,12 @@ +{ + "parent_commit": "dda535bdcfc321a13a1ebd3c2d70e2b5bb72368e", + "parent_file": "research/shrunk-frames/complex_deferred.py", + "parent_sha256": "fa1125e85ec73b185dc9eee117f62d10356bb6422c07ec793a7f77296c87707e", + "changed_block": "Replace PR125 shrink block with R12 completion/descent and deferral placement with complete marginal-cost filtering; add deterministic optimizer receipts. Screen separately omits C scalar replay and labels it unverified.", + "candidate_files": { + "complex_deferred.py": "2871de85529b65e07603b459f80159f9f884ada0a2081cee8ed3a266bf95e8f4", + "screen.py": "3eaed1cf5c07ff33e9bd244cc290494c7aea89b9a24b8bec2a4ba6c6e1c58c13", + "r12_frame_opt.py": "cb22a8c593b9dfe2bfcb8f83a998653e0f9b67988b8d691fd449d66019502fff", + "r12_defer_opt.py": "166d4a9f64b2f8a7440722f2b06e25d2dad8ebff8f64db562b39506514910d7e" + } +} diff --git a/research/shrunk-birth-terminal/search/evidence/portable-geometry-canary.json b/research/shrunk-birth-terminal/search/evidence/portable-geometry-canary.json new file mode 100644 index 0000000000..f1ef0bad70 --- /dev/null +++ b/research/shrunk-birth-terminal/search/evidence/portable-geometry-canary.json @@ -0,0 +1,25 @@ +{ + "canonical_geometry_sha256": "b2c682231b2d145b8f46f9ccfddb5aa9332feee069a40633bf8ca2144e624bc5", + "original_runtime_imports_sha256": "15d6082c8dd8f32f91ffc23a309dfcdcbb5bfc7c0d2512a2a145d0356b838286", + "reproduced_pickle_sha256": "d2b0615d1f9b8bd1e690a8ae09a0dd0659921bcb49dad24fa9f982793df2805f", + "scalar_dirty_word_replay": "Not repeated here; enclosing selected physical word has separate full exact rational source/dirty and reflection audits.", + "scope": "All geometric keys regenerated and compared, excluding descriptive base_profile metadata. Pickle bytes may differ. Explicit recorded legal moves reproduce a selected witness; no heuristic-search or global-optimality claim.", + "selected_fixture_sha256": "3e3b2158ebad61910433735562de52d51c2bf803474662e90b7c478f90112a83", + "stage_seconds": { + "F2_and_complete_profile": 11.803515083971433, + "all_input_adapter": 1.1176322910469025, + "carrier_matching": 0.38671950000571087, + "coordinates_recorded_moves_and_complete_frame_checks": 0.0917438329779543, + "deferral_placement": 0.55275808298029, + "expansion_recorded_moves_and_complete_frame_checks": 0.2138196669984609, + "frame_endpoint_optimization": 18.26809308398515, + "frame_lifting": 13.580551624996588, + "graph_build_and_input_checks": 0.14211129199247807, + "prune_recorded_moves_and_complete_frame_checks": 0.9517876669997349, + "role_compilation": 0.2204470409778878, + "source_values_and_phase_reach": 0.15818158304318786 + }, + "status": "PASS from-source graph and exact selected geometry regeneration", + "total_seconds": 48.463009166996926, + "wrapper_sha256": "66b8ca8acf3ba714b5821ab37eb2ee31d57f3adcc6253e3710d1b05ff3d40f08" +} diff --git a/research/shrunk-birth-terminal/search/evidence/portable-geometry-canary.log b/research/shrunk-birth-terminal/search/evidence/portable-geometry-canary.log new file mode 100644 index 0000000000..c99adc6bfb --- /dev/null +++ b/research/shrunk-birth-terminal/search/evidence/portable-geometry-canary.log @@ -0,0 +1,33 @@ +PR117 graph matched 91770 8120 71185 28705 +PR117 frames lifted 39989 +R12 frame optimization {'pass_index': 0, 'moves': 16031, 'shrink': 16031, 'grow': 0, 'radical_completions': 0, 'integer_score_gain': 49871856783307} +R12 frame optimization {'pass_index': 1, 'moves': 2, 'shrink': 0, 'grow': 2, 'radical_completions': 0, 'integer_score_gain': 5545177444} +R12 frame optimization {'pass_index': 2, 'moves': 0, 'shrink': 0, 'grow': 0, 'radical_completions': 0, 'integer_score_gain': 0} +PR117 candidates 15150 +PR117 placed 4706 +{"status": "PASS new-composition intermediate adapter and exact full input supports", "roles": 28705, "operations": 120475, "deferred": 4706, "shrunk_frames": 16029, "checkpoint_sha256": "4efe6de84e3de3c34219e1e5d569adfeb4cc41f3e05293b0d9365b3b9dc8fc1d"} +{ + "status": "PASS from-source graph and exact selected geometry regeneration", + "canonical_geometry_sha256": "b2c682231b2d145b8f46f9ccfddb5aa9332feee069a40633bf8ca2144e624bc5", + "selected_fixture_sha256": "3e3b2158ebad61910433735562de52d51c2bf803474662e90b7c478f90112a83", + "reproduced_pickle_sha256": "d2b0615d1f9b8bd1e690a8ae09a0dd0659921bcb49dad24fa9f982793df2805f", + "original_runtime_imports_sha256": "15d6082c8dd8f32f91ffc23a309dfcdcbb5bfc7c0d2512a2a145d0356b838286", + "wrapper_sha256": "66b8ca8acf3ba714b5821ab37eb2ee31d57f3adcc6253e3710d1b05ff3d40f08", + "stage_seconds": { + "graph_build_and_input_checks": 0.14211129199247807, + "carrier_matching": 0.38671950000571087, + "frame_lifting": 13.580551624996588, + "role_compilation": 0.2204470409778878, + "frame_endpoint_optimization": 18.26809308398515, + "source_values_and_phase_reach": 0.15818158304318786, + "deferral_placement": 0.55275808298029, + "F2_and_complete_profile": 11.803515083971433, + "all_input_adapter": 1.1176322910469025, + "prune_recorded_moves_and_complete_frame_checks": 0.9517876669997349, + "coordinates_recorded_moves_and_complete_frame_checks": 0.0917438329779543, + "expansion_recorded_moves_and_complete_frame_checks": 0.2138196669984609 + }, + "total_seconds": 48.463009166996926, + "scalar_dirty_word_replay": "Not repeated here; enclosing selected physical word has separate full exact rational source/dirty and reflection audits.", + "scope": "All geometric keys regenerated and compared, excluding descriptive base_profile metadata. Pickle bytes may differ. Explicit recorded legal moves reproduce a selected witness; no heuristic-search or global-optimality claim." +} diff --git a/research/shrunk-birth-terminal/search/evidence/protected-coordinates/BIRTH_AUDIT.json b/research/shrunk-birth-terminal/search/evidence/protected-coordinates/BIRTH_AUDIT.json new file mode 100644 index 0000000000..56c7a63672 --- /dev/null +++ b/research/shrunk-birth-terminal/search/evidence/protected-coordinates/BIRTH_AUDIT.json @@ -0,0 +1,24 @@ +{ + "status": "PASS original complete forward/reflected paid frame scan", + "source_head": "6ec868e8568ca9a74b7245494de1b187c7be78fe", + "matches": 2108, + "physical_original_roles": 26597, + "virtual_roles": 28705, + "word_blocks": 277775, + "workspace_forward_gates": 120475, + "all_data_source_target_banks_disjoint": true, + "targets_never_controls": true, + "donors_dead_before_birth": true, + "recipients_untouched_before_birth": true, + "all_selected_recipients_have_no_source_injection": true, + "inverse_order": 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Only frame geometry and deferred read timing changed. Exact old terminal-to-role responses are independent of these frames; the actual newly aliased word is separately audited." + }, + "scope": "Own local geometry candidate provenance. The historical SOURCE manifest pins the full imported runtime and original PR references. No portable publication or full repository verification claim.", + "status": "PASS immutable own source/input and response-cache binding" +} diff --git a/research/shrunk-birth-terminal/search/evidence/protected-prune/TRANSPORT.json b/research/shrunk-birth-terminal/search/evidence/protected-prune/TRANSPORT.json new file mode 100644 index 0000000000..74f53c3d90 --- /dev/null +++ b/research/shrunk-birth-terminal/search/evidence/protected-prune/TRANSPORT.json @@ -0,0 +1,10 @@ +{ + "flow": 2108, + "integer_surrogate_gain": 68118724681280917, + "augmentations": 1530, + "classes": [ + 1351, + 1234 + ], + "eligible_class_edges": 383227 +} diff --git a/research/shrunk-birth-terminal/search/evidence/pure-frame-full/ADAPTER.json b/research/shrunk-birth-terminal/search/evidence/pure-frame-full/ADAPTER.json new file mode 100644 index 0000000000..cd9dc3d4c6 --- /dev/null +++ b/research/shrunk-birth-terminal/search/evidence/pure-frame-full/ADAPTER.json @@ -0,0 +1,8 @@ +{ + "status": "PASS new-composition intermediate adapter and exact full input supports", + "roles": 28705, + "operations": 120475, + "deferred": 4706, + "shrunk_frames": 16029, + "checkpoint_sha256": "a3ffb97dbbc1062f157b21cabbc13a506b48e539025312da1d73e1b83647bd28" +} diff --git a/research/shrunk-birth-terminal/search/evidence/pure-frame-full/complex-profile.json b/research/shrunk-birth-terminal/search/evidence/pure-frame-full/complex-profile.json new file mode 100644 index 0000000000..90190f7c1a --- /dev/null +++ b/research/shrunk-birth-terminal/search/evidence/pure-frame-full/complex-profile.json @@ -0,0 +1,121 @@ +{ + "L": 2234496, + "N": 4096576, + "R": 28705, + "W": 124390992, + "additions": 91770, + "child_multiplicities": { + "1": 435601232, + "2": 267176096, + "3": 29238704, + "4": 61153136, + "5": 26425344, + "6": 15734576, + "7": 11876832, + "8": 22077792, + "9": 4562096, + "10": 7375456, + "11": 7019232, + "12": 31788944, + "13": 12536656, + "14": 1497760, + "15": 3440800, + "16": 854128, + "17": 506000, + "18": 2906464, + "19": 2092816, + "20": 817696, + "21": 1230592, + "22": 64768, + "23": 8363168, + "529": 8193152, + "552": 97147952, + "554": 3493424, + "556": 1445136, + "558": 2319504, + "560": 582912, + "562": 101200, + "564": 1307504, + "566": 975568, + "568": 1364176, + "569": 4048, + "570": 3643200, + "571": 2444992, + "572": 837936, + "573": 44528, + "574": 485760 + }, + "deferral_optimization": { + "mode": "original" + }, + "deferred_dims": { + "2": 863, + "4": 357, + "6": 573, + "8": 144, + "10": 25, + "12": 323, + "14": 241, + "16": 337, + "17": 1, + "18": 900, + "19": 604, + "20": 207, + "21": 11, + "22": 120 + }, + "deferred_roles": 4706, + "deficit": 1862080, + "frame_optimization": { + "changed_frames": 16029, + "mode": "both_endpoints", + "passes": [ + { + "grow": 0, + "integer_score_gain": 49871856783307, + "moves": 16031, + "pass_index": 0, + "radical_completions": 0, + "shrink": 16031 + }, + { + "grow": 2, + "integer_score_gain": 5545177444, + "moves": 2, + "pass_index": 1, + "radical_completions": 0, + "shrink": 0 + }, + { + "grow": 0, + "integer_score_gain": 0, + "moves": 0, + "pass_index": 2, + "radical_completions": 0, + "shrink": 0 + } + ], + "requested_rounds": 8, + "scope": "Heuristic integer rank-moment score; 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"8f05f04cf06217befd6d0ee0f2d7d0c5c5eb32cfab8c9a8ca7917fd6d620b7d2", + "repo/scripts/paired_network.py": "991223dc3c1374284c361ed017e42bf732dd971fa0bea2be2282cfb18257b3f7", + "repo/scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "repo/scripts/prepare_layers.py": "a6e2adc612f264b1c0e51d18ce6315de9ae5e2ae2420aa22e99a22d8bf304947", + "repo/scripts/search_network.py": "3a4faa5037d9b8e7ca5828afac193a96b6966a8b114f14937921795b24ec4f6a", + "repo/scripts/shared_point_circuit.py": "c9bb7a5df92d260a4e3ad532b53e26936730d7c93f7facfb0784957c1e81c8ba", + "repo/scripts/shared_point_network.py": "a85e7f0d8c42d6a27e3846308571ca324a1824ac5c2d59e4daa5c7673c33c697", + "repo/scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d", + "verify_candidate.py": "aa81ae77b4eda6533412d65044b6ac3839c4173762060f2c91f981f4e1598b3d" + }, + "inherited_credits": "eumemic PR117 DAG and PR114 saturated placement; Avi Eisenberg/ikeboy physical-role/deferred compiler; Rohan Arun deferred integration and paid bounded readout correction; Swapnil Jain round-seven bit word; icekylinx stopped-product/normal-form interfaces; all original NOTICE and source headers preserved.", + "own_contribution": "Chafik Boukhalfa with OpenAI Codex assistance: apply alternating lower/upper logical-frame moves to PR125, then filter saturated placements by complete paid marginal score at both existing target neighbors.", + "scope": "Local research evidence, not a published portable package or complete repository verification. Original PR125 verify.py/test_controls.py in the scratch copy remain foreign reference tools and were not claimed as R12 verification.", + "status": "Pinned R12 candidate runtime and accepted foreign inputs" +} diff --git a/research/shrunk-birth-terminal/search/original-runtime/certify_candidate.py b/research/shrunk-birth-terminal/search/original-runtime/certify_candidate.py new file mode 100644 index 0000000000..928b57740d --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/certify_candidate.py @@ -0,0 +1,27 @@ +"""Exact arithmetic for a new R12 complex profile using pinned PR125 assembly. +Chafik Boukhalfa with OpenAI Codex assistance; inherited solver credits retained. +This executes no foreign producer; the unchanged published bit profile remains +a working input and only the new composed complex profile is certified here. +""" +from pathlib import Path +from fractions import Fraction +from hashlib import sha256 +import importlib.util,json,math,sys,datetime +W=Path(__file__).resolve().parent;P=W/'repo/research/r12-logical-frames';O=Path(sys.argv[1]).resolve() +spec=importlib.util.spec_from_file_location('r12_exact',P/'certificate.py');m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m) +p=json.loads((O/'complex-profile.json').read_text());p['child_multiplicities']={int(t):c for t,c in p['child_multiplicities'].items()} +lo,hi=0.0,0.001 +for _ in range(70): + a=(lo+hi)/2 + if math.fsum(c*t*math.expm1(a*math.log(p['m']/t)) for t,c in p['child_multiplicities'].items())1: + mid=(left+right)//2 + if m.contracts(p,Fraction(mid,10**12)):left=mid + else:right=mid +m.COMPLEX=Fraction(left,10**12);result=m.js(m.exact(phase=p)) +(O/'certificate.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') +summary=dict(status='PASS exact own-profile moments and next-grid rejection, all47 strict constraints and7 assembly margins',checked_utc=datetime.datetime.now(datetime.timezone.utc).isoformat(),complex_saving=str(m.COMPLEX),kappa=result['kappa'],kappa_decimal=float(Fraction(result['kappa'])),profile_sha256=sha256((O/'complex-profile.json').read_bytes()).hexdigest(),certificate_sha256=sha256((O/'certificate.json').read_bytes()).hexdigest(),solver_sha256=sha256((P/'certificate.py').read_bytes()).hexdigest(),scope='Finite numerical certificate; physical/reflection verification is a separate receipt. Unchanged foreign bit profile is an accepted working input.') +(O/'arithmetic.json').write_text(json.dumps(summary,indent=2,sort_keys=True)+'\n');print(json.dumps(summary,indent=2)) diff --git a/research/shrunk-birth-terminal/search/original-runtime/references/birth_checkpoint.py b/research/shrunk-birth-terminal/search/original-runtime/references/birth_checkpoint.py new file mode 100644 index 0000000000..eec3282dd9 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/references/birth_checkpoint.py @@ -0,0 +1,74 @@ +"""Explicit adapter from PR125 virtual compiler to PR124 birth-read interface. + +Source graph/matching/frames and their credits remain in the producer files. +Only representation changes here; all represented identities are rechecked. +""" +import hashlib +import json +import pickle + + +def basis(rows): + piv = {} + for x in rows: + for p in sorted(piv, reverse=True): + if x >> p & 1: + x ^= piv[p] + if x: + p = x.bit_length()-1 + for q in piv: + if piv[q] >> p & 1: + piv[q] ^= x + piv[p] = x + return tuple(piv[p] for p in sorted(piv, reverse=True)) + + +def export_checkpoint(d, here): + n, v, R = (d[k] for k in ('n', 'v', 'Rr')) + args = [tuple(a) if a[0] else () for a in d['args']] + ops = [] + for o in d['ops']: + if o[0] == 'src': + ops.append((0, o[1], o[2], -1)) + else: + ops.append((1 if o[0] == 'add' else 2, *o[1:])) + support = [0]*n + for i in range(v): + support[i+1] = 1 << i + for x in d['order']: + if args[x]: + a, b = args[x] + assert not support[a] & support[b] + support[x] = support[a] | support[b] + values = [0]*R + for op, s, t, x in ops: + if op == 0: + assert values[s] == 0 + values[s] = 1 << (t-1) + elif op == 1: + assert not values[s] & values[t] + values[s] |= values[t] + assert values[s] == support[x] + else: + assert values[t] == 0 + values[t] = values[s] + assert values[t] == support[x] + assert all(values[s] == support[d['roots'][j]] for s, j in d['role_root'].items()) + g = dict(h=d['h'], v=v, args=args, core=list(d['core']), cover=list(d['cover']), + rank=list(d['ranks']), kind=list(d['types']), active=d['order'], + roots=list(d['roots']), targets=[-1 if t is None else t for t in d['target']], + support=support, holds=d['holds'], first=d['first_node'], ops=ops, + terminal=d['role_root'], last=[d['last'].get(s, -1) for s in range(R)], + phase=d['Anc'], touched=d['touched'], center_roles=d['centre_roles'], + U=[basis(d['U'].get(x, ())) for x in range(n)], tm=d['tmask'], + reach=[sum(1 << t for t in ts) for ts in d['reach']], reach_all=d['reach_all'], + placed={s:basis(F) for s,F in d['placed'].items()}, bytarget=dict(d['byT2']), + histogram=dict(d['z']), chain_dims=[ds[:-1] for ds in d['chain_dims']], + base_profile=d['out']) + raw = pickle.dumps(g, protocol=4) + (here/'FRAMES.pkl').write_bytes(raw) + receipt = dict(status='PASS new-composition intermediate adapter and exact full input supports', + roles=R, operations=len(ops), deferred=len(g['placed']), + shrunk_frames=d['shrunk'], checkpoint_sha256=hashlib.sha256(raw).hexdigest()) + (here/'ADAPTER.json').write_text(json.dumps(receipt, indent=2)+'\n') + print(json.dumps(receipt), flush=True) diff --git a/research/shrunk-birth-terminal/search/original-runtime/references/pr126/FETCH.json b/research/shrunk-birth-terminal/search/original-runtime/references/pr126/FETCH.json new file mode 100644 index 0000000000..ed6b1f3b9b --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/references/pr126/FETCH.json @@ -0,0 +1,6 @@ +{ + "head": "7534913786a5136710fa4de4b3738f7f5b1b58c4", + "pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/126", + "author": "DanieleCorso", + "purpose": "Source reading and credited endpoint/marginal-cost ideas; foreign producer not rerun as a correctness gate" +} diff --git a/research/shrunk-birth-terminal/search/original-runtime/references/pr126/LICENSE b/research/shrunk-birth-terminal/search/original-runtime/references/pr126/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/references/pr126/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 + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/shrunk-birth-terminal/search/original-runtime/references/pr126/NOTICE b/research/shrunk-birth-terminal/search/original-runtime/references/pr126/NOTICE new file mode 100644 index 0000000000..b565637758 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/references/pr126/NOTICE @@ -0,0 +1,304 @@ +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. diff --git a/research/shrunk-birth-terminal/search/original-runtime/references/pr126/research/physical-frame-kappa/complex_deferred.py b/research/shrunk-birth-terminal/search/original-runtime/references/pr126/research/physical-frame-kappa/complex_deferred.py new file mode 100644 index 0000000000..07850bb2eb --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/references/pr126/research/physical-frame-kappa/complex_deferred.py @@ -0,0 +1,481 @@ +#!/usr/bin/env python3 +"""Physical operation frames on PR117/118's fixed h=24 scalar DAG. + +The scalar DAG, maximum carrier matching and 28,705 roles are retained. +Backward operation frames, local nested-frame optimization and cost-aware +partial deferred readouts change the complete one-child profile. + +Credits: eumemic (PR117 DAG), Rohan Arun (PR118 composition), Avi Eisenberg +(PR110 physical/deferred compiler), Swapnil Jain (deferred readouts), and +icekylinx (PR104 stopped products and PR115 nondegenerate repair). Adapted +with OpenAI Codex assistance for DanieleCorso. Apache-2.0. +""" +import array +import json +import random +import struct +import sys +import tempfile +from collections import Counter, defaultdict +from itertools import combinations +from pathlib import Path +from functools import lru_cache +from lift115 import basis, safe_subspace + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(ROOT / 'scripts')) +import importlib.util +producer_path = HERE / 'references/pr118/producer.py' +spec = importlib.util.spec_from_file_location('cyclic_producer', producer_path) +producer = importlib.util.module_from_spec(spec); spec.loader.exec_module(producer) +build = producer.build + +P = (1 << 61) - 1 + + +def require(ok, msg): + if not ok: + raise SystemExit('FAIL: ' + msg) + + +def load(prefix): + def rd(fh, typ, cnt): + a = array.array(typ); a.fromfile(fh, cnt); return a + with open(str(prefix) + '.bin', 'rb') as f: + h, v, n, q = struct.unpack('<4I', f.read(16)) + flat = rd(f, 'I', 2 * n); core = rd(f, 'Q', n); cover = rd(f, 'Q', n) + roots = rd(f, 'I', q); kind = rd(f, 'I', q); active = rd(f, 'B', n) + with open(str(prefix) + '.labels', 'rb') as f: + ranks = rd(f, 'I', n); types = rd(f, 'B', n) + args = [(flat[2 * i], flat[2 * i + 1]) for i in range(n)] + return h, v, n, q, args, core, cover, roots, kind, active, ranks, types + + +# ---------------------------------------------------------------- F2 linear algebra on bit vectors +def dot(a, b): return bin(a & b).count('1') & 1 + + +def reduce(basis): + rows = []; piv = [] + for vec in basis: + for p, r in zip(piv, rows): + if vec >> p & 1: vec ^= r + if vec: + p = vec.bit_length() - 1 + for i in range(len(rows)): + if rows[i] >> p & 1: rows[i] ^= vec + rows.append(vec); piv.append(p) + return rows + + +def kernel(funcs, h): + K = reduce(funcs); piv = [r.bit_length() - 1 for r in K] + out = [] + for c in (i for i in range(h) if i not in piv): + vec = 1 << c + for r, p in zip(K, piv): + if r >> c & 1: vec |= 1 << p + out.append(vec) + return out + + +def restrict(basis, funcs): + B = reduce(basis) + for f in funcs: + if not B: break + vals = [dot(b, f) for b in B] + if not any(vals): continue + k = vals.index(1); pv = B[k] + B = [b ^ pv if val else b for b, val in zip(B, vals)]; B.pop(k) + return reduce(B) + + +def contains(A, B): + RB = reduce(B) + return len(reduce(RB + list(A))) == len(RB) + + +def cap(A, B): + A = reduce(A); B = reduce(B) + if not A or not B: return [] + ker = []; red = [] + for i, vec in enumerate(A + B): + tag = 1 << i + for rv, rt in red: + if vec >> (rv.bit_length() - 1) & 1: vec ^= rv; tag ^= rt + if vec: red.append((vec, tag)) + else: + comb_ = 0 + for k in range(len(A)): + if tag >> k & 1: comb_ ^= A[k] + ker.append(comb_) + return reduce(ker) + + +def nondeg(B): + B = reduce(B); k = len(B) + if not k: return True + M = [sum(dot(B[i], B[j]) << j for j in range(k)) for i in range(k)] + return len(reduce(M)) == k + + +def hopcroft_karp(left, adj): + """maximum bipartite matching; adj[x] = sorted list of right vertices.""" + INF = 1 << 60 + mate_l = {x: None for x in left}; mate_r = {} + while True: + dist = {}; queue = [] + for x in left: + if mate_l[x] is None: dist[x] = 0; queue.append(x) + else: dist[x] = INF + found = INF; head = 0 + while head < len(queue): + x = queue[head]; head += 1 + if dist[x] >= found: continue + for r in adj[x]: + y = mate_r.get(r) + if y is None: found = min(found, dist[x] + 1) + elif dist[y] == INF: dist[y] = dist[x] + 1; queue.append(y) + if found == INF: break + gained = 0 + for x0 in left: + if mate_l[x0] is not None: continue + stack = [(x0, iter(adj[x0]))]; path = [] + while stack: + x, it = stack[-1] + advanced = False + for r in it: + y = mate_r.get(r) + if (y is None and dist[x] + 1 == found) or (y is not None and dist[y] == dist[x] + 1): + path.append((x, r)) + if y is None: + for xx, rr in path: mate_l[xx] = rr; mate_r[rr] = xx + gained += 1; stack = []; break + stack.append((y, iter(adj[y]))); advanced = True; break + else: + dist[x] = INF; stack.pop() + if path: path.pop() + continue + if not advanced: break + if not gained: break + return mate_l + + +def main(): + require(not sys.flags.optimize, "optimized Python is forbidden") + with tempfile.TemporaryDirectory(prefix='deferred-stopped-') as work: + prefix = Path(work) / 'complex' + build(24, prefix, central_disjoint=24) + h, v, n, q, args, core, cover, roots, kind, active, ranks, types = load(prefix) + trip = list(combinations(range(h), 3)); require(len(trip) == v, 'triple count') + m = h * h; N = v * v; FULL = (1 << h) - 1 + tmask = [sum(1 << p for p in T) for T in trip] + tid = {T: i for i, T in enumerate(trip)} + + # ------------------------------------------------------------ uses and matching (inherited adjacency) + degree = [0] * n; uses = defaultdict(list); c_add = 0 + for x in range(1, n): + if active[x] and args[x][0]: + c_add += 1 + for pos, y in enumerate(args[x]): degree[y] += 1; uses[y].append(('gate', x, pos)) + for j, x in enumerate(roots): degree[x] += 1; uses[x].append(('root', j)) + def unode(u): return roots[u[1]] if u[0] == 'root' else u[1] + def before(x, u): + y = unode(u) + return (ranks[x], x) < (ranks[y], (n + u[1]) if u[0] == 'root' else y) + def incl(x, y): + tx, ty = types[x], types[y] + if tx == 1 and ty == 1: return not (core[y] & ~core[x]) and not (cover[x] & ~cover[y]) + if tx in (1, 2) and ty == 2: return not (cover[x] & ~cover[y]) + if tx == 1 and ty == 3: return bool(core[x] & core[y]) + if tx == 2 and ty == 3: return not (cover[x] & ~core[y]) + if tx == 3 and ty == 2: return cover[y] == FULL + if tx == 3 and ty == 3: return core[x] == core[y] + return False + left = []; adj = {} + for x in range(1, n): + if not (active[x] and args[x][0]): continue + rs = sorted({(y, k) for y in args[x] for k, u in enumerate(uses[y]) if before(x, u) and incl(x, unode(u))}) + if rs: left.append(x); adj[x] = rs + mate = hopcroft_karp(left, adj) + links = {x: r for x, r in mate.items() if r is not None} + R = c_add + q - len(links) + require((c_add, q, len(links), R) == (91770, 8120, 71185, 28705), + 'selected graph size: additions=%d, roots=%d, matching=%d, roles=%d' % (c_add, q, len(links), R)) + linked_use = {(y, k): x for x, (y, k) in links.items()} + + # ------------------------------------------------------------ root targets, read coefficients, root functionals + target = [None] * q + for j in range(v): target[j] = j + idx = v + for a, b in combinations(range(h), 2): + others = sorted((i for i in range(h) if i not in (a, b)), key=(lambda i: producer.ORDER(i, a, b)) if hasattr(producer, 'ORDER') else (lambda i: ((i ^ 1) in (a, b), i))) + for i in others: target[idx] = tid[tuple(sorted((a, b, i)))]; idx += 1 + centre_of = {} + for j in range(q): + if kind[j]: + miss = FULL & ~cover[roots[j]]; require(bin(miss).count('1') == 1, 'centre cover') + centre_of[j] = miss.bit_length() - 1 + require(idx + len(centre_of) == q, 'root order') + rootfun = [(1 << centre_of[j]) if kind[j] else tmask[target[j]] for j in range(q)] + + # ------------------------------------------------------------ lifted binary frames, monotone + succ = defaultdict(set); droot = defaultdict(set) + for x in range(1, n): + if not active[x]: continue + for k, u in enumerate(uses[x]): + if (x, k) in linked_use: continue + (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1])) + for x, (y, k) in links.items(): + u = uses[y][k]; (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1])) + order_desc = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x), reverse=True) + def envelope(x): + if not args[x][0]: return [tmask[x - 1]] + if types[x] == 2: return [1 << i for i in range(h) if cover[x] >> i & 1] + require(types[x] == 1, 'only ordinary and common-pair labels occur') + ks = [i for i in range(h) if (cover[x] & ~core[x]) >> i & 1] + require(len(ks) == ranks[x], 'common-pair support') + return [core[x] | (1 << k) for k in ks] + # Original envelopes suffice for the role-local backward pass below. + U = {x: envelope(x) for x in order_desc} + + # ------------------------------------------------------------ explicit role compile + order = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x)) + holds = []; first_node = []; ops = []; edge_key = {}; role_root = {} + def new_role(node): holds.append([node]); first_node.append(node); return len(holds) - 1 + def serve(s, y, k): + u = uses[y][k] + if u[0] == 'gate': edge_key[(y, k)] = s + else: role_root[s] = u[1] + for x in order: + free = [k for k in range(len(uses[x])) if (x, k) not in linked_use] + if not args[x][0]: + for k in free: + s = new_role(x); ops.append(('src', s, x)); serve(s, x, k) + continue + a, b = args[x] + ka = next(k for k, u in enumerate(uses[a]) if u == ('gate', x, 0)) + kb = next(k for k, u in enumerate(uses[b]) if u == ('gate', x, 1)) + sa, sb = edge_key.pop((a, ka)), edge_key.pop((b, kb)) + if x in links and links[x][0] == a: sa, sb = sb, sa + piv, oth = sa, sb + ops.append(('add', piv, oth, x)); holds[piv].append(x); holds[oth].append(x) + if x in links: serve(oth, *links[x]) + require(free, 'every use linked at node %d' % x) + serve(piv, x, free[0]) + for k in free[1:]: + f = new_role(x); ops.append(('copy', piv, f, x)); serve(f, x, k) + require(not edge_key and len(holds) == R, 'compile') + Rr = R + + # ------------------------------------------------------------ B. the word computes every root value + rng = random.Random(20261008) + xs = [rng.randrange(P) for _ in range(v)] + val = [0] * n + for i in range(v): val[i + 1] = xs[i] + for x in order: + if args[x][0]: val[x] = (val[args[x][0]] + val[args[x][1]]) % P + # Enlarge each physical operation independently. A logical DAG node can + # occur at several copy times with different remaining obligations. + full_frame = [1 << i for i in range(h)] + root_frame = {s: ([1 << i for i in range(h) if i != centre_of[j]] if kind[j] + else kernel([tmask[target[j]]], h)) for s, j in role_root.items()} + future = {s: root_frame.get(s, full_frame) for s in range(Rr)} + op_frames = {}; role_frames = [[] for _ in range(Rr)] + @lru_cache(None) + def extend(C, E): + require(contains(E, C) and nondeg(E), 'physical gate envelope') + result = basis(E + safe_subspace(restrict(C, E), ())) + require(nondeg(result) and contains(E, result) and contains(result, C), 'physical repair') + return result + for i in reversed(range(len(ops))): + o = ops[i] + if o[0] == 'src': continue + a, b, node = o[1:] + C = basis(cap(future[a], future[b])) + F = extend(C, tuple(envelope(node))) + op_frames[i] = list(F) + future[a] = future[b] = list(F) + from optimize_frames import optimize + op_frames, frame_search = optimize(ops, op_frames, root_frame, h, v, tmask, lambda node: ()) + for i, o in enumerate(ops): + if o[0] != 'src': + for s in o[1:3]: role_frames[s].append(op_frames[i]) + leaf_of = {s: first_node[s] for s in range(Rr) if not args[first_node[s]][0]} + source_frame = {s: [tmask[n-1]] for s, n in leaf_of.items()} + source_order = list(leaf_of) + source_by_node = defaultdict(list) + for s, n in leaf_of.items(): source_by_node[n].append(s) + a_ = [0] * Rr + for s, leaf in leaf_of.items(): a_[s] = xs[leaf - 1] + for o in ops: + if o[0] == 'add': a_[o[1]] = (a_[o[1]] + a_[o[2]]) % P + elif o[0] == 'copy': a_[o[2]] = (a_[o[2]] + a_[o[1]]) % P + require(all(a_[s] == val[roots[j]] for s, j in role_root.items()), 'root values') + + # ------------------------------------------------------------ phase one and garbage reach + def touch(o): return [o[1], o[2]] if o[0] in ('add', 'copy') else [] + prev = {}; pred = defaultdict(list); last = {} + for i, o in enumerate(ops): + for s in touch(o): + if s in prev: pred[i].append(prev[s]) + prev[s] = i; last[s] = i + centre_roles = [s for s, j in role_root.items() if kind[j]] + Anc = set(); st = [last[s] for s in centre_roles] + while st: + i = st.pop() + if i not in Anc: Anc.add(i); st.extend(pred[i]) + touched = set(centre_roles) + for i in Anc: touched.update(touch(ops[i])) + require(all(last[s] in Anc for s in centre_roles), 'centres complete in phase one') + reach = [set() for _ in range(Rr)]; reach_all = [False] * Rr + for s, j in role_root.items(): + if kind[j]: reach_all[s] = True + else: reach[s].add(target[j]) + for o in reversed(ops): + if o[0] == 'add': reach[o[2]] |= reach[o[1]]; reach_all[o[2]] = reach_all[o[2]] or reach_all[o[1]] + elif o[0] == 'copy': reach[o[1]] |= reach[o[2]]; reach_all[o[1]] = reach_all[o[1]] or reach_all[o[2]] + + # ------------------------------------------------------------ deferral frames, insertion nesting + def F0(s): return source_frame[s] if s in leaf_of else role_frames[s][0] + # PR115's descending intersection pass also repairs degenerate caps. + cand = {s: F0(s) for s in range(Rr) if s not in touched and not reach_all[s] and s not in leaf_of} + latest = {}; placed = {}; selection = [] + import math + f = [0.] + [x*math.log(x) for x in range(1, m+1)] + target_dim = {t: h-1 for t in range(v)} + @lru_cache(None) + def gauge(constraints): + B = kernel(constraints, h) + return tuple(B) if nondeg(B) else safe_subspace(B, ()) + for s in sorted(cand, key=lambda s: (-len(cand[s]), len(reach[s]), s)): + rows = list(kernel(cand[s], h)) + for t in sorted(reach[s]): + rows.append(tmask[t]) + rows.extend(latest.get(t, ())) + X = gauge(basis(rows)) + d = len(X); r = len(cand[s]); ext = m-h + gain = f[r-d]+f[ext+d]-f[r]-f[ext] + gain += sum(f[d]+f[target_dim[t]-d]-f[target_dim[t]] for t in reach[s]) + if X and gain > 1e-9: + for t in reach[s]: target_dim[t] = d + placed[s] = list(X); selection.append(s) + A = tuple(kernel(X, h)) + for t in reach[s]: latest[t] = A + deferred = list(reversed(selection)); dset = set(deferred) + + # ------------------------------------------------------------ C. replay with arbitrary scratch and data + inv = lambda a: pow(a % P, P - 2, P); HALF = inv(2); I21 = inv(21) + cvec = [None] * Rr; dpart = [dict() for _ in range(Rr)] + for s, j in role_root.items(): + if kind[j]: c = [0] * h; c[centre_of[j]] = 1; cvec[s] = c + else: dpart[s][target[j]] = (P - HALF) if j >= v else HALF + seed_c = {s: (None if cvec[s] is None else list(cvec[s])) for s in role_root} + seed_d = {s: dict(dpart[s]) for s in role_root} + def addc(dst, src): + if cvec[src] is not None: + cvec[dst] = list(cvec[src]) if cvec[dst] is None else [(p + q_) % P for p, q_ in zip(cvec[dst], cvec[src])] + for t, c in dpart[src].items(): dpart[dst][t] = (dpart[dst].get(t, 0) + c) % P + for o in reversed(ops): + if o[0] == 'add': addc(o[2], o[1]) + elif o[0] == 'copy': addc(o[1], o[2]) + scatter = [[(I21 - (HALF if i in trip[t] else 0)) % P for t in range(v)] for i in range(h)] + def readout(y, s, value, sign, seed=False): + cv = seed_c[s] if seed else cvec[s]; dp = seed_d[s] if seed else dpart[s] + if cv is not None: + for i, ci in enumerate(cv): + if ci: + f = sign * ci * value % P; row = scatter[i] + for t in range(v): y[t] = (y[t] + f * row[t]) % P + for t, c in dp.items(): y[t] = (y[t] + sign * c * value) % P + phase1 = sorted(Anc); rest = [i for i in range(len(ops)) if i not in Anc] + def replay(seed): + rng = random.Random(seed) + x = [rng.randrange(P) for _ in range(v)]; z = [rng.randrange(P) for _ in range(Rr)] + y0 = [rng.randrange(P) for _ in range(v)]; a = list(z); y = list(y0) + for s in range(Rr): + if s not in dset: readout(y, s, a[s], -1) + for s, leaf in leaf_of.items(): + if s not in dset: a[s] = (a[s] + x[leaf - 1]) % P + def run(i, sign=1): + o = ops[i] + if o[0] == 'add': a[o[1]] = (a[o[1]] + sign * a[o[2]]) % P + elif o[0] == 'copy': a[o[2]] = (a[o[2]] + sign * a[o[1]]) % P + for i in phase1: run(i) + for s in centre_roles: readout(y, s, a[s], +1, True) + for s in deferred: readout(y, s, a[s], -1) + for s in deferred: + if s in leaf_of: a[s] = (a[s] + x[leaf_of[s] - 1]) % P + for i in rest: run(i) + for s, j in role_root.items(): + if not kind[j]: readout(y, s, a[s], +1, True) + for i in reversed(range(len(ops))): run(i, -1) + for s, leaf in leaf_of.items(): a[s] = (a[s] - x[leaf - 1]) % P + return a == z, all((y[t] - y0[t] - x[t]) % P == 0 for t in range(v)) + rep = [replay(seed) for seed in (1, 2)] + require(all(r == (True, True) for r in rep), 'replay %s' % rep) + + # ------------------------------------------------------------ D. exact F2 frame facts + root_frame = {} + for s, j in role_root.items(): + root_frame[s] = [1 << i for i in range(h) if i != centre_of[j]] if kind[j] else kernel([tmask[target[j]]], h) + FULLB = [1 << i for i in range(h)] + chain_dims = [] + for s in range(Rr): + seq = [placed.get(s, []), F0(s)] + role_frames[s] + if s in root_frame: seq.append(root_frame[s]) + seq.append(FULLB) + require(all(contains(A, B) for A, B in zip(seq, seq[1:])), 'role chain nesting %d' % s) + require(all(nondeg(B) for B in seq[1:-1] if B), 'degenerate frame on role %d' % s) + chain_dims.append([len(reduce(B)) for B in seq]) + for s, X in placed.items(): + require(contains(X, F0(s)) and nondeg(X), 'deferral frame %d' % s) + require(all(not any(dot(xv, tmask[t]) for xv in X) for t in reach[s]), 'target frame %d' % s) + byT2 = defaultdict(list) + for s in deferred: + for t in reach[s]: byT2[t].append(s) + for t, ss in byT2.items(): + ss.sort(key=lambda s: (len(placed[s]), s)) + require(all(contains(placed[p], placed[q_]) for p, q_ in zip(ss, ss[1:])), 'target chain %d' % t) + + # ------------------------------------------------------------ E. one-child histogram + z = Counter() + for s in range(Rr): + ds = chain_dims[s] + for a, b in zip(ds[:-1], ds[1:-1]): + if b > a: z[b - a] += 2 * v + lastd = ds[-2] + if s in role_root and kind[role_root[s]]: z[h - 1] += 2 * v # copied centre transform + z[h - lastd] += 2 * v # final growth to F + z[m - h + ds[0]] += 2 * v # exterior, gauged by sigma + levels = defaultdict(set) + for s in deferred: + for t in reach[s]: levels[t].add(len(placed[s])) + for t in range(v): + ds = sorted(levels[t] | {0, h - 1}) + for a, b in zip(ds, ds[1:]): z[b - a] += 2 * v # target fronts + for node, slots in sorted(source_by_node.items()): + ds = [1] + [len(source_frame[s]) for s in source_order if leaf_of[s] == node] + [h] + require(all(b >= a for a, b in zip(ds, ds[1:])), 'source chain dimensions') + for a, b in zip(ds, ds[1:]): z[b - a] += 2 * v + z[(h - 1) ** 2] += 2 * N # data macros + z[1] += N # endpoint copies + z.pop(0, None) + W = 2 * N + 2 * v * R; L = 2 * v * h * (h - 1); s_ = W * m - N + L + require(sum(t * c for t, c in z.items()) == s_, 'complex rank mass') + require(all(0 < t < m for t in z), 'children below m') + out = dict(h=h, v=v, additions=c_add, roots=q, links=len(links), R=R, m=m, N=N, W=W, L=L, total_rank=s_, + deficit=N - L, maxchild=max(z), phase_one_ops=len(Anc), phase_one_roles=len(touched), + deferred_roles=len(deferred), source_lifted_roles=sum(len(B)>1 for B in source_frame.values()), + deferred_dims=dict(sorted(Counter(len(X) for X in placed.values()).items())), + enlarged_operations=sum(len(F) > ranks[ops[i][3]] for i, F in op_frames.items()), + frame_search=frame_search, + replay=dict(seeds=[1, 2], scratch_restored=True, y_plus_x=True, field='Z/(2^61-1)'), + child_multiplicities=dict(sorted(z.items()))) + (HERE / 'complex-profile.json').write_text(json.dumps(out, indent=1) + '\n') + print('PASS complex: R=%d, deferred roles %d, maxchild %d, rank mass %d' % (R, len(deferred), max(z), s_)) + + +if __name__ == '__main__': + main() diff --git a/research/shrunk-birth-terminal/search/original-runtime/references/pr126/research/physical-frame-kappa/lift115.py b/research/shrunk-birth-terminal/search/original-runtime/references/pr126/research/physical-frame-kappa/lift115.py new file mode 100644 index 0000000000..a9f3577416 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/references/pr126/research/physical-frame-kappa/lift115.py @@ -0,0 +1,64 @@ +# Copyright 2026 icekylinx. Apache-2.0. +# Prepared with OpenAI GPT-6 Astra and Codex assistance; see NOTICE. +#!/usr/bin/env python3 +"""Construct maximal nondegenerate backward frames containing every old frame. +Existing carrier dependencies are included before the backward pass. Exact F2 +linear algebra only; the general Gauss compiler permits alternating residuals. +""" +from pathlib import Path +from collections import Counter +import json,argparse + +def basis(rows): + b={} + for x in rows: + for p,y in sorted(b.items(),reverse=True): + if x>>p&1:x^=y + if x: + p=x.bit_length()-1 + for k,y in list(b.items()): + if y>>p&1:b[k]=y^x + b[p]=x + return tuple(b[p] for p in sorted(b,reverse=True)) + +def perp(rows,h): + rows=basis(rows);piv={r.bit_length()-1:r for r in rows};out=[] + for j in range(h): + if j in piv:continue + x=1<>j&1:x|=1<

    len(old): + extra = intersection(upper, perp(old, h), h) + candidates.append(basis(old + safe_subspace(extra, ()))) + def score(F): + d = len(F) + return sum(weight[d-len(A)] + weight[len(B)-d] for A, B in sides) + best = max(candidates, key=score) + delta = score(best) - score(old) + if delta > 0: + assert nondeg(best) and all(inside(A, best) and inside(best, B) for A, B in sides) + frames[i] = best; changed += 1; gain += delta + changes.append(dict(pass_index=cycle, changed=changed, objective_gain= gain)) + print('frame search', changes[-1], flush=True) + if not changed: break + return {i: list(F) for i, F in frames.items()}, changes diff --git a/research/shrunk-birth-terminal/search/original-runtime/references/verification-driver-tested.py b/research/shrunk-birth-terminal/search/original-runtime/references/verification-driver-tested.py new file mode 100644 index 0000000000..6d631cfdbd --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/references/verification-driver-tested.py @@ -0,0 +1,17 @@ +from pathlib import Path +from hashlib import sha256 +import datetime,importlib.util,json,os,sys,time,pickle +W=Path(__file__).resolve().parent;P=W/'repo/research/r12-logical-frames' +name=sys.argv[1];O=W/name;O.mkdir(exist_ok=True) +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 +config={k:os.environ[k] for k in ('R12_FRAME_MODE','R12_FRAME_ROUNDS','R12_DEFER_MODE')};sources={str(p.relative_to(P)):sha256(p.read_bytes()).hexdigest() for p in P.glob('*.py')};start=time.monotonic() +(O/'process.json').write_text(json.dumps(dict(started_utc=datetime.datetime.now(datetime.timezone.utc).isoformat(),config=config,sources=sources),indent=2)+'\n') +sys.path.insert(0,str(P));ref=load('r12_reflection',P/'reflection_audit.py');d=ref.capture(P/'complex_deferred.py') +(O/'complex-profile.json').write_text(json.dumps(d['out'],indent=2,sort_keys=True)+'\n') +adapter=load('r12_birth_checkpoint',W.parent/'research-r12/birth_checkpoint.py');adapter.export_checkpoint(d,O) +result=ref.audit(d);result['source_sha256']=sha256((P/'complex_deferred.py').read_bytes()).hexdigest();result['audit_sha256']=sha256((P/'reflection_audit.py').read_bytes()).hexdigest() +(O/'reflection-audit.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') +assert sources=={str(p.relative_to(P)):sha256(p.read_bytes()).hexdigest() for p in P.glob('*.py')} +receipt=dict(status='PASS complete own-candidate compiler, dirty replay, exact binary frames, exact all-input supports and independent literal reflection',elapsed_seconds=round(time.monotonic()-start,3),config=config,sources=sources,profile_sha256=sha256((O/'complex-profile.json').read_bytes()).hexdigest(),checkpoint_sha256=sha256((O/'FRAMES.pkl').read_bytes()).hexdigest(),reflection_sha256=sha256((O/'reflection-audit.json').read_bytes()).hexdigest()) +(O/'verification.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt,indent=2)) diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/LICENSE b/research/shrunk-birth-terminal/search/original-runtime/repo/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/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 + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/NOTICE b/research/shrunk-birth-terminal/search/original-runtime/repo/NOTICE new file mode 100644 index 0000000000..50c6d1236d --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/NOTICE @@ -0,0 +1,321 @@ +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. + +Stopped product-ring extension, 9 October 2026 +Copyright 2026 icekylinx + +The opposite-bank generic projector factorization, componentwise atom-ring +adapters, stopped recurrence and outer ordinary-interchange conversion, +aligned pair-star producer with rational centers, exact denominator-21 +grid and selected (23,23)/(24,24) composition are contributed by icekylinx +with substantial OpenAI GPT-6 Astra and Codex assistance. This extension +builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is +integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37. + +The retained ordinary leaf uses the preceding projector, corner and +copied-center proofs. The selected two-stage topology retains Aurel Prosz +(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly +retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching, +original source notices and each imported license remain unchanged. diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/certificates/copied-centers-network.json b/research/shrunk-birth-terminal/search/original-runtime/repo/certificates/copied-centers-network.json new file mode 100644 index 0000000000..20bbb6806c --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/certificates/copied-centers-network.json @@ -0,0 +1,684 @@ +{ + "adopted_sources": { + "files": { + "PROVENANCE.json": "27df488b36b4fa599b6e6b92408a4b37169125f40918c6ff29bb035e4342a7d4", + "README.md": "add72b080a24707aeda0d7a9ab8147003e3dc972575954d597b078aa82fb9619", + "SOURCES.json": "fd12f8ce03a9f504cbf62351e8f5f09b6209e6f9929081f7ad24a8e55cf09d64", + "pr29/LICENSE": "c95bae1d1ce0235ecccd3560b772ec1efb97f348a79f0fbe0a634f0c2ccefe2c", + "pr29/NOTICE": "1b4512d2fe2063aca8e59529f5f1552641b41128872fefa1f3411c991097a49f", + "pr29/SOURCE.json": 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Copied-stream scheduling, simultaneous basis existence, analytic and tape interfaces remain written proof dependencies.", + "source_sha256": { + "certificates/copied-centers-bit-axes.json": "ed307cef595091b11ba8f8e6ff11302ad8db190227a2fbf34c232fd680206254", + "certificates/copied-centers-complex-input.json": "91a9e54b455ecc36c3150abcf4a1c9138691c8faab464b5ce159ba8e376764e7", + "certificates/copied-centers-corner-25-23.json": "23b0540ddc1d98a775383bfc65c7cf512aad86b399bf71167220b2a8182f5610", + "certificates/copied-centers-input.json": "5f8a57b1a4dd3f271d4e859ad350db3674b74f744127e74a989e7790718cea24", + "notes/copied-centers-assembly.tex": "00117892971ae766188ace0af03030c44164fda105e42b70d84f52c3339a7dcb", + "notes/copied-centers-bit.tex": "ccc8191ddb51698251ed4461a4c26104501b9b2ee37ce3cbe82fa73e85ae40dd", + "notes/copied-centers-complex.tex": "18eac6d5c5755e53230c0c12a633f38b6ce9666ef0322c1aff79394f2952af72", + "notes/copied-centers-lemma.tex": "d0ce6d3d504996aadb098227885224e48df46101daec8893523a0a8b7364d8fe", + "notes/copied-centers-note.tex": "1099559bea3090399a2496bfb8fdf8966ac39d22fd413e35643af5ee0bb08556", + "references/copied-centers/MANIFEST.json": "5636f7beb34ae439f076d36e13d95d3057ce41ccbdba9da63d7727198b093ccb", + "scripts/copied_centers/README.md": "8d348a28fc11615fb686f7d47548db06a5000378b54e0e47438d17292b5942b9", + "scripts/copied_centers/__init__.py": "13db4f09038a2ff5335cbd4dbd93274b0fb16b3c7b51e4de67cbb2801a3f78e1", + "scripts/copied_centers/corners.py": "9eecdc39c67cc18c806a33f0be03986c28591d322881fd60c11f52c625c8067b", + "scripts/copied_centers/physical.py": "837345d1f8753eab0e70f105b1d1bb0db965b993da037b1825ddef3672609d7d", + "scripts/copied_centers_network.py": "409ebfbd8a41c4c4d089aa0949fcf5a949415dc26f57440ffd48b7bd8881e6a9", + "scripts/copied_centers_producer.py": "33afa6fe25677e13656fa8a200a25ed3510ef70c1ff9f1186612cbd9ee75d209", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + }, + "status": "Conditional copied-center multiplication witness" +} diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/bit-profile.json b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/bit-profile.json new file mode 100644 index 0000000000..36105e819a --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/bit-profile.json @@ -0,0 +1,69 @@ +{ + "h": 23, + "v": 1771, + "R": 28866, + "m": 529, + "N": 3136441, + "W": 108516254, + "L": 1792252, + "total_rank": 57403754177, + "deficit": 1344189, + "maxchild": 528, + "deferred_slots": 11565, + "source": { + "repository": "https://github.com/Swapnil-jain/integer-mult-kappa", + "commit": "741e7aa078392553815df7926ee17ac5e25a8c38", + "sha256": { + "witness_23.json.gz": "b2486aa2bb222bacea6e52162a3920780e45dd8edc5d7cb03eabea336a1c6588", + "deferred_23.json.gz": "8c38e947ff9e021e308000dd82bb5e2194eb265d8b75194e22ce783d3e75317c" + } + }, + "child_multiplicities": { + "1": 239511811, + "2": 238288050, + "3": 53377940, + "4": 46970462, + "5": 23632224, + "6": 7409864, + "7": 4105178, + "8": 5755750, + "9": 2082696, + "10": 878416, + "11": 1388464, + "12": 1080310, + "13": 945714, + "14": 226688, + "15": 2451064, + "16": 1508892, + "17": 4771074, + "18": 2149994, + "19": 7367360, + "20": 8182020, + "21": 1466388, + "22": 88550, + "484": 6272882, + "506": 61280142, + "507": 545468, + "508": 173558, + "509": 293986, + "510": 580888, + "511": 14168, + "512": 322322, + "513": 17710, + "514": 1129898, + "515": 127512, + "516": 410872, + "517": 99176, + "518": 1186570, + "519": 340032, + "520": 322322, + "521": 106260, + "522": 1583274, + "523": 626934, + "524": 2854852, + "525": 13711082, + "526": 4629394, + "527": 5653032, + "528": 6233920 + } +} diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/certificate.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/certificate.py new file mode 100644 index 0000000000..5e00159bfe --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/certificate.py @@ -0,0 +1,114 @@ +#!/usr/bin/env python3 +"""Exact finite assembly for cyclic strips with deferred readouts. + +Built on Avi Eisenberg's PR110 (Anthropic Claude assistance), icekylinx's +PR104 stopped-product and copied-center interfaces, and Zhihao Chen's +assembly of the RaD interfaces. Integration for eumemic with OpenAI Codex +assistance. Apache-2.0. General transfer hypotheses remain inherited. +""" +import argparse +import json +import sys +from fractions import Fraction as Q +from pathlib import Path +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap_network import moment +from copied_centers_network import finite_bridge as copied_bridge +from structured_bulk_assembly import assembly, js +ATOM = Q(1, 1000) +OLD = Q(384599, 10**10) +BETA = Q(1, 10**6) +COARSE = Q(620523, 5000000000) +COMPLEX = Q(110616162, 10**12) +KGRID = 10**15 + +def profile(name): + p = json.loads((HERE / name).read_text()) + p['child_multiplicities'] = {int(t): c for t, c in p['child_multiplicities'].items()} + z = p['child_multiplicities'] + assert all(0 < t < p['m'] and c > 0 for t,c in z.items()) + assert sum(t*c for t,c in z.items()) == p['total_rank'] == p['W']*p['m']-p['N']+p['L'] + assert max(z) == p['maxchild'] + return p + +def contracts(p, a): + try: moment(p['m'],p['W'],p['child_multiplicities'],a,True) + except ValueError: return False + return True + +def exact(bit=None, phase=None): + bit = profile('bit-profile.json') if bit is None else bit + phase = profile('complex-profile.json') if phase is None else phase + assert (bit['h'], phase['h']) == (23,24) + bm = moment(bit['m'],bit['W'],bit['child_multiplicities'],COARSE,True) + cm = moment(phase['m'],phase['W'],phase['child_multiplicities'],COMPLEX,True) + assert not contracts(bit,COARSE+Q(1,10**10)) + assert not contracts(phase,COMPLEX+Q(1,10**12)) + ab = (1-ATOM)*COARSE+ATOM*OLD + assert 0 < OLD < COARSE < ATOM and ab < ATOM + a = min(ab,(1-BETA)*COMPLEX-Q(1,10**14)) + row = dict(h=phase['h'],v=phase['v'],c=phase['additions'],central_disjoint=24) + bridge = copied_bridge(bit,phase,[row,row]) + # Logical readouts are expanded into same-frame shears with |coefficient|<=1. + # Exact numerators over42 are split into signed42 chunks and a remainder. + # The independent audit counts every chunk and checks this guard covers it. + # Each row has <=c+R mixer operations and <=R leaf copies. There are + # <=R+q readouts, each containing <=h center coefficients and <=v direct + # coefficients; <=4*v*(h+1) scalar groups suffice per readout. A factor + # eight covers forward/inverse words, both reflected words, and copies. + h,v,R,q,c = (phase[k] for k in ('h','v','R','roots','additions')) + local = 8*(c+2*R+(R+q)*v*(h+1)+h*h+h+1) + G = phase['N'] + 2*v*local + m,W,s = (phase[k] for k in ('m','W','total_rank')) + E=64*(W+m+G+1)**3 + charge=2*G*W*W+8*s+4*W+4+32*m + B=s+E; C0=32*m*B*B + assert charge= s+E and 2*B+181: + mid=(lo+hi)//2 + if accepts(mid): lo=mid + else: hi=mid + k=Q(lo,KGRID) + assembled=assembly(a,COMPLEX,bridge,k,beta=BETA) + assert len(assembled['strict_constraints'])==47 and len(assembled['margins'])==7 + assert not accepts(lo+1) + return dict(status='Finite conditional cyclic/deferred witness',kappa=k, + complex_saving=COMPLEX,coarse_bit_saving=COARSE,actual_bit_saving=ab, + bit_parameter=a,complex_profile=phase,bit_profile=bit, + bit_moment_gap=bm['strict_gap'],complex_moment_gap=cm['strict_gap'], + finite_bridge=bridge,assembly=assembled, + next_grid_rejections=dict(bit='1e-10',complex='1e-12',kappa='1e-15')) + +def main(): + parser=argparse.ArgumentParser();parser.add_argument('--write',action='store_true');args=parser.parse_args() + assert not sys.flags.optimize + result=js(exact()); path=HERE/'certificate.json' + if args.write:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:assert result==json.loads(path.read_text()),'Frozen exact certificate mismatch' + print('PASS conditional kappa = %s = %.12e; 47 constraints, 7 margins; expanded scalar charge' % (result['kappa'],float(Q(result['kappa'])))) +if __name__=='__main__':main() diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/complex_deferred.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/complex_deferred.py new file mode 100644 index 0000000000..00ea2cafd8 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/complex_deferred.py @@ -0,0 +1,580 @@ +# R12 derived compiler by Chafik Boukhalfa with OpenAI Codex assistance. +# PR125 source by Joel Pulikkan; all inherited notices below remain attached. +# This variant replaces the single shrink pass; it is a new candidate. +#!/usr/bin/env python3 +"""Shrunk lifted frames and saturated deferred readouts on the PR117 complex DAG. + +After the role compile, a forward pass shrinks a lifted frame to the minimal +nondegenerate span of its label and predecessor frames when that merges +increments of the role chains holding it (16,031 frames). Section D rechecks +every chain. The shrink step was prepared by Joel Pulikkan with Anthropic +Claude assistance; everything else is PR114 (eumemic) unchanged. + + +PR117 credits its searched DAG to eumemic with Anthropic Claude assistance; +this experiment imports and replays that witness unchanged. PR110/PR114 +saturation and exact finite checks are applied to the resulting graph. +Logical readout macros are realized as signed numerator/42 chunks of magnitude +at most one. The literal audit expands and charges those same-frame shears, +checks exact reconstruction, and reverses the chunks under reflection. +Inherited Avi Eisenberg, Rohan Arun, icekylinx and Swapnil Jain credits retained. +This integration prepared with OpenAI Codex assistance. Apache-2.0. +""" +import array +import json +import random +import struct +import sys +import tempfile +from collections import Counter, defaultdict +from itertools import combinations +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(ROOT / 'scripts')) +sys.path.insert(0, str(HERE)) +import importlib.util +producer_path = HERE / 'producer.py' +spec = importlib.util.spec_from_file_location('replayed_producer_wrapper', producer_path) +producer = importlib.util.module_from_spec(spec); spec.loader.exec_module(producer) +build = producer.build + +P = (1 << 61) - 1 +SHRUNK = 16031 + + +def require(ok, msg): + if not ok: + raise SystemExit('FAIL: ' + msg) + + +def load(prefix): + def rd(fh, typ, cnt): + a = array.array(typ); a.fromfile(fh, cnt); return a + with open(str(prefix) + '.bin', 'rb') as f: + h, v, n, q = struct.unpack('<4I', f.read(16)) + flat = rd(f, 'I', 2 * n); core = rd(f, 'Q', n); cover = rd(f, 'Q', n) + roots = rd(f, 'I', q); kind = rd(f, 'I', q); active = rd(f, 'B', n) + with open(str(prefix) + '.labels', 'rb') as f: + ranks = rd(f, 'I', n); types = rd(f, 'B', n) + args = [(flat[2 * i], flat[2 * i + 1]) for i in range(n)] + return h, v, n, q, args, core, cover, roots, kind, active, ranks, types + + +# ---------------------------------------------------------------- F2 linear algebra on bit vectors +def dot(a, b): return bin(a & b).count('1') & 1 + + +def reduce(basis): + rows = []; piv = [] + for vec in basis: + for p, r in zip(piv, rows): + if vec >> p & 1: vec ^= r + if vec: + p = vec.bit_length() - 1 + for i in range(len(rows)): + if rows[i] >> p & 1: rows[i] ^= vec + rows.append(vec); piv.append(p) + return rows + + +def kernel(funcs, h): + K = reduce(funcs); piv = [r.bit_length() - 1 for r in K] + out = [] + for c in (i for i in range(h) if i not in piv): + vec = 1 << c + for r, p in zip(K, piv): + if r >> c & 1: vec |= 1 << p + out.append(vec) + return out + + +def restrict(basis, funcs): + B = reduce(basis) + for f in funcs: + if not B: break + vals = [dot(b, f) for b in B] + if not any(vals): continue + k = vals.index(1); pv = B[k] + B = [b ^ pv if val else b for b, val in zip(B, vals)]; B.pop(k) + return reduce(B) + + +def contains(A, B): + RB = reduce(B) + return len(reduce(RB + list(A))) == len(RB) + + +def cap(A, B): + A = reduce(A); B = reduce(B) + if not A or not B: return [] + ker = []; red = [] + for i, vec in enumerate(A + B): + tag = 1 << i + for rv, rt in red: + if vec >> (rv.bit_length() - 1) & 1: vec ^= rv; tag ^= rt + if vec: red.append((vec, tag)) + else: + comb_ = 0 + for k in range(len(A)): + if tag >> k & 1: comb_ ^= A[k] + ker.append(comb_) + return reduce(ker) + + +def nondeg(B): + B = reduce(B); k = len(B) + if not k: return True + M = [sum(dot(B[i], B[j]) << j for j in range(k)) for i in range(k)] + return len(reduce(M)) == k + + +def hopcroft_karp(left, adj): + """maximum bipartite matching; adj[x] = sorted list of right vertices.""" + INF = 1 << 60 + mate_l = {x: None for x in left}; mate_r = {} + while True: + dist = {}; queue = [] + for x in left: + if mate_l[x] is None: dist[x] = 0; queue.append(x) + else: dist[x] = INF + found = INF; head = 0 + while head < len(queue): + x = queue[head]; head += 1 + if dist[x] >= found: continue + for r in adj[x]: + y = mate_r.get(r) + if y is None: found = min(found, dist[x] + 1) + elif dist[y] == INF: dist[y] = dist[x] + 1; queue.append(y) + if found == INF: break + gained = 0 + for x0 in left: + if mate_l[x0] is not None: continue + stack = [(x0, iter(adj[x0]))]; path = [] + while stack: + x, it = stack[-1] + advanced = False + for r in it: + y = mate_r.get(r) + if (y is None and dist[x] + 1 == found) or (y is not None and dist[y] == dist[x] + 1): + path.append((x, r)) + if y is None: + for xx, rr in path: mate_l[xx] = rr; mate_r[rr] = xx + gained += 1; stack = []; break + stack.append((y, iter(adj[y]))); advanced = True; break + else: + dist[x] = INF; stack.pop() + if path: path.pop() + continue + if not advanced: break + if not gained: break + return mate_l + + +from functools import lru_cache +from fractions import Fraction + +def sat_basis(vectors): + piv = {} + for x in vectors: + for p in sorted(piv, reverse=True): + if x >> p & 1: + x ^= piv[p] + if x: + p = x.bit_length() - 1 + for q in piv: + if piv[q] >> p & 1: + piv[q] ^= x + piv[p] = x + return tuple((piv[p] for p in sorted(piv, reverse=True))) + +def sat_dot(a, b): + return (a & b).bit_count() & 1 + +@lru_cache(None) +def sat_contained(A, B): + for x in A: + for r in B: + if x >> r.bit_length() - 1 & 1: + x ^= r + if x: + return False + return True + +@lru_cache(None) +def sat_cap(A, B): + if not A or not B: + return () + red = {} + out = [] + for i, x in enumerate(A + B): + tag = 1 << i + for p in sorted(red, reverse=True): + if x >> p & 1: + r, t = red[p] + x ^= r + tag ^= t + if x: + red[x.bit_length() - 1] = (x, tag) + else: + y = 0 + for j, r in enumerate(A): + if tag >> j & 1: + y ^= r + if y: + out.append(y) + return sat_basis(out) + +@lru_cache(None) +def sat_nondeg(B): + return len(sat_basis((sum((sat_dot(a, b) << j for j, b in enumerate(B))) for a in B))) == len(B) + +@lru_cache(None) +def sat_nonsingular_part(B): + rows = list(B) + out = [] + while rows: + i = next((i for i, x in enumerate(rows) if sat_dot(x, x)), None) + if i is not None: + a = rows.pop(i) + out.append(a) + rows = [x ^ a if sat_dot(x, a) else x for x in rows] + continue + pair = next(((i, j) for i in range(len(rows)) for j in range(i + 1, len(rows)) if sat_dot(rows[i], rows[j])), None) + if pair is None: + break + i, j = pair + a, b = (rows[i], rows[j]) + out.extend((a, b)) + rows = [x ^ (a if sat_dot(x, b) else 0) ^ (b if sat_dot(x, a) else 0) for k, x in enumerate(rows) if k not in (i, j)] + return sat_basis(out) + +def saturated_placement(cand, reach): + # Each extracted block is orthogonal to previously selected blocks. + # A diagonal-one pivot contributes a nondegenerate line; when all + # remaining diagonals vanish, a dot-one pair contributes a hyperbolic + # plane. The residual radical is discarded, not counted as a frame. + cand = {s: sat_basis(B) for s, B in cand.items()} + order = sorted(cand, key=lambda s: (Fraction(-(1 << len(cand[s])), max(1, len(reach[s]))**2), -len(cand[s]), s)) + byT = defaultdict(list); placed = {} + for s in order: + X = cand[s]; changed = True + while changed and X: + changed = False + for t in sorted(reach[s]): + for w in byT[t]: + B = placed[w] + if (len(B) >= len(X) and not sat_contained(X, B)) or (len(B) < len(X) and not sat_contained(B, X)): + X = sat_cap(X, B); changed = True + if not X: break + if not X: break + if X and not sat_nondeg(X): + before = X; X = sat_nonsingular_part(X) + assert sat_contained(X, before) and sat_nondeg(X) + assert len(X) < len(before) + changed = True # Extraction can break containment of a smaller target frame. + if X: + assert sat_nondeg(X) and sat_contained(X, cand[s]) + placed[s] = X + for t in reach[s]: byT[t].append(s) + for t, ss in byT.items(): + ss.sort(key=lambda s: (len(placed[s]), s)) + assert all(sat_contained(placed[a], placed[b]) for a, b in zip(ss, ss[1:])) + return placed + +def main(): + with tempfile.TemporaryDirectory(prefix='deferred-stopped-') as work: + prefix = Path(work) / 'complex' + build(24, prefix, central_disjoint=24) + h, v, n, q, args, core, cover, roots, kind, active, ranks, types = load(prefix) + trip = list(combinations(range(h), 3)); require(len(trip) == v, 'triple count') + m = h * h; N = v * v; FULL = (1 << h) - 1 + tmask = [sum(1 << p for p in T) for T in trip] + tid = {T: i for i, T in enumerate(trip)} + + # ------------------------------------------------------------ uses and matching (inherited adjacency) + degree = [0] * n; uses = defaultdict(list); c_add = 0 + for x in range(1, n): + if active[x] and args[x][0]: + c_add += 1 + for pos, y in enumerate(args[x]): degree[y] += 1; uses[y].append(('gate', x, pos)) + for j, x in enumerate(roots): degree[x] += 1; uses[x].append(('root', j)) + def unode(u): return roots[u[1]] if u[0] == 'root' else u[1] + def before(x, u): + y = unode(u) + return (ranks[x], x) < (ranks[y], (n + u[1]) if u[0] == 'root' else y) + def incl(x, y): + tx, ty = types[x], types[y] + if tx == 1 and ty == 1: return not (core[y] & ~core[x]) and not (cover[x] & ~cover[y]) + if tx in (1, 2) and ty == 2: return not (cover[x] & ~cover[y]) + if tx == 1 and ty == 3: return bool(core[x] & core[y]) + if tx == 2 and ty == 3: return not (cover[x] & ~core[y]) + if tx == 3 and ty == 2: return cover[y] == FULL + if tx == 3 and ty == 3: return core[x] == core[y] + return False + left = []; adj = {} + for x in range(1, n): + if not (active[x] and args[x][0]): continue + rs = sorted({(y, k) for y in args[x] for k, u in enumerate(uses[y]) if before(x, u) and incl(x, unode(u))}) + if rs: left.append(x); adj[x] = rs + mate = hopcroft_karp(left, adj) + links = {x: r for x, r in mate.items() if r is not None} + R = c_add + q - len(links) + require((c_add,q,len(links),R)==(91770,8120,71185,28705),'selected PR117 graph') + print('PR117 graph matched', c_add, q, len(links), R, flush=True) + linked_use = {(y, k): x for x, (y, k) in links.items()} + + # ------------------------------------------------------------ root targets, read coefficients, root functionals + target = [None] * q + for j in range(v): target[j] = j + idx = v + # PR117 witness stores pair-star roots in natural excluded-point order. + for a, b in combinations(range(h), 2): + others = [i for i in range(h) if i not in (a, b)] + for i in others: target[idx] = tid[tuple(sorted((a, b, i)))]; idx += 1 + centre_of = {} + for j in range(q): + if kind[j]: + miss = FULL & ~cover[roots[j]]; require(bin(miss).count('1') == 1, 'centre cover') + centre_of[j] = miss.bit_length() - 1 + require(idx + len(centre_of) == q, 'root order') + rootfun = [(1 << centre_of[j]) if kind[j] else tmask[target[j]] for j in range(q)] + + # ------------------------------------------------------------ lifted binary frames, monotone + succ = defaultdict(set); droot = defaultdict(set) + for x in range(1, n): + if not active[x]: continue + for k, u in enumerate(uses[x]): + if (x, k) in linked_use: continue + (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1])) + for x, (y, k) in links.items(): + u = uses[y][k]; (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1])) + order_desc = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x), reverse=True) + K = {} + for x in order_desc: + rows = [rootfun[j] for j in droot[x]] + for t in succ[x]: rows += K[t] + K[x] = reduce(rows) + def envelope(x): + if not args[x][0]: return [tmask[x - 1]] + if types[x] == 2: return [1 << i for i in range(h) if cover[x] >> i & 1] + require(types[x] == 1, 'only ordinary and common-pair labels occur') + ks = [i for i in range(h) if (cover[x] & ~core[x]) >> i & 1] + require(len(ks) == ranks[x], 'common-pair support') + return [core[x] | (1 << k) for k in ks] + U = {} + for x in range(1, n): + if not active[x]: continue + if not args[x][0]: U[x] = envelope(x); continue + B = kernel(K[x], h) + require(contains(envelope(x), B), 'label outside lifted frame') + U[x] = B if nondeg(B) else envelope(x) + changed = True + while changed: + changed = False + for x in order_desc: + if args[x][0] and any(not contains(U[x], U[t]) for t in succ[x]): + env = envelope(x) + if len(reduce(U[x])) != len(reduce(env)) or not contains(U[x], env): U[x] = env; changed = True + dimU = {x: len(reduce(B)) for x, B in U.items()} + print('PR117 frames lifted',sum(dimU[x]>ranks[x] for x in U),flush=True) + + # ------------------------------------------------------------ explicit role compile + order = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x)) + holds = []; first_node = []; ops = []; edge_key = {}; role_root = {} + def new_role(node): holds.append([node]); first_node.append(node); return len(holds) - 1 + def serve(s, y, k): + u = uses[y][k] + if u[0] == 'gate': edge_key[(y, k)] = s + else: role_root[s] = u[1] + for x in order: + free = [k for k in range(len(uses[x])) if (x, k) not in linked_use] + if not args[x][0]: + for k in free: + s = new_role(x); ops.append(('src', s, x)); serve(s, x, k) + continue + a, b = args[x] + ka = next(k for k, u in enumerate(uses[a]) if u == ('gate', x, 0)) + kb = next(k for k, u in enumerate(uses[b]) if u == ('gate', x, 1)) + sa, sb = edge_key.pop((a, ka)), edge_key.pop((b, kb)) + if x in links and links[x][0] == a: sa, sb = sb, sa + piv, oth = sa, sb + ops.append(('add', piv, oth, x)); holds[piv].append(x); holds[oth].append(x) + if x in links: serve(oth, *links[x]) + require(free, 'every use linked at node %d' % x) + serve(piv, x, free[0]) + for k in free[1:]: + f = new_role(x); ops.append(('copy', piv, f, x)); serve(f, x, k) + require(not edge_key and len(holds) == R, 'compile') + Rr = R + + # R12 logical-frame nondegenerate completion and endpoint descent. + from r12_frame_opt import optimize as r12_optimize + U, dimU, frame_optimization = r12_optimize(U, order, args, succ, holds, role_root, envelope, h, globals()) + shrunk = frame_optimization['shrunk_frames'] + + # ------------------------------------------------------------ B. the word computes every root value + rng = random.Random(20261008) + xs = [rng.randrange(P) for _ in range(v)] + val = [0] * n + for i in range(v): val[i + 1] = xs[i] + for x in order: + if args[x][0]: val[x] = (val[args[x][0]] + val[args[x][1]]) % P + leaf_of = {s: first_node[s] for s in range(Rr) if not args[first_node[s]][0]} + a_ = [0] * Rr + for s, leaf in leaf_of.items(): a_[s] = xs[leaf - 1] + for o in ops: + if o[0] == 'add': a_[o[1]] = (a_[o[1]] + a_[o[2]]) % P + elif o[0] == 'copy': a_[o[2]] = (a_[o[2]] + a_[o[1]]) % P + require(all(a_[s] == val[roots[j]] for s, j in role_root.items()), 'root values') + + # ------------------------------------------------------------ phase one and garbage reach + def touch(o): return [o[1], o[2]] if o[0] in ('add', 'copy') else [] + prev = {}; pred = defaultdict(list); last = {} + for i, o in enumerate(ops): + for s in touch(o): + if s in prev: pred[i].append(prev[s]) + prev[s] = i; last[s] = i + centre_roles = [s for s, j in role_root.items() if kind[j]] + Anc = set(); st = [last[s] for s in centre_roles] + while st: + i = st.pop() + if i not in Anc: Anc.add(i); st.extend(pred[i]) + touched = set(centre_roles) + for i in Anc: touched.update(touch(ops[i])) + require(all(last[s] in Anc for s in centre_roles), 'centres complete in phase one') + reach = [set() for _ in range(Rr)]; reach_all = [False] * Rr + for s, j in role_root.items(): + if kind[j]: reach_all[s] = True + else: reach[s].add(target[j]) + for o in reversed(ops): + if o[0] == 'add': reach[o[2]] |= reach[o[1]]; reach_all[o[2]] = reach_all[o[2]] or reach_all[o[1]] + elif o[0] == 'copy': reach[o[1]] |= reach[o[2]]; reach_all[o[1]] = reach_all[o[1]] or reach_all[o[2]] + + # ------------------------------------------------------------ deferral frames, insertion nesting + def F0(s): return U[first_node[s]] + from r12_defer_opt import repair_candidate, place as r12_place + cand = {} + for s in range(Rr): + if s in touched or reach_all[s]: continue + S_ = restrict(F0(s), [tmask[t] for t in reach[s]]) + S_ = repair_candidate(S_, globals()) if S_ else [] + if S_: cand[s] = S_ + print('PR117 candidates',len(cand),flush=True) + placed, deferral_optimization = r12_place(cand, reach, F0, h, m, globals()) + print('PR117 placed',len(placed),flush=True) + deferred = sorted(placed, key=lambda s: (len(placed[s]), s)); dset = set(deferred) + + # ------------------------------------------------------------ C. replay with arbitrary scratch and data + inv = lambda a: pow(a % P, P - 2, P); HALF = inv(2); I21 = inv(21) + cvec = [None] * Rr; dpart = [dict() for _ in range(Rr)] + for s, j in role_root.items(): + if kind[j]: c = [0] * h; c[centre_of[j]] = 1; cvec[s] = c + else: dpart[s][target[j]] = (P - HALF) if j >= v else HALF + seed_c = {s: (None if cvec[s] is None else list(cvec[s])) for s in role_root} + seed_d = {s: dict(dpart[s]) for s in role_root} + def addc(dst, src): + if cvec[src] is not None: + cvec[dst] = list(cvec[src]) if cvec[dst] is None else [(p + q_) % P for p, q_ in zip(cvec[dst], cvec[src])] + for t, c in dpart[src].items(): dpart[dst][t] = (dpart[dst].get(t, 0) + c) % P + for o in reversed(ops): + if o[0] == 'add': addc(o[2], o[1]) + elif o[0] == 'copy': addc(o[1], o[2]) + scatter = [[(I21 - (HALF if i in trip[t] else 0)) % P for t in range(v)] for i in range(h)] + def readout(y, s, value, sign, seed=False): + # Logical readout macro: the literal audit combines its exact rational + # target coefficients and expands each numerator/42 into bounded shears. + cv = seed_c[s] if seed else cvec[s]; dp = seed_d[s] if seed else dpart[s] + if cv is not None: + for i, ci in enumerate(cv): + if ci: + f = sign * ci * value % P; row = scatter[i] + for t in range(v): y[t] = (y[t] + f * row[t]) % P + for t, c in dp.items(): y[t] = (y[t] + sign * c * value) % P + phase1 = sorted(Anc); rest = [i for i in range(len(ops)) if i not in Anc] + def replay(seed): + rng = random.Random(seed) + x = [rng.randrange(P) for _ in range(v)]; z = [rng.randrange(P) for _ in range(Rr)] + y0 = [rng.randrange(P) for _ in range(v)]; a = list(z); y = list(y0) + for s in range(Rr): + if s not in dset: readout(y, s, a[s], -1) + for s, leaf in leaf_of.items(): + if s not in dset: a[s] = (a[s] + x[leaf - 1]) % P + def run(i, sign=1): + o = ops[i] + if o[0] == 'add': a[o[1]] = (a[o[1]] + sign * a[o[2]]) % P + elif o[0] == 'copy': a[o[2]] = (a[o[2]] + sign * a[o[1]]) % P + for i in phase1: run(i) + for s in centre_roles: readout(y, s, a[s], +1, True) + for s in deferred: readout(y, s, a[s], -1) + for s in deferred: + if s in leaf_of: a[s] = (a[s] + x[leaf_of[s] - 1]) % P + for i in rest: run(i) + for s, j in role_root.items(): + if not kind[j]: readout(y, s, a[s], +1, True) + for i in reversed(range(len(ops))): run(i, -1) + for s, leaf in leaf_of.items(): a[s] = (a[s] - x[leaf - 1]) % P + return a == z, all((y[t] - y0[t] - x[t]) % P == 0 for t in range(v)) + rep = [replay(seed) for seed in (1, 2)] + require(all(r == (True, True) for r in rep), 'replay %s' % rep) + + # ------------------------------------------------------------ D. exact F2 frame facts + root_frame = {} + for s, j in role_root.items(): + root_frame[s] = [1 << i for i in range(h) if i != centre_of[j]] if kind[j] else kernel([tmask[target[j]]], h) + FULLB = [1 << i for i in range(h)] + chain_dims = [] + for s in range(Rr): + seq = [placed.get(s, []), F0(s)] + [U[x] for x in holds[s][1:]] + if s in root_frame: seq.append(root_frame[s]) + seq.append(FULLB) + require(all(contains(A, B) for A, B in zip(seq, seq[1:])), 'role chain nesting %d' % s) + require(all(nondeg(B) for B in seq[1:-1] if B), 'degenerate frame on role %d' % s) + chain_dims.append([len(reduce(B)) for B in seq]) + for s, X in placed.items(): + require(contains(X, F0(s)) and nondeg(X), 'deferral frame %d' % s) + require(all(not any(dot(xv, tmask[t]) for xv in X) for t in reach[s]), 'target frame %d' % s) + byT2 = defaultdict(list) + for s in deferred: + for t in reach[s]: byT2[t].append(s) + for t, ss in byT2.items(): + ss.sort(key=lambda s: (len(placed[s]), s)) + require(all(contains(placed[p], placed[q_]) for p, q_ in zip(ss, ss[1:])), 'target chain %d' % t) + + # ------------------------------------------------------------ E. one-child histogram + z = Counter() + for s in range(Rr): + ds = chain_dims[s] + for a, b in zip(ds[:-1], ds[1:-1]): + if b > a: z[b - a] += 2 * v + lastd = ds[-2] + if s in role_root and kind[role_root[s]]: z[h - 1] += 2 * v # copied centre transform + z[h - lastd] += 2 * v # final growth to F + z[m - h + ds[0]] += 2 * v # exterior, gauged by sigma + levels = defaultdict(set) + for s in deferred: + for t in reach[s]: levels[t].add(len(placed[s])) + for t in range(v): + ds = sorted(levels[t] | {0, h - 1}) + for a, b in zip(ds, ds[1:]): z[b - a] += 2 * v # target fronts + z[h - 1] += 2 * N # data-wire fronts + z[(h - 1) ** 2] += 2 * N # data macros + z[1] += N # endpoint copies + z.pop(0, None) + W = 2 * N + 2 * v * R; L = 2 * v * h * (h - 1); s_ = W * m - N + L + require(sum(t * c for t, c in z.items()) == s_, 'complex rank mass') + require(all(0 < t < m for t in z), 'children below m') + out = dict(frame_optimization=frame_optimization, deferral_optimization=deferral_optimization, h=h, v=v, additions=c_add, roots=q, links=len(links), R=R, m=m, N=N, W=W, L=L, total_rank=s_, + deficit=N - L, maxchild=max(z), phase_one_ops=len(Anc), phase_one_roles=len(touched), + deferred_roles=len(deferred), + deferred_dims=dict(sorted(Counter(len(X) for X in placed.values()).items())), + lifted_additions=sum(1 for x in U if args[x][0] and dimU[x] > ranks[x]), + replay=dict(seeds=[1, 2], scratch_restored=True, y_plus_x=True, field='Z/(2^61-1)'), + child_multiplicities=dict(sorted(z.items()))) + (HERE / 'complex-profile.json').write_text(json.dumps(out, indent=1) + '\n') + print('PASS complex: R=%d, deferred roles %d, maxchild %d, rank mass %d' % (R, len(deferred), max(z), s_)) + + +if __name__ == '__main__': + main() diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/inputs/complex-dag.json.gz b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/inputs/complex-dag.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..a5b0598e4c328acef11baaa32852acdbfc97eeef GIT binary patch literal 362071 zcmXV0V{j-<(~WK8#wr$(C%^TacZGL&`{r2D1O!rK6pFVwhYw;o>AOLWdS(^|R$2>3TN?o7?x|^Fo+uMny6zega^m>;%?R|s5L3Na zeOF)}SX-}$We#N{Z{S7j|}!mEb`x3(<2kK7T*kD0Pu&eXfoDW$R8 zmnJjm2#kJ`pQeYKri$E?g%b*^9IUsW87|qkGr1(Gnb8Mx>hts_=bVA*)CY#Q z!cz%VvTAnJ9L>)=&)K!Sy1b5s+J&N*Ci1rf5>LF+?310h=w%Hxw|p7_aI>qoBd=2L 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g+=weight[d-a]+weight[b-d]-weight[b-a] + return g + if mode=='gain_priority':order=sorted(cand,key=lambda s:(-gain(s,len(cand[s])), -len(cand[s]),s)) + else:order=sorted(cand,key=lambda s:(Fraction(-(1<=len(X) and not inside(X,B)) or (len(B)0: + assert nondeg(best) and inside(lower,best) + assert inside(best,original[x]) and all(inside(best,frames[t]) for t in succ[x]) + frames[x]=best;counts['moves']+=1;counts['integer_score_gain']+=gain + counts['shrink' if len(best)>p&1:x^=piv[p] + if x: + p=x.bit_length()-1 + for q in piv: + if piv[q]>>p&1:piv[q]^=x + piv[p]=x + return tuple(piv[p] for p in sorted(piv,reverse=True)) + + +def dot(a,b):return (a&b).bit_count()&1 + + +@lru_cache(None) +def contained(A,B):return len(basis(A+B))==len(B) + + +@lru_cache(None) +def complement(A,h): + A=basis(A);piv={x.bit_length()-1:x for x in A};result=[] + for j in range(h): + if j not in piv: + x=1<>j&1:x|=1<
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    =0 else -1 + parts=(sign*42,)*q+((sign*r,) if r else ()) + check_chunks(numerator,parts) + return parts + +def reverse_row(row): + if row[0]=='old':return (row[0],row[1],row[3],row[2]) + return row + + +def check_reflection(forward,backward,h,v): + def bank(s):return s+v if s1) + readcount+=len(parts);maxchunk=max(maxchunk,max(map(abs,parts))) + for part in parts: + reached.append(t);records.append(struct.pack('len(old):hist[len(F)-len(old)]+=1 + current[s]=F + for event in events: + k,a,b,c,F,*rest=event + assert c in (-1,1) + promote(a,F) + if k=='gate':promote(b,F);scalar+=1 + elif k=='read': + for t in b:promote(t,F) + scalar+=len(b) + else: + assert k=='centre';G=rest[0] + assert contained(G,F) or contained(F,G) + assert nondeg(G);copies[abs(len(F)-len(G))]+=1 + for t in b:promote(t,G) + scalar+=len(b)+2 # temporary copy and erasure + digest.update(repr(event).encode()+b'\n') + # Each literal role cleanup reaches full space; any unused final + # endpoint is still represented explicitly in the expected chain. + for s,F in enumerate(expected):promote(s,F) + assert current==expected + return hist,copies,scalar,digest.hexdigest() + start=tm+[ZERO]*v+[sigma.get(s,ZERO) for s in range(R)] + finish=[FULL]*v+[complement(T,h) for T in tm]+[FULL]*R + H,C,scalar,digest=framescan(word,start,finish) + revstart=[None]*len(start);revfinish=[None]*len(start) + for s in range(len(start)): + revstart[swap(s)]=complement(finish[s],h);revfinish[swap(s)]=complement(start[s],h) + HR,CR,scalarR,reverse_digest=framescan(reverse,revstart,revfinish) + assert (H,C,scalar)==(HR,CR,scalarR) + z=Counter({r:2*v*n for r,n in (H+C).items()}) + for s in range(R):z[h*h-h+len(sigma.get(s,ZERO))]+=2*v + z[(h-1)**2]+=2*v*v;z[1]+=v*v + z.pop(0,None) + assert dict(sorted(z.items()))=={int(r):n for r,n in d['out']['child_multiplicities'].items()},'Literal reflected child histogram' + assert sum(r*n for r,n in z.items())==d['out']['total_rank'] + G=v*v+2*v*scalar + safe=8*(d['c_add']+2*R+(R+q)*v*(h+1)+h*h+h+1) if 'c_add' in d else 8*(d['out']['additions']+2*R+(R+q)*v*(h+1)+h*h+h+1) + assert safe>=scalar + return dict(h=h,v=v,R=R,exact_fresh_source_map=True,exact_integer_old_readout_transpose=True, + exact_arbitrary_dirty_cancellation_by_dependency_cut=True, + reflected_word_rule='Reverse literal order including each bounded readout chunk, negate every shear, swap X/Y ports, complement every frame; auxiliary bank is separate.', + reflected_scalar_map='X becomes X-Y; Y unchanged; all auxiliary coordinates restored.', + two_stage_scalar_map='(X,Y) becomes (-Y,X+Y) before inherited endpoint correction.', + literal_frame_incidences_both_directions=True,all_frames_nondegenerate=True, + reflected_residual_rank_histogram_equal=True,child_multiplicities=dict(sorted(z.items())), + word_blocks=len(word),expanded_scalar_operations_per_stage=scalar, + expanded_old_readout_additions=readcount,largest_readout_numerator_over_42=maxcoef, + unsplit_old_readout_macros=unsplit_readcount,split_readout_macros=split_macros, + largest_bounded_chunk_numerator_over_42=maxchunk, + bounded_readout_chunks_sha256=chunk_digest.hexdigest(), + scalar_readout_normalization='Each exact numerator n/42 becomes signed42 chunks plus a signed remainder. Exact reconstruction and chunk magnitude<=1 checked; every same-frame shear is charged; reflection reverses chunk order.', + exact_chunk_reconstruction=True,bounded_chunk_coefficients=True, + old_readout_coefficients_over_42_sha256=coefficient_digest.hexdigest(), + literal_global_scalar_groups=G,conservative_local_G=safe, + forward_incidence_sha256=digest,reflected_incidence_sha256=reverse_digest, + rejected_controls=rejected, + scope='Exact finite source coefficients, dirty cancellation algebra and literal reflected frame/charge ledger. Copied-centre transforms, endpoint correction and residual-to-child/all-size transfer retain their stated inherited contracts.') + + +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--source',type=Path);ap.add_argument('--state',type=Path) + ap.add_argument('--output',type=Path);ap.add_argument('--check',type=Path);a=ap.parse_args() + assert bool(a.source)!=bool(a.state) + d=capture(a.source) if a.source else pickle.loads(a.state.read_bytes()) + result=audit(d);source=Path(d['source']) + result['source_sha256']=sha256(source.read_bytes()).hexdigest() + result['audit_sha256']=sha256(Path(__file__).read_bytes()).hexdigest() + result=json.loads(json.dumps(result));encoded=json.dumps(result,indent=2,sort_keys=True)+'\n' + if a.check:assert result==json.loads(a.check.read_text()) + if a.output:a.output.write_text(encoded) + else:print(encoded,end='') + print('PASS exact scalar and literal complement reflection audit',file=sys.stderr) + + +if __name__=='__main__':main() diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/replayed_producer.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/replayed_producer.py new file mode 100644 index 0000000000..673fbbba70 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/replayed_producer.py @@ -0,0 +1,179 @@ +"""Replayed h=24 complex producer with all centers disjoint (rational divisor 21). + +Copyright 2026 eumemic, Apache-2.0. AI-assisted (Claude). The DAG was found by an +automated search over producers of the retained paired-triple, pair-star and +center-disjoint interfaces. The checks below are adapted from +stopped_product/complex.py (copyright 2026 icekylinx, Apache-2.0, PR #104). + +The witness complex-dag.json.gz lists the ordinary +additions after the v triple inputs and the retained roots: the disjoint sums +D[t], the pair stars P(a,b,i) and the center-disjoint sums A_i. Every support, +core, cover, type and rank is recomputed here from the operands; nothing is +read from the witness except the operand pairs and the root indices. +""" +import gzip, json, struct, sys, array +from fractions import Fraction +from itertools import combinations +from pathlib import Path + + +def write_array(f, values): + """Little-endian array writer, as partial_swap.binary.write_array.""" + if sys.byteorder != 'little' and values.itemsize > 1: + values = array.array(values.typecode, values) + values.byteswap() + values.tofile(f) + + +def build(witness, prefix): + w = json.loads(gzip.decompress(Path(witness).read_bytes())) + h, v, d = w['h'], w['v'], w['central_disjoint'] + assert (h, d, w['center_denominator']) == (24, 24, 21) + triples = list(combinations(range(h), 3)) + assert v == len(triples) + args = [(0, 0)]; support = [0]; core = [0]; cover = [0]; types = [0]; ranks = [0] + for j, t in enumerate(triples): + mask = sum(1 << a for a in t) + args.append((0, 0)); support.append(1 << j); core.append(mask); cover.append(mask) + types.append(1); ranks.append(1) + flat = w['args'] + assert len(flat) % 2 == 0 + for k in range(0, len(flat), 2): + a, b, x = flat[k], flat[k+1], len(args) + assert 0 < a < x and 0 < b < x, 'Operands must precede their sum' + assert not support[a] & support[b], 'Ordinary additions must be cancellation-free' + args.append((a, b)); support.append(support[a] | support[b]) + core.append(core[a] & core[b]); cover.append(cover[a] | cover[b]) + if core[x].bit_count() >= 2: + types.append(1); ranks.append(support[x].bit_count()) + else: + types.append(2); ranks.append(cover[x].bit_count()) + n = len(args) + point_masks = [sum(1 << j for j, t in enumerate(triples) if a in t) for a in range(h)] + full_support = (1 << v) - 1 + roots, kind = [], [] + assert len(w['D']) == v + for t, node in zip(triples, w['D']): + assert 0 < node < n + assert support[node] == full_support & ~(point_masks[t[0]]|point_masks[t[1]]|point_masks[t[2]]) + target_mask = sum(1 << a for a in t) + if types[node] == 2: + assert not cover[node] & target_mask + else: + assert types[node] == 1 + assert not support[node] & (point_masks[t[0]]^point_masks[t[1]]^point_masks[t[2]]) + roots.append(node); kind.append(0) + stars = [(a, b, i) for a, b in combinations(range(h), 2) for i in range(h) if i not in (a, b)] + assert len(w['P']) == len(stars) + pair_outputs = {} + for (a, b, i), node in zip(stars, w['P']): + assert 0 < node < n + assert support[node] == point_masks[a] & point_masks[b] & ~point_masks[i] + assert types[node] == 1 + assert not support[node] & (point_masks[a]^point_masks[b]^point_masks[i]) + pair_outputs[a, b, i] = node + roots.append(node); kind.append(0) + assert len(w['A']) == d + for i, node in enumerate(w['A']): + assert 0 < node < n + assert support[node] == full_support & ~point_masks[i] + assert types[node] == 2 and cover[node] == ((1 << h)-1) ^ (1 << i) + assert ranks[node] == h-1 + roots.append(node); kind.append(1) + # Every A_i avoids i, so sum A_i = (h-3)T. The decoder is T=sum A_i/21 + # and the scatter is T-(1/2)sum_{i in target} A_i. + decoder = Fraction(1, h-3) + assert decoder == Fraction(1, 21) + scatter_coefficients = [decoder, decoder-Fraction(1, 2)] + for coefficient in scatter_coefficients: + odd_denominator = coefficient.denominator + while odd_denominator % 2 == 0: + odd_denominator //= 2 + assert 21 % odd_denominator == 0 and abs(coefficient) <= 1 + for source in triples: + assert sum(i not in source for i in range(h))*decoder == 1 + Dset = set(range(d)) + for triple in triples: + k = len(Dset.intersection(triple)) + assert 2*(3-k)-2*(d-k) == 2*(3-d) + patterns = {} + for target in triples: + chosen = len(Dset.intersection(target)) + if chosen not in patterns: + patterns[chosen] = target + for chosen, target in patterns.items(): + target_set = set(target) + for source in triples: + k = len(Dset.intersection(source)) + total_coefficient = Fraction(2*(3-k)-2*(d-k), 2*(3-d)) + scalar = Fraction(len((target_set-Dset).intersection(source)), 2) + scalar -= Fraction(len((target_set & Dset)-set(source)), 2) + scalar += Fraction(chosen-1, 2)*total_coefficient + assert scalar == Fraction(len(target_set.intersection(source))-1, 2) + for j, t in enumerate(triples): + masks = [point_masks[a] for a in t] + two = (masks[0]&masks[1]&~masks[2]) | (masks[0]&masks[2]&~masks[1]) | (masks[1]&masks[2]&~masks[0]) + actual = 0 + for a, b in combinations(t, 2): + excluded = next(i for i in t if i not in (a, b)) + actual |= support[pair_outputs[a, b, excluded]] + assert actual == two + assert masks[0]&masks[1]&masks[2] == 1 << j + assert [((k-1)+(k == 0)-(k == 2)) for k in range(4)] == [0, 0, 0, 2] + + def contained(x, y): + tx, ty = types[x], types[y] + if tx == 1 and ty == 1: return not(core[y]&~core[x] or cover[x]&~cover[y]) + if tx in (1, 2) and ty == 2: return not cover[x]&~cover[y] + return False + active = [0]*n; stack = list(roots) + while stack: + x = stack.pop() + if not x or active[x]: continue + active[x] = 1 + if args[x][0]: stack.extend(args[x]) + degree = [0]*n + for x in range(1, n): + if active[x]: + if types[x] == 1: + assert core[x].bit_count() >= 2 and ranks[x] == support[x].bit_count() + else: + assert types[x] == 2 and ranks[x] == cover[x].bit_count() + if active[x] and args[x][0]: + for y in args[x]: + assert y < x and contained(y, x), 'Binary frame nesting failed' + degree[y] += 1 + for x in roots: degree[x] += 1 + H = [0]*(h+1); c = 0; loss = 0 + for x in range(1, n): + if not active[x]: continue + r = ranks[x] + if args[x][0]: + c += 1; H[r] += degree[x]-1; H[h-r] += 1 + for y in args[x]: + assert r >= ranks[y] + H[r-ranks[y]] += 1 + else: H[1] += degree[x] + for x, k in zip(roots, kind): + r = ranks[x] + if k: H[r] += 1; H[h] += 1; loss += r + else: H[h-1-r] += 1; H[1] += 1 + q = len(roots); R = c+q + result = dict(h=h, v=v, c=c, q=q, R=R, loss=loss, central_disjoint=d, histogram=H, + rank_sum=sum(r*m for r, m in enumerate(H))) + assert loss == h*(h-1) and result['rank_sum'] == h*R+2*loss + result['center_denominator'] = 21 + result['scalar_validation'] = dict(ordinary_supports_exact=True, centers_exact=True, + center_decoder='sum A_i / 21', scatter_coefficients=list(map(str, scatter_coefficients)), + rational_scalar_identity_exact=True, mixed_center_scatter_exact=True, binary_frames_nested=True, + binary_frames_nondegenerate=True) + with open(str(prefix)+'.bin', 'wb') as f: + f.write(struct.pack('<4I', h, v, n, q)) + write_array(f, array.array('I', (a for pair in args for a in pair))) + write_array(f, array.array('Q', core)); write_array(f, array.array('Q', cover)) + write_array(f, array.array('I', roots)); write_array(f, array.array('I', kind)) + write_array(f, array.array('B', active)) + with open(str(prefix)+'.labels', 'wb') as f: + write_array(f, array.array('I', ranks)); write_array(f, array.array('B', types)) + Path(str(prefix)+'.json').write_text(json.dumps(result, indent=2)+'\n') + return result diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/screen.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/screen.py new file mode 100644 index 0000000000..7705719dd6 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/screen.py @@ -0,0 +1,528 @@ +# R12 derived compiler by Chafik Boukhalfa with OpenAI Codex assistance. +# PR125 source by Joel Pulikkan; all inherited notices below remain attached. +# This variant replaces the single shrink pass; it is a new candidate. +#!/usr/bin/env python3 +"""Shrunk lifted frames and saturated deferred readouts on the PR117 complex DAG. + +After the role compile, a forward pass shrinks a lifted frame to the minimal +nondegenerate span of its label and predecessor frames when that merges +increments of the role chains holding it (16,031 frames). Section D rechecks +every chain. The shrink step was prepared by Joel Pulikkan with Anthropic +Claude assistance; everything else is PR114 (eumemic) unchanged. + + +PR117 credits its searched DAG to eumemic with Anthropic Claude assistance; +this experiment imports and replays that witness unchanged. PR110/PR114 +saturation and exact finite checks are applied to the resulting graph. +Logical readout macros are realized as signed numerator/42 chunks of magnitude +at most one. The literal audit expands and charges those same-frame shears, +checks exact reconstruction, and reverses the chunks under reflection. +Inherited Avi Eisenberg, Rohan Arun, icekylinx and Swapnil Jain credits retained. +This integration prepared with OpenAI Codex assistance. Apache-2.0. +""" +import array +import json +import random +import struct +import sys +import tempfile +from collections import Counter, defaultdict +from itertools import combinations +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(ROOT / 'scripts')) +sys.path.insert(0, str(HERE)) +import importlib.util +producer_path = HERE / 'producer.py' +spec = importlib.util.spec_from_file_location('replayed_producer_wrapper', producer_path) +producer = importlib.util.module_from_spec(spec); spec.loader.exec_module(producer) +build = producer.build + +P = (1 << 61) - 1 +SHRUNK = 16031 + + +def require(ok, msg): + if not ok: + raise SystemExit('FAIL: ' + msg) + + +def load(prefix): + def rd(fh, typ, cnt): + a = array.array(typ); a.fromfile(fh, cnt); return a + with open(str(prefix) + '.bin', 'rb') as f: + h, v, n, q = struct.unpack('<4I', f.read(16)) + flat = rd(f, 'I', 2 * n); core = rd(f, 'Q', n); cover = rd(f, 'Q', n) + roots = rd(f, 'I', q); kind = rd(f, 'I', q); active = rd(f, 'B', n) + with open(str(prefix) + '.labels', 'rb') as f: + ranks = rd(f, 'I', n); types = rd(f, 'B', n) + args = [(flat[2 * i], flat[2 * i + 1]) for i in range(n)] + return h, v, n, q, args, core, cover, roots, kind, active, ranks, types + + +# ---------------------------------------------------------------- F2 linear algebra on bit vectors +def dot(a, b): return bin(a & b).count('1') & 1 + + +def reduce(basis): + rows = []; piv = [] + for vec in basis: + for p, r in zip(piv, rows): + if vec >> p & 1: vec ^= r + if vec: + p = vec.bit_length() - 1 + for i in range(len(rows)): + if rows[i] >> p & 1: rows[i] ^= vec + rows.append(vec); piv.append(p) + return rows + + +def kernel(funcs, h): + K = reduce(funcs); piv = [r.bit_length() - 1 for r in K] + out = [] + for c in (i for i in range(h) if i not in piv): + vec = 1 << c + for r, p in zip(K, piv): + if r >> c & 1: vec |= 1 << p + out.append(vec) + return out + + +def restrict(basis, funcs): + B = reduce(basis) + for f in funcs: + if not B: break + vals = [dot(b, f) for b in B] + if not any(vals): continue + k = vals.index(1); pv = B[k] + B = [b ^ pv if val else b for b, val in zip(B, vals)]; B.pop(k) + return reduce(B) + + +def contains(A, B): + RB = reduce(B) + return len(reduce(RB + list(A))) == len(RB) + + +def cap(A, B): + A = reduce(A); B = reduce(B) + if not A or not B: return [] + ker = []; red = [] + for i, vec in enumerate(A + B): + tag = 1 << i + for rv, rt in red: + if vec >> (rv.bit_length() - 1) & 1: vec ^= rv; tag ^= rt + if vec: red.append((vec, tag)) + else: + comb_ = 0 + for k in range(len(A)): + if tag >> k & 1: comb_ ^= A[k] + ker.append(comb_) + return reduce(ker) + + +def nondeg(B): + B = reduce(B); k = len(B) + if not k: return True + M = [sum(dot(B[i], B[j]) << j for j in range(k)) for i in range(k)] + return len(reduce(M)) == k + + +def hopcroft_karp(left, adj): + """maximum bipartite matching; adj[x] = sorted list of right vertices.""" + INF = 1 << 60 + mate_l = {x: None for x in left}; mate_r = {} + while True: + dist = {}; queue = [] + for x in left: + if mate_l[x] is None: dist[x] = 0; queue.append(x) + else: dist[x] = INF + found = INF; head = 0 + while head < len(queue): + x = queue[head]; head += 1 + if dist[x] >= found: continue + for r in adj[x]: + y = mate_r.get(r) + if y is None: found = min(found, dist[x] + 1) + elif dist[y] == INF: dist[y] = dist[x] + 1; queue.append(y) + if found == INF: break + gained = 0 + for x0 in left: + if mate_l[x0] is not None: continue + stack = [(x0, iter(adj[x0]))]; path = [] + while stack: + x, it = stack[-1] + advanced = False + for r in it: + y = mate_r.get(r) + if (y is None and dist[x] + 1 == found) or (y is not None and dist[y] == dist[x] + 1): + path.append((x, r)) + if y is None: + for xx, rr in path: mate_l[xx] = rr; mate_r[rr] = xx + gained += 1; stack = []; break + stack.append((y, iter(adj[y]))); advanced = True; break + else: + dist[x] = INF; stack.pop() + if path: path.pop() + continue + if not advanced: break + if not gained: break + return mate_l + + +from functools import lru_cache +from fractions import Fraction + +def sat_basis(vectors): + piv = {} + for x in vectors: + for p in sorted(piv, reverse=True): + if x >> p & 1: + x ^= piv[p] + if x: + p = x.bit_length() - 1 + for q in piv: + if piv[q] >> p & 1: + piv[q] ^= x + piv[p] = x + return tuple((piv[p] for p in sorted(piv, reverse=True))) + +def sat_dot(a, b): + return (a & b).bit_count() & 1 + +@lru_cache(None) +def sat_contained(A, B): + for x in A: + for r in B: + if x >> r.bit_length() - 1 & 1: + x ^= r + if x: + return False + return True + +@lru_cache(None) +def sat_cap(A, B): + if not A or not B: + return () + red = {} + out = [] + for i, x in enumerate(A + B): + tag = 1 << i + for p in sorted(red, reverse=True): + if x >> p & 1: + r, t = red[p] + x ^= r + tag ^= t + if x: + red[x.bit_length() - 1] = (x, tag) + else: + y = 0 + for j, r in enumerate(A): + if tag >> j & 1: + y ^= r + if y: + out.append(y) + return sat_basis(out) + +@lru_cache(None) +def sat_nondeg(B): + return len(sat_basis((sum((sat_dot(a, b) << j for j, b in enumerate(B))) for a in B))) == len(B) + +@lru_cache(None) +def sat_nonsingular_part(B): + rows = list(B) + out = [] + while rows: + i = next((i for i, x in enumerate(rows) if sat_dot(x, x)), None) + if i is not None: + a = rows.pop(i) + out.append(a) + rows = [x ^ a if sat_dot(x, a) else x for x in rows] + continue + pair = next(((i, j) for i in range(len(rows)) for j in range(i + 1, len(rows)) if sat_dot(rows[i], rows[j])), None) + if pair is None: + break + i, j = pair + a, b = (rows[i], rows[j]) + out.extend((a, b)) + rows = [x ^ (a if sat_dot(x, b) else 0) ^ (b if sat_dot(x, a) else 0) for k, x in enumerate(rows) if k not in (i, j)] + return sat_basis(out) + +def saturated_placement(cand, reach): + # Each extracted block is orthogonal to previously selected blocks. + # A diagonal-one pivot contributes a nondegenerate line; when all + # remaining diagonals vanish, a dot-one pair contributes a hyperbolic + # plane. The residual radical is discarded, not counted as a frame. + cand = {s: sat_basis(B) for s, B in cand.items()} + order = sorted(cand, key=lambda s: (Fraction(-(1 << len(cand[s])), max(1, len(reach[s]))**2), -len(cand[s]), s)) + byT = defaultdict(list); placed = {} + for s in order: + X = cand[s]; changed = True + while changed and X: + changed = False + for t in sorted(reach[s]): + for w in byT[t]: + B = placed[w] + if (len(B) >= len(X) and not sat_contained(X, B)) or (len(B) < len(X) and not sat_contained(B, X)): + X = sat_cap(X, B); changed = True + if not X: break + if not X: break + if X and not sat_nondeg(X): + before = X; X = sat_nonsingular_part(X) + assert sat_contained(X, before) and sat_nondeg(X) + assert len(X) < len(before) + changed = True # Extraction can break containment of a smaller target frame. + if X: + assert sat_nondeg(X) and sat_contained(X, cand[s]) + placed[s] = X + for t in reach[s]: byT[t].append(s) + for t, ss in byT.items(): + ss.sort(key=lambda s: (len(placed[s]), s)) + assert all(sat_contained(placed[a], placed[b]) for a, b in zip(ss, ss[1:])) + return placed + +def main(): + with tempfile.TemporaryDirectory(prefix='deferred-stopped-') as work: + prefix = Path(work) / 'complex' + build(24, prefix, central_disjoint=24) + h, v, n, q, args, core, cover, roots, kind, active, ranks, types = load(prefix) + trip = list(combinations(range(h), 3)); require(len(trip) == v, 'triple count') + m = h * h; N = v * v; FULL = (1 << h) - 1 + tmask = [sum(1 << p for p in T) for T in trip] + tid = {T: i for i, T in enumerate(trip)} + + # ------------------------------------------------------------ uses and matching (inherited adjacency) + degree = [0] * n; uses = defaultdict(list); c_add = 0 + for x in range(1, n): + if active[x] and args[x][0]: + c_add += 1 + for pos, y in enumerate(args[x]): degree[y] += 1; uses[y].append(('gate', x, pos)) + for j, x in enumerate(roots): degree[x] += 1; uses[x].append(('root', j)) + def unode(u): return roots[u[1]] if u[0] == 'root' else u[1] + def before(x, u): + y = unode(u) + return (ranks[x], x) < (ranks[y], (n + u[1]) if u[0] == 'root' else y) + def incl(x, y): + tx, ty = types[x], types[y] + if tx == 1 and ty == 1: return not (core[y] & ~core[x]) and not (cover[x] & ~cover[y]) + if tx in (1, 2) and ty == 2: return not (cover[x] & ~cover[y]) + if tx == 1 and ty == 3: return bool(core[x] & core[y]) + if tx == 2 and ty == 3: return not (cover[x] & ~core[y]) + if tx == 3 and ty == 2: return cover[y] == FULL + if tx == 3 and ty == 3: return core[x] == core[y] + return False + left = []; adj = {} + for x in range(1, n): + if not (active[x] and args[x][0]): continue + rs = sorted({(y, k) for y in args[x] for k, u in enumerate(uses[y]) if before(x, u) and incl(x, unode(u))}) + if rs: left.append(x); adj[x] = rs + mate = hopcroft_karp(left, adj) + links = {x: r for x, r in mate.items() if r is not None} + R = c_add + q - len(links) + require((c_add,q,len(links),R)==(91770,8120,71185,28705),'selected PR117 graph') + print('PR117 graph matched', c_add, q, len(links), R, flush=True) + linked_use = {(y, k): x for x, (y, k) in links.items()} + + # ------------------------------------------------------------ root targets, read coefficients, root functionals + target = [None] * q + for j in range(v): target[j] = j + idx = v + # PR117 witness stores pair-star roots in natural excluded-point order. + for a, b in combinations(range(h), 2): + others = [i for i in range(h) if i not in (a, b)] + for i in others: target[idx] = tid[tuple(sorted((a, b, i)))]; idx += 1 + centre_of = {} + for j in range(q): + if kind[j]: + miss = FULL & ~cover[roots[j]]; require(bin(miss).count('1') == 1, 'centre cover') + centre_of[j] = miss.bit_length() - 1 + require(idx + len(centre_of) == q, 'root order') + rootfun = [(1 << centre_of[j]) if kind[j] else tmask[target[j]] for j in range(q)] + + # ------------------------------------------------------------ lifted binary frames, monotone + succ = defaultdict(set); droot = defaultdict(set) + for x in range(1, n): + if not active[x]: continue + for k, u in enumerate(uses[x]): + if (x, k) in linked_use: continue + (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1])) + for x, (y, k) in links.items(): + u = uses[y][k]; (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1])) + order_desc = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x), reverse=True) + K = {} + for x in order_desc: + rows = [rootfun[j] for j in droot[x]] + for t in succ[x]: rows += K[t] + K[x] = reduce(rows) + def envelope(x): + if not args[x][0]: return [tmask[x - 1]] + if types[x] == 2: return [1 << i for i in range(h) if cover[x] >> i & 1] + require(types[x] == 1, 'only ordinary and common-pair labels occur') + ks = [i for i in range(h) if (cover[x] & ~core[x]) >> i & 1] + require(len(ks) == ranks[x], 'common-pair support') + return [core[x] | (1 << k) for k in ks] + U = {} + for x in range(1, n): + if not active[x]: continue + if not args[x][0]: U[x] = envelope(x); continue + B = kernel(K[x], h) + require(contains(envelope(x), B), 'label outside lifted frame') + U[x] = B if nondeg(B) else envelope(x) + changed = True + while changed: + changed = False + for x in order_desc: + if args[x][0] and any(not contains(U[x], U[t]) for t in succ[x]): + env = envelope(x) + if len(reduce(U[x])) != len(reduce(env)) or not contains(U[x], env): U[x] = env; changed = True + dimU = {x: len(reduce(B)) for x, B in U.items()} + print('PR117 frames lifted',sum(dimU[x]>ranks[x] for x in U),flush=True) + + # ------------------------------------------------------------ explicit role compile + order = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x)) + holds = []; first_node = []; ops = []; edge_key = {}; role_root = {} + def new_role(node): holds.append([node]); first_node.append(node); return len(holds) - 1 + def serve(s, y, k): + u = uses[y][k] + if u[0] == 'gate': edge_key[(y, k)] = s + else: role_root[s] = u[1] + for x in order: + free = [k for k in range(len(uses[x])) if (x, k) not in linked_use] + if not args[x][0]: + for k in free: + s = new_role(x); ops.append(('src', s, x)); serve(s, x, k) + continue + a, b = args[x] + ka = next(k for k, u in enumerate(uses[a]) if u == ('gate', x, 0)) + kb = next(k for k, u in enumerate(uses[b]) if u == ('gate', x, 1)) + sa, sb = edge_key.pop((a, ka)), edge_key.pop((b, kb)) + if x in links and links[x][0] == a: sa, sb = sb, sa + piv, oth = sa, sb + ops.append(('add', piv, oth, x)); holds[piv].append(x); holds[oth].append(x) + if x in links: serve(oth, *links[x]) + require(free, 'every use linked at node %d' % x) + serve(piv, x, free[0]) + for k in free[1:]: + f = new_role(x); ops.append(('copy', piv, f, x)); serve(f, x, k) + require(not edge_key and len(holds) == R, 'compile') + Rr = R + + # R12 logical-frame nondegenerate completion and endpoint descent. + from r12_frame_opt import optimize as r12_optimize + U, dimU, frame_optimization = r12_optimize(U, order, args, succ, holds, role_root, envelope, h, globals()) + shrunk = frame_optimization['shrunk_frames'] + + # ------------------------------------------------------------ B. the word computes every root value + rng = random.Random(20261008) + xs = [rng.randrange(P) for _ in range(v)] + val = [0] * n + for i in range(v): val[i + 1] = xs[i] + for x in order: + if args[x][0]: val[x] = (val[args[x][0]] + val[args[x][1]]) % P + leaf_of = {s: first_node[s] for s in range(Rr) if not args[first_node[s]][0]} + a_ = [0] * Rr + for s, leaf in leaf_of.items(): a_[s] = xs[leaf - 1] + for o in ops: + if o[0] == 'add': a_[o[1]] = (a_[o[1]] + a_[o[2]]) % P + elif o[0] == 'copy': a_[o[2]] = (a_[o[2]] + a_[o[1]]) % P + require(all(a_[s] == val[roots[j]] for s, j in role_root.items()), 'root values') + + # ------------------------------------------------------------ phase one and garbage reach + def touch(o): return [o[1], o[2]] if o[0] in ('add', 'copy') else [] + prev = {}; pred = defaultdict(list); last = {} + for i, o in enumerate(ops): + for s in touch(o): + if s in prev: pred[i].append(prev[s]) + prev[s] = i; last[s] = i + centre_roles = [s for s, j in role_root.items() if kind[j]] + Anc = set(); st = [last[s] for s in centre_roles] + while st: + i = st.pop() + if i not in Anc: Anc.add(i); st.extend(pred[i]) + touched = set(centre_roles) + for i in Anc: touched.update(touch(ops[i])) + require(all(last[s] in Anc for s in centre_roles), 'centres complete in phase one') + reach = [set() for _ in range(Rr)]; reach_all = [False] * Rr + for s, j in role_root.items(): + if kind[j]: reach_all[s] = True + else: reach[s].add(target[j]) + for o in reversed(ops): + if o[0] == 'add': reach[o[2]] |= reach[o[1]]; reach_all[o[2]] = reach_all[o[2]] or reach_all[o[1]] + elif o[0] == 'copy': reach[o[1]] |= reach[o[2]]; reach_all[o[1]] = reach_all[o[1]] or reach_all[o[2]] + + # ------------------------------------------------------------ deferral frames, insertion nesting + def F0(s): return U[first_node[s]] + from r12_defer_opt import repair_candidate, place as r12_place + cand = {} + for s in range(Rr): + if s in touched or reach_all[s]: continue + S_ = restrict(F0(s), [tmask[t] for t in reach[s]]) + S_ = repair_candidate(S_, globals()) if S_ else [] + if S_: cand[s] = S_ + print('PR117 candidates',len(cand),flush=True) + placed, deferral_optimization = r12_place(cand, reach, F0, h, m, globals()) + print('PR117 placed',len(placed),flush=True) + deferred = sorted(placed, key=lambda s: (len(placed[s]), s)); dset = set(deferred) + + # SCREENING ONLY: scalar/dirty replay intentionally deferred to full verification. + # ------------------------------------------------------------ D. exact F2 frame facts + root_frame = {} + for s, j in role_root.items(): + root_frame[s] = [1 << i for i in range(h) if i != centre_of[j]] if kind[j] else kernel([tmask[target[j]]], h) + FULLB = [1 << i for i in range(h)] + chain_dims = [] + for s in range(Rr): + seq = [placed.get(s, []), F0(s)] + [U[x] for x in holds[s][1:]] + if s in root_frame: seq.append(root_frame[s]) + seq.append(FULLB) + require(all(contains(A, B) for A, B in zip(seq, seq[1:])), 'role chain nesting %d' % s) + require(all(nondeg(B) for B in seq[1:-1] if B), 'degenerate frame on role %d' % s) + chain_dims.append([len(reduce(B)) for B in seq]) + for s, X in placed.items(): + require(contains(X, F0(s)) and nondeg(X), 'deferral frame %d' % s) + require(all(not any(dot(xv, tmask[t]) for xv in X) for t in reach[s]), 'target frame %d' % s) + byT2 = defaultdict(list) + for s in deferred: + for t in reach[s]: byT2[t].append(s) + for t, ss in byT2.items(): + ss.sort(key=lambda s: (len(placed[s]), s)) + require(all(contains(placed[p], placed[q_]) for p, q_ in zip(ss, ss[1:])), 'target chain %d' % t) + + # ------------------------------------------------------------ E. one-child histogram + z = Counter() + for s in range(Rr): + ds = chain_dims[s] + for a, b in zip(ds[:-1], ds[1:-1]): + if b > a: z[b - a] += 2 * v + lastd = ds[-2] + if s in role_root and kind[role_root[s]]: z[h - 1] += 2 * v # copied centre transform + z[h - lastd] += 2 * v # final growth to F + z[m - h + ds[0]] += 2 * v # exterior, gauged by sigma + levels = defaultdict(set) + for s in deferred: + for t in reach[s]: levels[t].add(len(placed[s])) + for t in range(v): + ds = sorted(levels[t] | {0, h - 1}) + for a, b in zip(ds, ds[1:]): z[b - a] += 2 * v # target fronts + z[h - 1] += 2 * N # data-wire fronts + z[(h - 1) ** 2] += 2 * N # data macros + z[1] += N # endpoint copies + z.pop(0, None) + W = 2 * N + 2 * v * R; L = 2 * v * h * (h - 1); s_ = W * m - N + L + require(sum(t * c for t, c in z.items()) == s_, 'complex rank mass') + require(all(0 < t < m for t in z), 'children below m') + out = dict(frame_optimization=frame_optimization, deferral_optimization=deferral_optimization, h=h, v=v, additions=c_add, roots=q, links=len(links), R=R, m=m, N=N, W=W, L=L, total_rank=s_, + deficit=N - L, maxchild=max(z), phase_one_ops=len(Anc), phase_one_roles=len(touched), + deferred_roles=len(deferred), + deferred_dims=dict(sorted(Counter(len(X) for X in placed.values()).items())), + lifted_additions=sum(1 for x in U if args[x][0] and dimU[x] > ranks[x]), + replay=dict(screening_only=True, scratch_restored=None, y_plus_x=None), + child_multiplicities=dict(sorted(z.items()))) + (HERE / 'screen-profile.json').write_text(json.dumps(out, indent=1) + '\n') + print('PASS complex: R=%d, deferred roles %d, maxchild %d, rank mass %d' % (R, len(deferred), max(z), s_)) + + +if __name__ == '__main__': + main() diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/SOURCE.json b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/SOURCE.json new file mode 100644 index 0000000000..e7f712ae00 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/SOURCE.json @@ -0,0 +1,69 @@ +{ + "attribution": "Avi Eisenberg / ikeboy (PR62 and PR110, Anthropic Claude assistance); Rohan Arun (PR111, Anthropic Claude assistance); Swapnil Jain (round-seven bit word); icekylinx (retained stopped-product, copied-center and finite assembly interfaces); Zhihao Chen and RaD (retained assembly). PR117 scalar DAG is separate upstream work by eumemic with Anthropic Claude assistance, retained byte for byte with its original attribution. Saturated deferred-frame integration and verification for eumemic with OpenAI Codex assistance. Shrunk-frame step by Joel Pulikkan with Anthropic Claude assistance (PR114 base). Original source notices remain authoritative.", + "package_files": { + "bit-profile.json": "7293f330518b78650bd86d76b93681e43f3a55541cdb8110993714148a4b4a6a", + "bit_round7.py": "35d261a9248c2e06f9179e3c47e554a96b8fe763a9a3de2731256b8c0fbc74b0", + "certificate.json": "e5965daf4346b6a695384f8eda957d954529add921cb384f969856cdef81f845", + "certificate.py": "fa1846facc5eeb33017afd96e9a7b440d3a3d7ff813f76312f1ea865bf2277ca", + "complex-profile.json": "7e7c0c28c0983d117b3006b96719a6102ce31ec0273160dd7fc8b9a0fef0dbeb", + "complex_deferred.py": "fa1125e85ec73b185dc9eee117f62d10356bb6422c07ec793a7f77296c87707e", + "controls/pr114-complex-profile.json": "a54d2a6023ff73f7476057b5f6a4ff02e65ded840b7254d906aadde2dd01940d", + "inputs/complex-dag.json.gz": "3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b", + "inputs/deferred_23.json.gz": "8c38e947ff9e021e308000dd82bb5e2194eb265d8b75194e22ce783d3e75317c", + "inputs/witness_23.json.gz": "b2486aa2bb222bacea6e52162a3920780e45dd8edc5d7cb03eabea336a1c6588", + "producer.py": "017e50713943e6c2a98d1c23ec93e7da9580896de1b6bde24563b4b6961c74c0", + "reflection-audit.json": "7caee26f3747b88b41137527175d41b08c4849a7302368bd50b1cfae74779c5a", + "reflection_audit.py": "6761fb01f93ef89f2455388b2f5a71f19c0bbd870e6aaeba457ede0a949a163b", + "replayed_producer.py": "99c1e3694ae06a7ce7a370b04ecb45ea3fcfe69a6e6e7f4c4606e0a6c74c3184", + "test_controls.py": "87dbc9945a5057cf1b7b6ba776590f5c20548f5b2b63893b34bd6280f534f036", + "verify.py": "b49c45f0fa06ab7de987110f3756c445220e1b2e08127cfa891eca7330e6d8da" + }, + "provenance": { + "base": "https://github.com/CrocSwap/integer-mult-bounds/pull/110", + "cyclic_strips": "https://github.com/CrocSwap/integer-mult-bounds/pull/111", + "round7_commit": "741e7aa078392553815df7926ee17ac5e25a8c38", + "round7_repository": "https://github.com/Swapnil-jain/integer-mult-kappa", + "round7_sha256": { + "deferred_23.json.gz": "8c38e947ff9e021e308000dd82bb5e2194eb265d8b75194e22ce783d3e75317c", + "witness_23.json.gz": "b2486aa2bb222bacea6e52162a3920780e45dd8edc5d7cb03eabea336a1c6588" + }, + "saturated_base": { + "commit": "7dfa16edfa5d6452f2b10dadcbef20d26222827e", + "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/114" + }, + "scalar_dag": { + "commit": "cbb05ce504d571546d9b7794c186a613c659c3bf", + "file": "inputs/complex-dag.json.gz", + "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/117", + "sha256": "3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b" + } + }, + "reflection": { + "receipt": "reflection-audit.json", + "script": "reflection_audit.py" + }, + "repository_files": { + "certificates/copied-centers-network.json": "7dbd675e42e22ac076280360f8750031851564bb7a56079e66236fee5d0a6cdf", + "scripts/audit_short_guards.py": "c2c929c956e617bee739963b517b9069e0d067cfebc6820f401a4e90a1769eb1", + "scripts/certify.py": "2348d95008276c5d5764f7e028c3918e484582cd589bd4d9b82919161745e53e", + "scripts/compact_control_layer.py": "e814c9f8d84f2e5d3aa2e06c36697f27f110218addc40ff8df2801fde861ff9f", + "scripts/complex_circuit.py": "d623617f7c5cb3189580883a8ab30c0bd3832688ae3f1f0c1f881bbbbff8e0c1", + "scripts/complex_network.py": "0da395e67ac04fa213494e71012c1b19b544596d34cdce5a3b172b1fb6af5f1b", + "scripts/copied_centers/__init__.py": "13db4f09038a2ff5335cbd4dbd93274b0fb16b3c7b51e4de67cbb2801a3f78e1", + "scripts/copied_centers/corners.py": "9eecdc39c67cc18c806a33f0be03986c28591d322881fd60c11f52c625c8067b", + "scripts/copied_centers/physical.py": "837345d1f8753eab0e70f105b1d1bb0db965b993da037b1825ddef3672609d7d", + "scripts/copied_centers_network.py": "409ebfbd8a41c4c4d089aa0949fcf5a949415dc26f57440ffd48b7bd8881e6a9", + "scripts/exclusion_circuit.py": "b253f9d7318becda1c1f3b24e2287ed44a9c27fcea00cf9d531afb950d0457a0", + "scripts/fast_gaussian.py": "11430c2df0783b933dc91080595bb7514bb052b8c7b12107e27a1ef701e31e43", + "scripts/paired_exclusion_circuit.py": "8f05f04cf06217befd6d0ee0f2d7d0c5c5eb32cfab8c9a8ca7917fd6d620b7d2", + "scripts/paired_network.py": "991223dc3c1374284c361ed017e42bf732dd971fa0bea2be2282cfb18257b3f7", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/prepare_layers.py": "a6e2adc612f264b1c0e51d18ce6315de9ae5e2ae2420aa22e99a22d8bf304947", + "scripts/search_network.py": "3a4faa5037d9b8e7ca5828afac193a96b6966a8b114f14937921795b24ec4f6a", + "scripts/shared_point_circuit.py": "c9bb7a5df92d260a4e3ad532b53e26936730d7c93f7facfb0784957c1e81c8ba", + "scripts/shared_point_network.py": "a85e7f0d8c42d6a27e3846308571ca324a1824ac5c2d59e4daa5c7673c33c697", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + }, + "schema": 1, + "scope": "Frozen finite producer, profiles, exact assembly and reflection audit; inherited all-size transfer remains conditional." +} diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/bit-profile.json b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/bit-profile.json new file mode 100644 index 0000000000..36105e819a --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/bit-profile.json @@ -0,0 +1,69 @@ +{ + "h": 23, + "v": 1771, + "R": 28866, + "m": 529, + "N": 3136441, + "W": 108516254, + "L": 1792252, + "total_rank": 57403754177, + "deficit": 1344189, + "maxchild": 528, + "deferred_slots": 11565, + "source": { + "repository": "https://github.com/Swapnil-jain/integer-mult-kappa", + "commit": "741e7aa078392553815df7926ee17ac5e25a8c38", + "sha256": { + "witness_23.json.gz": "b2486aa2bb222bacea6e52162a3920780e45dd8edc5d7cb03eabea336a1c6588", + "deferred_23.json.gz": "8c38e947ff9e021e308000dd82bb5e2194eb265d8b75194e22ce783d3e75317c" + } + }, + "child_multiplicities": { + "1": 239511811, + "2": 238288050, + "3": 53377940, + "4": 46970462, + "5": 23632224, + "6": 7409864, + "7": 4105178, + "8": 5755750, + "9": 2082696, + "10": 878416, + "11": 1388464, + "12": 1080310, + "13": 945714, + "14": 226688, + "15": 2451064, + "16": 1508892, + "17": 4771074, + "18": 2149994, + "19": 7367360, + "20": 8182020, + "21": 1466388, + "22": 88550, + "484": 6272882, + "506": 61280142, + "507": 545468, + "508": 173558, + "509": 293986, + "510": 580888, + "511": 14168, + "512": 322322, + "513": 17710, + "514": 1129898, + "515": 127512, + "516": 410872, + "517": 99176, + "518": 1186570, + "519": 340032, + "520": 322322, + "521": 106260, + "522": 1583274, + "523": 626934, + "524": 2854852, + "525": 13711082, + "526": 4629394, + "527": 5653032, + "528": 6233920 + } +} diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/bit_round7.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/bit_round7.py new file mode 100644 index 0000000000..3c5df409a6 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/bit_round7.py @@ -0,0 +1,129 @@ +#!/usr/bin/env python3 +"""One-child bit profile of Swapnil Jain's round-seven deferred word (h=23), under PR104's opposite-bank rule. + +Reads the two frozen round-seven data files (vendored in inputs/; pinned by SHA-256 below) from a directory given on +the command line, e.g. a checkout of https://github.com/Swapnil-jain/integer-mult-kappa at +741e7aa078392553815df7926ee17ac5e25a8c38 (certificates/round7/), or PR97's imported copy +(research/deferred-signed/swapnil-round7/certificates/round7/). The frame dimensions are the ones recorded in +the data file; Swapnil's check_frames.py re-derives each of them exactly and PR97 replays the word. + +Every projector residual of rank r is one child of width r (PR104, notes/stopped-product-factorization.tex): + each slot: its chain steps from the deferral frame sigma_u to F, and one exterior child m - (h - dim sigma_u); + each retained centre: one copied transform of width h-1; + each target y_T: its chain 0 -> deferred readout levels -> t_T^perp; each data wire X_S: its chain of V frames; + each data pair: one data residual of width (h-1)^2 and one endpoint copy. +Usage: python3 research/deferred-stopped/bit_round7.py DIR (writes bit-profile.json next to this file) +Prepared by Avi Eisenberg (ikeboy) with Anthropic Claude assistance. Apache-2.0. +""" +import gzip +import hashlib +import json +import sys +from collections import Counter, defaultdict +from itertools import combinations +from pathlib import Path + +HERE = Path(__file__).resolve().parent +PINS = {'witness_23.json.gz': 'b2486aa2bb222bacea6e52162a3920780e45dd8edc5d7cb03eabea336a1c6588', + 'deferred_23.json.gz': '8c38e947ff9e021e308000dd82bb5e2194eb265d8b75194e22ce783d3e75317c'} + + +def require(ok, msg): + if not ok: + raise SystemExit('FAIL: ' + msg) + + +def main(directory): + data = {} + for name, digest in PINS.items(): + raw = (Path(directory) / name).read_bytes() + require(hashlib.sha256(raw).hexdigest() == digest, 'pinned hash of ' + name) + data[name] = json.loads(gzip.decompress(raw)) + W, D = data['witness_23.json.gz'], data['deferred_23.json.gz'] + h = D['h']; R = D['R']; trip = list(combinations(range(h), 3)); v = len(trip); m = h * h; N = v * v + tid = {T: i for i, T in enumerate(trip)} + args = {int(n): (tuple(a) if a else None) for n, a in W['args'].items()} + late = {int(n): (list(e), list(l)) for n, (e, l) in W['late'].items()} + ops = [tuple(o[:2]) + (tuple(o[2]),) if o[0] == 'fan' else tuple(o) for o in D['ops']] + hold, start = D['hold'], D['start'] + out = {s: (c, tuple(T)) for s, c, T in D['out']}; ret = {s: c for s, c in D['ret']} + sigma = dict(zip(D['readout_order'], D['sigma'])); sel = set(D['readout_order']) + f = [0] * R + for s, B in sigma.items(): f[s] = len(B) + vstart = dict(zip(D['vleaf_slots'], D['vleaf_start'])) + node_dims = {n: d for n, d in D['node_dims']} + late_dims = {(n, tuple(lt)): d for n, lt, d in D['late_dims']} + pivslot = {o[3]: o[1] for o in ops if o[0] == 'add'} + + def start_key(s): + n0 = hold[s][0] + if args[n0] is None: return ('v', s) + st = start[s]; k = st[2] if len(st) > 2 else None; dec = late.get(n0) + if dec is None or k in dec[0]: return ('n', n0) + lt = dec[1]; return ('c', n0, tuple(lt[lt.index(k):])) + + def chain(s): + ch = [('sigma', s) if s in sel else ('0',), start_key(s)] + for idx, n in enumerate(hold[s]): + if idx > 0: ch.append(('n', n)) + if args[n] is not None and pivslot.get(n) == s and n in late: + lt = late[n][1] + for i in range(len(lt) - 1): ch.append(('c', n, tuple(lt[i:]))) + if s in out: ch.append(('out',)) + if s in ret: ch.append(('ret',)) + ch.append(('F',)); return ch + + def dim(key): + k = key[0] + if k == '0': return 0 + if k == 'F': return h + if k in ('out', 'ret'): return h - 1 + if k == 'n': return node_dims[key[1]] + if k == 'c': return late_dims[key[1], key[2]] + if k == 'sigma': return f[key[1]] + if k == 'v': return len(vstart[key[1]]) + raise KeyError(key) + + # garbage supports (transpose sweep) for the deferred levels on each target + cov = [set() for _ in range(R)] + for s, (c, T) in out.items(): cov[s].add(tid[T]) + for s, c in ret.items(): cov[s].update(t for t, T in enumerate(trip) if c in T) + for o in reversed(ops): + if o[0] == 'add': cov[o[2]] |= cov[o[1]] + elif o[0] == 'fan': + for g in o[2]: cov[o[1]] |= cov[g] + levels = defaultdict(set) + for s in sel: + for t in cov[s]: levels[t].add(f[s]) + + z = Counter() + for s in range(R): + ds = [dim(k) for k in chain(s)] + require(all(b >= a for a, b in zip(ds, ds[1:])) and ds[-1] == h, 'monotone chain %d' % s) + for a, b in zip(ds, ds[1:]): + if b > a: z[b - a] += 2 * v + z[m - (h - f[s])] += 2 * v + z[h - 1] += 2 * v * h + for t in range(v): + ls = sorted(levels[t] | {0, h - 1}) + for a, b in zip(ls, ls[1:]): z[b - a] += 2 * v + for n, us in D['xs_order']: + ds = [1] + [len(vstart[s]) for s in us] + [h] + ds = [d for i, d in enumerate(ds) if i == 0 or d != ds[i - 1]] + require(all(b > a for a, b in zip(ds, ds[1:])), 'data-wire chain') + for a, b in zip(ds, ds[1:]): z[b - a] += 2 * v + z[(h - 1) ** 2] += 2 * N + z[1] += N + Wb = 2 * N + 2 * v * R; L = 2 * v * h * (h - 1); s_ = Wb * m - N + L + require(sum(t * c for t, c in z.items()) == s_, 'bit rank mass') + require(all(0 < t < m for t in z), 'children below m') + prof = dict(h=h, v=v, R=R, m=m, N=N, W=Wb, L=L, total_rank=s_, deficit=N - L, maxchild=max(z), + deferred_slots=len(sel), source=dict(repository='https://github.com/Swapnil-jain/integer-mult-kappa', + commit='741e7aa078392553815df7926ee17ac5e25a8c38', sha256=PINS), + child_multiplicities=dict(sorted(z.items()))) + (HERE / 'bit-profile.json').write_text(json.dumps(prof, indent=1) + '\n') + print('PASS bit: R=%d, deferred slots %d, maxchild %d, rank mass %d' % (R, len(sel), max(z), s_)) + + +if __name__ == '__main__': + main(sys.argv[1] if len(sys.argv) > 1 else '.') diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/certificate.json b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/certificate.json new file mode 100644 index 0000000000..6e0a5f02d1 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/certificate.json @@ -0,0 +1,313 @@ +{ + "actual_bit_saving": "1240189553/10000000000000", + "assembly": { + "absorption_gap": "1423799823581924404745614798375593/2500553080248572986091654124313081000000000000000", + "margins": { + "Gaussian_arithmetic": "331855646931470668996733908345875686919/2000442464198858388873323299450464800000000", + "bulk_exposure": "55308025686919/500000000000000000", + "compact_phase_layer": "276540120138391202270175686919/2500553080248572986091654124313081", + "coordinate_movement": "55308025686919/500000000000000000", + "dimension": "2499999975000000000000000000000000/2500553080248572986091654124313081", + "original_prefix": "27656512566919368800003660346024313081/250055308024857298609165412431308100000000", + "scalar_work": "442481698305308624750313358810675686919/2000442464198858388873323299450464800000000" + }, + "minimum_margin": "276540120138391202270175686919/2500553080248572986091654124313081", + "parameters": { + "C0": 3646615615709474302231996852324339320426087077316912790823030645920872744002225026973564928, + "C1": 1, + "a_bit": "55308025686919/500000000000000000", + "a_complex": "55308081/500000000000", + "alpha_squared_power": "414822684355688646962150000000/2500553080248572986091654124313081", + "beta": "1/1000000", + "c": "276540125669193660346024313081/2500000000000000000000000000000000", + "delta": "1/800000000", + "epsilon": "2499999975000000000000000000000000/2500553080248572986091654124313081", + "eta": "1/100000000", + "kappa": "110591581647/1000000000000000", + "lambda_": "49994469197486616125686919/50000000000000000000000000", + "lambda_prime": "24997234598770962075686919/25000000000000000000000000", + "q": "2765401229037924313081/25000000000000000000000000", + "sigma": "499944691919/500000000000", + "tau": "499944691974313081/500000000000000000" + }, + "recurrence": { + "internal": "499944691974313081/500000000000000000", + "leaf": "499944691974308081/500000000000000000", + "reservations": "2499723459874330806339653975686919/2500000000000000000000000000000000" + }, + "strict_constraints": { + "Gaussian_arithmetic_above_kappa": "138279438527370933799323622918090223447125593/2500553080248572986091654124313081000000000000000", + "K_dominates_log": "27654012290379240365408770962075686919/250055308024857298609165412431308100000000", + "K_geometry": "27656512566919368800003660346024313081/250055308024857298609165412431308100000000", + "alpha_below_one": "2500138257564217297444691974313081/2500553080248572986091654124313081", + "alpha_below_one_fourth": "2498893789511150231503805524313081/10002212320994291944366616497252324", + "alpha_positive": "414822684355688646962150000000/2500553080248572986091654124313081", + "artificial_boundary": "14003650357141687868693766988962529075686919/2000442464198858388873323299450464800000000", + "beta_below_one": "999999/1000000", + "beta_positive": "1/1000000", + "bit_positive": "55308025686919/500000000000000000", + "bulk_exposure_above_kappa": "12234863419/500000000000000000", + "c_below_one": "2499723459874330806339653975686919/2500000000000000000000000000000000", + "c_positive": "276540125669193660346024313081/2500000000000000000000000000000000", + "cell_above_band": "2499861692435782702555308025686919/5001106160497145972183308248626162", + "compact_leaf": "55558025686919/25000000000000000000000000", + "compact_phase_layer_above_kappa": "1423799823581924404745614798375593/2500553080248572986091654124313081000000000000000", + "compact_reservations": "2765401229037924313081/2500000000000000000000000000000000", + "complex_above_bit": "55313081/500000000000000000", + "complex_below_one_over32": "15569691919/500000000000", + "coordinate_movement_above_kappa": "12234863419/500000000000000000", + "delta_below_one_eighth": "99999999/800000000", + "delta_positive": "1/800000000", + "dimension_above_kappa": "2499723434879863032597553406237485745614798375593/2500553080248572986091654124313081000000000000000", + "epsilon_below_one": "553105248572986091654124313081/2500553080248572986091654124313081", + "epsilon_positive": "2499999975000000000000000000000000/2500553080248572986091654124313081", + "gamma_sublinear": "138282564217297444691974313081/2500553080248572986091654124313081", + "guard_width": "553105248572986091654124313081/2500553080248572986091654124313081", + "lambda_above_internal": "55308025686919/50000000000000000000000000", + "lambda_above_sigma": "5586616125686919/50000000000000000000000000", + "lambda_above_tau": "55308025686919/50000000000000000000000000", + "lambda_prime_above_lambda": "55308025686919/50000000000000000000000000", + "lambda_prime_below_one": "2765401229037924313081/25000000000000000000000000", + "leaf_saving_above_bit": "1/100000000000000", + "literal_scalar_guard": "14065616197378741718443193606139245678291196", + "original_prefix_above_kappa": "25005532226285553442840945988745608375593/2500553080248572986091654124313081000000000000000", + "phase_boundary": "331855646931470668996733908345875686919/2000442464198858388873323299450464800000000", + "phase_local": "442481698305308624750313358810675686919/2000442464198858388873323299450464800000000", + "prime_interval_packing": "553105248572986091654124313081/2500553080248572986091654124313081", + "q_below_internal": "55308025686919/25000000000000000000000000", + "q_below_leaf": "55558025686919/25000000000000000000000000", + "q_below_reservations": "2765401229037924313081/2500000000000000000000000000000000", + "q_positive": "2765401229037924313081/25000000000000000000000000", + "record_suffix": "553105248572986091654124313081/2500553080248572986091654124313081", + "row_product_gap": "6389/25", + "scalar_work_above_kappa": "276562002744668378491297935999090223447125593/2500553080248572986091654124313081000000000000000", + "short_record_fallback": "1249861686846006107497739648634368046048805957712561/1250276540124286493045827062156540500000000000000000", + "small_field_exposure": "276565128434594889383948626162/2500553080248572986091654124313081" + } + }, + "bit_moment_gap": 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1344189, + "h": 23, + "m": 529, + "maxchild": 528, + "source": { + "commit": "741e7aa078392553815df7926ee17ac5e25a8c38", + "repository": "https://github.com/Swapnil-jain/integer-mult-kappa", + "sha256": { + "deferred_23.json.gz": "8c38e947ff9e021e308000dd82bb5e2194eb265d8b75194e22ce783d3e75317c", + "witness_23.json.gz": "b2486aa2bb222bacea6e52162a3920780e45dd8edc5d7cb03eabea336a1c6588" + } + }, + "total_rank": 57403754177, + "v": 1771 + }, + "coarse_bit_saving": "620523/5000000000", + "complex_moment_gap": 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+ "complex_profile": { + "L": 2234496, + "N": 4096576, + "R": 28705, + "W": 124390992, + "additions": 91770, + "child_multiplicities": { + "1": 435601232, + "10": 7375456, + "11": 7019232, + "12": 31788944, + "13": 12536656, + "14": 1497760, + "15": 3440800, + "16": 854128, + "17": 506000, + "18": 2906464, + "19": 2092816, + "2": 267192288, + "20": 817696, + "21": 1230592, + "22": 64768, + "23": 8363168, + "3": 29238704, + "4": 61145040, + "5": 26425344, + "529": 8193152, + "552": 97147952, + "554": 3493424, + "556": 1445136, + "558": 2319504, + "560": 582912, + "562": 101200, + "564": 1307504, + "566": 975568, + "568": 1364176, + "569": 4048, + "570": 3643200, + "571": 2444992, + "572": 837936, + "573": 44528, + "574": 485760, + "6": 15734576, + "7": 11876832, + "8": 22077792, + "9": 4562096 + }, + "deferred_dims": { + "10": 25, + "12": 323, + "14": 241, + "16": 337, + "17": 1, + "18": 900, + "19": 604, + "2": 863, + "20": 207, + "21": 11, + "22": 120, + "4": 357, + "6": 573, + "8": 144 + }, + "deferred_roles": 4706, + "deficit": 1862080, + "h": 24, + "lifted_additions": 24792, + "links": 71185, + "m": 576, + "maxchild": 574, + "phase_one_ops": 18844, + "phase_one_roles": 13555, + "replay": { + "field": "Z/(2^61-1)", + "scratch_restored": true, + "seeds": [ + 1, + 2 + ], + "y_plus_x": true + }, + "roots": 8120, + "total_rank": 71647349312, + "v": 2024 + }, + "complex_saving": "55308081/500000000000", + "finite_bridge": { + "bit_coarse": { + "W": 108516254, + "halving_degree": 367, + "m": 529, + "maxchild": 528, + "wire_bits": 27 + }, + "complex": { + "W": 124390992, + "halving_degree": 200, + "m": 576, + "maxchild": 574, + "s": 71647349312, + "scalar_group_upper": 60347419084480, + "scalar_terms": [ + { + "R": 28705, + "c": 91770, + "description": "Expanded deferred readouts and forward/inverse/reflected words", + "h": 24, + "invocations": 2024, + "local_group_upper": 14907958248, + "q": 8120, + "v": 2024 + }, + { + "R": 28705, + "c": 91770, + "description": "Expanded deferred readouts and forward/inverse/reflected words", + "h": 24, + "invocations": 2024, + "local_group_upper": 14907958248, + "q": 8120, + "v": 2024 + } + ], + "wire_bits": 27 + }, + "ordinary_leaf_row_degree": 252, + "rows": { + "coefficient": 15561, + "contract": "W_complex^D_complex * W_coarse^D_coarse * W_old^D_old; prefix and padding; sequential reuse", + "degree": 32000, + "degree_gap": "6389/25", + "suffix_slope": 128000 + }, + "semantic": { + "B": 14065616197380609244023681038811612751070848, + "C0": 3646615615709474302231996852324339320426087077316912790823030645920872744002225026973564928, + "C1": 1, + "E": 14065616197380609244023681038811541103721536, + "exact_grid": "2^(-P)*21^(-K), K=G*(D_complex+1); completed children preserve incoming odd denominator; no child rounding", + "fixed_odd_divisor": 21, + "induction_gap": 42196848592141827732071043116434838253212544, + "literal_charge": 1867525580487432672295425430340, + "strict_literal_gap": 14065616197378741718443193606139245678291196 + } + }, + "kappa": "110591581647/1000000000000000", + "next_grid_rejections": { + "bit": "1e-10", + "complex": "1e-12", + "kappa": "1e-15" + }, + "status": "Finite conditional cyclic/deferred witness" +} diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/certificate.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/certificate.py new file mode 100644 index 0000000000..5e00159bfe --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/certificate.py @@ -0,0 +1,114 @@ +#!/usr/bin/env python3 +"""Exact finite assembly for cyclic strips with deferred readouts. + +Built on Avi Eisenberg's PR110 (Anthropic Claude assistance), icekylinx's +PR104 stopped-product and copied-center interfaces, and Zhihao Chen's +assembly of the RaD interfaces. Integration for eumemic with OpenAI Codex +assistance. Apache-2.0. General transfer hypotheses remain inherited. +""" +import argparse +import json +import sys +from fractions import Fraction as Q +from pathlib import Path +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(ROOT / 'scripts')) +from partial_swap_network import moment +from copied_centers_network import finite_bridge as copied_bridge +from structured_bulk_assembly import assembly, js +ATOM = Q(1, 1000) +OLD = Q(384599, 10**10) +BETA = Q(1, 10**6) +COARSE = Q(620523, 5000000000) +COMPLEX = Q(110616162, 10**12) +KGRID = 10**15 + +def profile(name): + p = json.loads((HERE / name).read_text()) + p['child_multiplicities'] = {int(t): c for t, c in p['child_multiplicities'].items()} + z = p['child_multiplicities'] + assert all(0 < t < p['m'] and c > 0 for t,c in z.items()) + assert sum(t*c for t,c in z.items()) == p['total_rank'] == p['W']*p['m']-p['N']+p['L'] + assert max(z) == p['maxchild'] + return p + +def contracts(p, a): + try: moment(p['m'],p['W'],p['child_multiplicities'],a,True) + except ValueError: return False + return True + +def exact(bit=None, phase=None): + bit = profile('bit-profile.json') if bit is None else bit + phase = profile('complex-profile.json') if phase is None else phase + assert (bit['h'], phase['h']) == (23,24) + bm = moment(bit['m'],bit['W'],bit['child_multiplicities'],COARSE,True) + cm = moment(phase['m'],phase['W'],phase['child_multiplicities'],COMPLEX,True) + assert not contracts(bit,COARSE+Q(1,10**10)) + assert not contracts(phase,COMPLEX+Q(1,10**12)) + ab = (1-ATOM)*COARSE+ATOM*OLD + assert 0 < OLD < COARSE < ATOM and ab < ATOM + a = min(ab,(1-BETA)*COMPLEX-Q(1,10**14)) + row = dict(h=phase['h'],v=phase['v'],c=phase['additions'],central_disjoint=24) + bridge = copied_bridge(bit,phase,[row,row]) + # Logical readouts are expanded into same-frame shears with |coefficient|<=1. + # Exact numerators over42 are split into signed42 chunks and a remainder. + # The independent audit counts every chunk and checks this guard covers it. + # Each row has <=c+R mixer operations and <=R leaf copies. There are + # <=R+q readouts, each containing <=h center coefficients and <=v direct + # coefficients; <=4*v*(h+1) scalar groups suffice per readout. A factor + # eight covers forward/inverse words, both reflected words, and copies. + h,v,R,q,c = (phase[k] for k in ('h','v','R','roots','additions')) + local = 8*(c+2*R+(R+q)*v*(h+1)+h*h+h+1) + G = phase['N'] + 2*v*local + m,W,s = (phase[k] for k in ('m','W','total_rank')) + E=64*(W+m+G+1)**3 + charge=2*G*W*W+8*s+4*W+4+32*m + B=s+E; C0=32*m*B*B + assert charge= s+E and 2*B+181: + mid=(lo+hi)//2 + if accepts(mid): lo=mid + else: hi=mid + k=Q(lo,KGRID) + assembled=assembly(a,COMPLEX,bridge,k,beta=BETA) + assert len(assembled['strict_constraints'])==47 and len(assembled['margins'])==7 + assert not accepts(lo+1) + return dict(status='Finite conditional cyclic/deferred witness',kappa=k, + complex_saving=COMPLEX,coarse_bit_saving=COARSE,actual_bit_saving=ab, + bit_parameter=a,complex_profile=phase,bit_profile=bit, + bit_moment_gap=bm['strict_gap'],complex_moment_gap=cm['strict_gap'], + finite_bridge=bridge,assembly=assembled, + next_grid_rejections=dict(bit='1e-10',complex='1e-12',kappa='1e-15')) + +def main(): + parser=argparse.ArgumentParser();parser.add_argument('--write',action='store_true');args=parser.parse_args() + assert not sys.flags.optimize + result=js(exact()); path=HERE/'certificate.json' + if args.write:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:assert result==json.loads(path.read_text()),'Frozen exact certificate mismatch' + print('PASS conditional kappa = %s = %.12e; 47 constraints, 7 margins; expanded scalar charge' % (result['kappa'],float(Q(result['kappa'])))) +if __name__=='__main__':main() diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/complex-profile.json b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/complex-profile.json new file mode 100644 index 0000000000..1b07c25523 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/complex-profile.json @@ -0,0 +1,85 @@ +{ + "h": 24, + "v": 2024, + "additions": 91770, + "roots": 8120, + "links": 71185, + "R": 28705, + "m": 576, + "N": 4096576, + "W": 124390992, + "L": 2234496, + "total_rank": 71647349312, + "deficit": 1862080, + "maxchild": 574, + "phase_one_ops": 18844, + "phase_one_roles": 13555, + "deferred_roles": 4706, + "deferred_dims": { + "2": 863, + "4": 357, + "6": 573, + "8": 144, + "10": 25, + "12": 323, + "14": 241, + "16": 337, + "17": 1, + "18": 900, + "19": 604, + "20": 207, + "21": 11, + "22": 120 + }, + "lifted_additions": 24792, + "replay": { + "seeds": [ + 1, + 2 + ], + "scratch_restored": true, + "y_plus_x": true, + "field": "Z/(2^61-1)" + }, + "child_multiplicities": { + "1": 435601232, + "2": 267192288, + "3": 29238704, + "4": 61145040, + "5": 26425344, + "6": 15734576, + "7": 11876832, + "8": 22077792, + "9": 4562096, + "10": 7375456, + "11": 7019232, + "12": 31788944, + "13": 12536656, + "14": 1497760, + "15": 3440800, + "16": 854128, + "17": 506000, + "18": 2906464, + "19": 2092816, + "20": 817696, + "21": 1230592, + "22": 64768, + "23": 8363168, + "529": 8193152, + "552": 97147952, + "554": 3493424, + "556": 1445136, + "558": 2319504, + "560": 582912, + "562": 101200, + "564": 1307504, + "566": 975568, + "568": 1364176, + "569": 4048, + "570": 3643200, + "571": 2444992, + "572": 837936, + "573": 44528, + "574": 485760 + } +} diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/complex_deferred.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/complex_deferred.py new file mode 100644 index 0000000000..d2190bc2b7 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/complex_deferred.py @@ -0,0 +1,606 @@ +#!/usr/bin/env python3 +"""Shrunk lifted frames and saturated deferred readouts on the PR117 complex DAG. + +After the role compile, a forward pass shrinks a lifted frame to the minimal +nondegenerate span of its label and predecessor frames when that merges +increments of the role chains holding it (16,031 frames). Section D rechecks +every chain. The shrink step was prepared by Joel Pulikkan with Anthropic +Claude assistance; everything else is PR114 (eumemic) unchanged. + + +PR117 credits its searched DAG to eumemic with Anthropic Claude assistance; +this experiment imports and replays that witness unchanged. PR110/PR114 +saturation and exact finite checks are applied to the resulting graph. +Logical readout macros are realized as signed numerator/42 chunks of magnitude +at most one. The literal audit expands and charges those same-frame shears, +checks exact reconstruction, and reverses the chunks under reflection. +Inherited Avi Eisenberg, Rohan Arun, icekylinx and Swapnil Jain credits retained. +This integration prepared with OpenAI Codex assistance. Apache-2.0. +""" +import array +import json +import random +import struct +import sys +import tempfile +from collections import Counter, defaultdict +from itertools import combinations +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(ROOT / 'scripts')) +sys.path.insert(0, str(HERE)) +import importlib.util +producer_path = HERE / 'producer.py' +spec = importlib.util.spec_from_file_location('replayed_producer_wrapper', producer_path) +producer = importlib.util.module_from_spec(spec); spec.loader.exec_module(producer) +build = producer.build + +P = (1 << 61) - 1 +SHRUNK = 16031 + + +def require(ok, msg): + if not ok: + raise SystemExit('FAIL: ' + msg) + + +def load(prefix): + def rd(fh, typ, cnt): + a = array.array(typ); a.fromfile(fh, cnt); return a + with open(str(prefix) + '.bin', 'rb') as f: + h, v, n, q = struct.unpack('<4I', f.read(16)) + flat = rd(f, 'I', 2 * n); core = rd(f, 'Q', n); cover = rd(f, 'Q', n) + roots = rd(f, 'I', q); kind = rd(f, 'I', q); active = rd(f, 'B', n) + with open(str(prefix) + '.labels', 'rb') as f: + ranks = rd(f, 'I', n); types = rd(f, 'B', n) + args = [(flat[2 * i], flat[2 * i + 1]) for i in range(n)] + return h, v, n, q, args, core, cover, roots, kind, active, ranks, types + + +# ---------------------------------------------------------------- F2 linear algebra on bit vectors +def dot(a, b): return bin(a & b).count('1') & 1 + + +def reduce(basis): + rows = []; piv = [] + for vec in basis: + for p, r in zip(piv, rows): + if vec >> p & 1: vec ^= r + if vec: + p = vec.bit_length() - 1 + for i in range(len(rows)): + if rows[i] >> p & 1: rows[i] ^= vec + rows.append(vec); piv.append(p) + return rows + + +def kernel(funcs, h): + K = reduce(funcs); piv = [r.bit_length() - 1 for r in K] + out = [] + for c in (i for i in range(h) if i not in piv): + vec = 1 << c + for r, p in zip(K, piv): + if r >> c & 1: vec |= 1 << p + out.append(vec) + return out + + +def restrict(basis, funcs): + B = reduce(basis) + for f in funcs: + if not B: break + vals = [dot(b, f) for b in B] + if not any(vals): continue + k = vals.index(1); pv = B[k] + B = [b ^ pv if val else b for b, val in zip(B, vals)]; B.pop(k) + return reduce(B) + + +def contains(A, B): + RB = reduce(B) + return len(reduce(RB + list(A))) == len(RB) + + +def cap(A, B): + A = reduce(A); B = reduce(B) + if not A or not B: return [] + ker = []; red = [] + for i, vec in enumerate(A + B): + tag = 1 << i + for rv, rt in red: + if vec >> (rv.bit_length() - 1) & 1: vec ^= rv; tag ^= rt + if vec: red.append((vec, tag)) + else: + comb_ = 0 + for k in range(len(A)): + if tag >> k & 1: comb_ ^= A[k] + ker.append(comb_) + return reduce(ker) + + +def nondeg(B): + B = reduce(B); k = len(B) + if not k: return True + M = [sum(dot(B[i], B[j]) << j for j in range(k)) for i in range(k)] + return len(reduce(M)) == k + + +def hopcroft_karp(left, adj): + """maximum bipartite matching; adj[x] = sorted list of right vertices.""" + INF = 1 << 60 + mate_l = {x: None for x in left}; mate_r = {} + while True: + dist = {}; queue = [] + for x in left: + if mate_l[x] is None: dist[x] = 0; queue.append(x) + else: dist[x] = INF + found = INF; head = 0 + while head < len(queue): + x = queue[head]; head += 1 + if dist[x] >= found: continue + for r in adj[x]: + y = mate_r.get(r) + if y is None: found = min(found, dist[x] + 1) + elif dist[y] == INF: dist[y] = dist[x] + 1; queue.append(y) + if found == INF: break + gained = 0 + for x0 in left: + if mate_l[x0] is not None: continue + stack = [(x0, iter(adj[x0]))]; path = [] + while stack: + x, it = stack[-1] + advanced = False + for r in it: + y = mate_r.get(r) + if (y is None and dist[x] + 1 == found) or (y is not None and dist[y] == dist[x] + 1): + path.append((x, r)) + if y is None: + for xx, rr in path: mate_l[xx] = rr; mate_r[rr] = xx + gained += 1; stack = []; break + stack.append((y, iter(adj[y]))); advanced = True; break + else: + dist[x] = INF; stack.pop() + if path: path.pop() + continue + if not advanced: break + if not gained: break + return mate_l + + +from functools import lru_cache +from fractions import Fraction + +def sat_basis(vectors): + piv = {} + for x in vectors: + for p in sorted(piv, reverse=True): + if x >> p & 1: + x ^= piv[p] + if x: + p = x.bit_length() - 1 + for q in piv: + if piv[q] >> p & 1: + piv[q] ^= x + piv[p] = x + return tuple((piv[p] for p in sorted(piv, reverse=True))) + +def sat_dot(a, b): + return (a & b).bit_count() & 1 + +@lru_cache(None) +def sat_contained(A, B): + for x in A: + for r in B: + if x >> r.bit_length() - 1 & 1: + x ^= r + if x: + return False + return True + +@lru_cache(None) +def sat_cap(A, B): + if not A or not B: + return () + red = {} + out = [] + for i, x in enumerate(A + B): + tag = 1 << i + for p in sorted(red, reverse=True): + if x >> p & 1: + r, t = red[p] + x ^= r + tag ^= t + if x: + red[x.bit_length() - 1] = (x, tag) + else: + y = 0 + for j, r in enumerate(A): + if tag >> j & 1: + y ^= r + if y: + out.append(y) + return sat_basis(out) + +@lru_cache(None) +def sat_nondeg(B): + return len(sat_basis((sum((sat_dot(a, b) << j for j, b in enumerate(B))) for a in B))) == len(B) + +@lru_cache(None) +def sat_nonsingular_part(B): + rows = list(B) + out = [] + while rows: + i = next((i for i, x in enumerate(rows) if sat_dot(x, x)), None) + if i is not None: + a = rows.pop(i) + out.append(a) + rows = [x ^ a if sat_dot(x, a) else x for x in rows] + continue + pair = next(((i, j) for i in range(len(rows)) for j in range(i + 1, len(rows)) if sat_dot(rows[i], rows[j])), None) + if pair is None: + break + i, j = pair + a, b = (rows[i], rows[j]) + out.extend((a, b)) + rows = [x ^ (a if sat_dot(x, b) else 0) ^ (b if sat_dot(x, a) else 0) for k, x in enumerate(rows) if k not in (i, j)] + return sat_basis(out) + +def saturated_placement(cand, reach): + # Each extracted block is orthogonal to previously selected blocks. + # A diagonal-one pivot contributes a nondegenerate line; when all + # remaining diagonals vanish, a dot-one pair contributes a hyperbolic + # plane. The residual radical is discarded, not counted as a frame. + cand = {s: sat_basis(B) for s, B in cand.items()} + order = sorted(cand, key=lambda s: (Fraction(-(1 << len(cand[s])), max(1, len(reach[s]))**2), -len(cand[s]), s)) + byT = defaultdict(list); placed = {} + for s in order: + X = cand[s]; changed = True + while changed and X: + changed = False + for t in sorted(reach[s]): + for w in byT[t]: + B = placed[w] + if (len(B) >= len(X) and not sat_contained(X, B)) or (len(B) < len(X) and not sat_contained(B, X)): + X = sat_cap(X, B); changed = True + if not X: break + if not X: break + if X and not sat_nondeg(X): + before = X; X = sat_nonsingular_part(X) + assert sat_contained(X, before) and sat_nondeg(X) + assert len(X) < len(before) + changed = True # Extraction can break containment of a smaller target frame. + if X: + assert sat_nondeg(X) and sat_contained(X, cand[s]) + placed[s] = X + for t in reach[s]: byT[t].append(s) + for t, ss in byT.items(): + ss.sort(key=lambda s: (len(placed[s]), s)) + assert all(sat_contained(placed[a], placed[b]) for a, b in zip(ss, ss[1:])) + return placed + +def main(): + with tempfile.TemporaryDirectory(prefix='deferred-stopped-') as work: + prefix = Path(work) / 'complex' + build(24, prefix, central_disjoint=24) + h, v, n, q, args, core, cover, roots, kind, active, ranks, types = load(prefix) + trip = list(combinations(range(h), 3)); require(len(trip) == v, 'triple count') + m = h * h; N = v * v; FULL = (1 << h) - 1 + tmask = [sum(1 << p for p in T) for T in trip] + tid = {T: i for i, T in enumerate(trip)} + + # ------------------------------------------------------------ uses and matching (inherited adjacency) + degree = [0] * n; uses = defaultdict(list); c_add = 0 + for x in range(1, n): + if active[x] and args[x][0]: + c_add += 1 + for pos, y in enumerate(args[x]): degree[y] += 1; uses[y].append(('gate', x, pos)) + for j, x in enumerate(roots): degree[x] += 1; uses[x].append(('root', j)) + def unode(u): return roots[u[1]] if u[0] == 'root' else u[1] + def before(x, u): + y = unode(u) + return (ranks[x], x) < (ranks[y], (n + u[1]) if u[0] == 'root' else y) + def incl(x, y): + tx, ty = types[x], types[y] + if tx == 1 and ty == 1: return not (core[y] & ~core[x]) and not (cover[x] & ~cover[y]) + if tx in (1, 2) and ty == 2: return not (cover[x] & ~cover[y]) + if tx == 1 and ty == 3: return bool(core[x] & core[y]) + if tx == 2 and ty == 3: return not (cover[x] & ~core[y]) + if tx == 3 and ty == 2: return cover[y] == FULL + if tx == 3 and ty == 3: return core[x] == core[y] + return False + left = []; adj = {} + for x in range(1, n): + if not (active[x] and args[x][0]): continue + rs = sorted({(y, k) for y in args[x] for k, u in enumerate(uses[y]) if before(x, u) and incl(x, unode(u))}) + if rs: left.append(x); adj[x] = rs + mate = hopcroft_karp(left, adj) + links = {x: r for x, r in mate.items() if r is not None} + R = c_add + q - len(links) + require((c_add,q,len(links),R)==(91770,8120,71185,28705),'selected PR117 graph') + print('PR117 graph matched', c_add, q, len(links), R, flush=True) + linked_use = {(y, k): x for x, (y, k) in links.items()} + + # ------------------------------------------------------------ root targets, read coefficients, root functionals + target = [None] * q + for j in range(v): target[j] = j + idx = v + # PR117 witness stores pair-star roots in natural excluded-point order. + for a, b in combinations(range(h), 2): + others = [i for i in range(h) if i not in (a, b)] + for i in others: target[idx] = tid[tuple(sorted((a, b, i)))]; idx += 1 + centre_of = {} + for j in range(q): + if kind[j]: + miss = FULL & ~cover[roots[j]]; require(bin(miss).count('1') == 1, 'centre cover') + centre_of[j] = miss.bit_length() - 1 + require(idx + len(centre_of) == q, 'root order') + rootfun = [(1 << centre_of[j]) if kind[j] else tmask[target[j]] for j in range(q)] + + # ------------------------------------------------------------ lifted binary frames, monotone + succ = defaultdict(set); droot = defaultdict(set) + for x in range(1, n): + if not active[x]: continue + for k, u in enumerate(uses[x]): + if (x, k) in linked_use: continue + (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1])) + for x, (y, k) in links.items(): + u = uses[y][k]; (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1])) + order_desc = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x), reverse=True) + K = {} + for x in order_desc: + rows = [rootfun[j] for j in droot[x]] + for t in succ[x]: rows += K[t] + K[x] = reduce(rows) + def envelope(x): + if not args[x][0]: return [tmask[x - 1]] + if types[x] == 2: return [1 << i for i in range(h) if cover[x] >> i & 1] + require(types[x] == 1, 'only ordinary and common-pair labels occur') + ks = [i for i in range(h) if (cover[x] & ~core[x]) >> i & 1] + require(len(ks) == ranks[x], 'common-pair support') + return [core[x] | (1 << k) for k in ks] + U = {} + for x in range(1, n): + if not active[x]: continue + if not args[x][0]: U[x] = envelope(x); continue + B = kernel(K[x], h) + require(contains(envelope(x), B), 'label outside lifted frame') + U[x] = B if nondeg(B) else envelope(x) + changed = True + while changed: + changed = False + for x in order_desc: + if args[x][0] and any(not contains(U[x], U[t]) for t in succ[x]): + env = envelope(x) + if len(reduce(U[x])) != len(reduce(env)) or not contains(U[x], env): U[x] = env; changed = True + dimU = {x: len(reduce(B)) for x, B in U.items()} + print('PR117 frames lifted',sum(dimU[x]>ranks[x] for x in U),flush=True) + + # ------------------------------------------------------------ explicit role compile + order = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x)) + holds = []; first_node = []; ops = []; edge_key = {}; role_root = {} + def new_role(node): holds.append([node]); first_node.append(node); return len(holds) - 1 + def serve(s, y, k): + u = uses[y][k] + if u[0] == 'gate': edge_key[(y, k)] = s + else: role_root[s] = u[1] + for x in order: + free = [k for k in range(len(uses[x])) if (x, k) not in linked_use] + if not args[x][0]: + for k in free: + s = new_role(x); ops.append(('src', s, x)); serve(s, x, k) + continue + a, b = args[x] + ka = next(k for k, u in enumerate(uses[a]) if u == ('gate', x, 0)) + kb = next(k for k, u in enumerate(uses[b]) if u == ('gate', x, 1)) + sa, sb = edge_key.pop((a, ka)), edge_key.pop((b, kb)) + if x in links and links[x][0] == a: sa, sb = sb, sa + piv, oth = sa, sb + ops.append(('add', piv, oth, x)); holds[piv].append(x); holds[oth].append(x) + if x in links: serve(oth, *links[x]) + require(free, 'every use linked at node %d' % x) + serve(piv, x, free[0]) + for k in free[1:]: + f = new_role(x); ops.append(('copy', piv, f, x)); serve(f, x, k) + require(not edge_key and len(holds) == R, 'compile') + Rr = R + + # ------------------------------------------------------------ shrunk frames + # Any nondegenerate U_x with label(x) + sum of predecessor frames <= U_x + # <= lifted kernel, contained in every successor frame, satisfies the + # PR110 frame contract (the inherited label fallback is one such choice). + # One forward pass replaces U_x by its minimal span Lb_x when Lb_x is + # nondegenerate and that lowers the local one-child cost of the role + # chains holding x; a merged increment a+b replaces a and b, and + # t*log(m/t) is subadditive. Section D rechecks every resulting chain. + import math + fcost = lambda t: t * math.log(m / t) if t > 0 else 0.0 + preds = defaultdict(list) + for x, ts in succ.items(): + for t in ts: preds[t].append(x) + occ = defaultdict(list) + for s in range(R): + for i, x in enumerate(holds[s]): occ[x].append((s, i)) + def local_cost(x, d): + c = 0.0 + for s, i in occ[x]: + hs = holds[s] + c += fcost(d - dimU[hs[i - 1]]) if i else fcost(d) + if i + 1 < len(hs): c += fcost(dimU[hs[i + 1]] - d) + elif s in role_root: c += fcost(h - 1 - d) + else: c += fcost(h - d) + return c + shrunk = 0 + for x in order: + if not args[x][0]: continue + Lb = reduce(envelope(x) + [b for p in preds[x] for b in U[p]]) + if len(Lb) >= dimU[x] or not contains(Lb, U[x]) or not nondeg(Lb): continue + if not all(contains(Lb, U[t]) for t in succ[x]): continue + if local_cost(x, len(Lb)) < local_cost(x, dimU[x]) - 1e-9: + U[x] = Lb; dimU[x] = len(Lb); shrunk += 1 + print('shrunk frames', shrunk, flush=True) + require(SHRUNK is None or shrunk == SHRUNK, 'shrunk frames: %d' % shrunk) + + # ------------------------------------------------------------ B. the word computes every root value + rng = random.Random(20261008) + xs = [rng.randrange(P) for _ in range(v)] + val = [0] * n + for i in range(v): val[i + 1] = xs[i] + for x in order: + if args[x][0]: val[x] = (val[args[x][0]] + val[args[x][1]]) % P + leaf_of = {s: first_node[s] for s in range(Rr) if not args[first_node[s]][0]} + a_ = [0] * Rr + for s, leaf in leaf_of.items(): a_[s] = xs[leaf - 1] + for o in ops: + if o[0] == 'add': a_[o[1]] = (a_[o[1]] + a_[o[2]]) % P + elif o[0] == 'copy': a_[o[2]] = (a_[o[2]] + a_[o[1]]) % P + require(all(a_[s] == val[roots[j]] for s, j in role_root.items()), 'root values') + + # ------------------------------------------------------------ phase one and garbage reach + def touch(o): return [o[1], o[2]] if o[0] in ('add', 'copy') else [] + prev = {}; pred = defaultdict(list); last = {} + for i, o in enumerate(ops): + for s in touch(o): + if s in prev: pred[i].append(prev[s]) + prev[s] = i; last[s] = i + centre_roles = [s for s, j in role_root.items() if kind[j]] + Anc = set(); st = [last[s] for s in centre_roles] + while st: + i = st.pop() + if i not in Anc: Anc.add(i); st.extend(pred[i]) + touched = set(centre_roles) + for i in Anc: touched.update(touch(ops[i])) + require(all(last[s] in Anc for s in centre_roles), 'centres complete in phase one') + reach = [set() for _ in range(Rr)]; reach_all = [False] * Rr + for s, j in role_root.items(): + if kind[j]: reach_all[s] = True + else: reach[s].add(target[j]) + for o in reversed(ops): + if o[0] == 'add': reach[o[2]] |= reach[o[1]]; reach_all[o[2]] = reach_all[o[2]] or reach_all[o[1]] + elif o[0] == 'copy': reach[o[1]] |= reach[o[2]]; reach_all[o[1]] = reach_all[o[1]] or reach_all[o[2]] + + # ------------------------------------------------------------ deferral frames, insertion nesting + def F0(s): return U[first_node[s]] + cand = {} + for s in range(Rr): + if s in touched or reach_all[s]: continue + S_ = restrict(F0(s), [tmask[t] for t in reach[s]]) + if S_ and nondeg(S_): cand[s] = S_ + print('PR117 candidates',len(cand),flush=True) + placed = saturated_placement(cand, reach) + print('PR117 placed',len(placed),flush=True) + deferred = sorted(placed, key=lambda s: (len(placed[s]), s)); dset = set(deferred) + + # ------------------------------------------------------------ C. replay with arbitrary scratch and data + inv = lambda a: pow(a % P, P - 2, P); HALF = inv(2); I21 = inv(21) + cvec = [None] * Rr; dpart = [dict() for _ in range(Rr)] + for s, j in role_root.items(): + if kind[j]: c = [0] * h; c[centre_of[j]] = 1; cvec[s] = c + else: dpart[s][target[j]] = (P - HALF) if j >= v else HALF + seed_c = {s: (None if cvec[s] is None else list(cvec[s])) for s in role_root} + seed_d = {s: dict(dpart[s]) for s in role_root} + def addc(dst, src): + if cvec[src] is not None: + cvec[dst] = list(cvec[src]) if cvec[dst] is None else [(p + q_) % P for p, q_ in zip(cvec[dst], cvec[src])] + for t, c in dpart[src].items(): dpart[dst][t] = (dpart[dst].get(t, 0) + c) % P + for o in reversed(ops): + if o[0] == 'add': addc(o[2], o[1]) + elif o[0] == 'copy': addc(o[1], o[2]) + scatter = [[(I21 - (HALF if i in trip[t] else 0)) % P for t in range(v)] for i in range(h)] + def readout(y, s, value, sign, seed=False): + # Logical readout macro: the literal audit combines its exact rational + # target coefficients and expands each numerator/42 into bounded shears. + cv = seed_c[s] if seed else cvec[s]; dp = seed_d[s] if seed else dpart[s] + if cv is not None: + for i, ci in enumerate(cv): + if ci: + f = sign * ci * value % P; row = scatter[i] + for t in range(v): y[t] = (y[t] + f * row[t]) % P + for t, c in dp.items(): y[t] = (y[t] + sign * c * value) % P + phase1 = sorted(Anc); rest = [i for i in range(len(ops)) if i not in Anc] + def replay(seed): + rng = random.Random(seed) + x = [rng.randrange(P) for _ in range(v)]; z = [rng.randrange(P) for _ in range(Rr)] + y0 = [rng.randrange(P) for _ in range(v)]; a = list(z); y = list(y0) + for s in range(Rr): + if s not in dset: readout(y, s, a[s], -1) + for s, leaf in leaf_of.items(): + if s not in dset: a[s] = (a[s] + x[leaf - 1]) % P + def run(i, sign=1): + o = ops[i] + if o[0] == 'add': a[o[1]] = (a[o[1]] + sign * a[o[2]]) % P + elif o[0] == 'copy': a[o[2]] = (a[o[2]] + sign * a[o[1]]) % P + for i in phase1: run(i) + for s in centre_roles: readout(y, s, a[s], +1, True) + for s in deferred: readout(y, s, a[s], -1) + for s in deferred: + if s in leaf_of: a[s] = (a[s] + x[leaf_of[s] - 1]) % P + for i in rest: run(i) + for s, j in role_root.items(): + if not kind[j]: readout(y, s, a[s], +1, True) + for i in reversed(range(len(ops))): run(i, -1) + for s, leaf in leaf_of.items(): a[s] = (a[s] - x[leaf - 1]) % P + return a == z, all((y[t] - y0[t] - x[t]) % P == 0 for t in range(v)) + rep = [replay(seed) for seed in (1, 2)] + require(all(r == (True, True) for r in rep), 'replay %s' % rep) + + # ------------------------------------------------------------ D. exact F2 frame facts + root_frame = {} + for s, j in role_root.items(): + root_frame[s] = [1 << i for i in range(h) if i != centre_of[j]] if kind[j] else kernel([tmask[target[j]]], h) + FULLB = [1 << i for i in range(h)] + chain_dims = [] + for s in range(Rr): + seq = [placed.get(s, []), F0(s)] + [U[x] for x in holds[s][1:]] + if s in root_frame: seq.append(root_frame[s]) + seq.append(FULLB) + require(all(contains(A, B) for A, B in zip(seq, seq[1:])), 'role chain nesting %d' % s) + require(all(nondeg(B) for B in seq[1:-1] if B), 'degenerate frame on role %d' % s) + chain_dims.append([len(reduce(B)) for B in seq]) + for s, X in placed.items(): + require(contains(X, F0(s)) and nondeg(X), 'deferral frame %d' % s) + require(all(not any(dot(xv, tmask[t]) for xv in X) for t in reach[s]), 'target frame %d' % s) + byT2 = defaultdict(list) + for s in deferred: + for t in reach[s]: byT2[t].append(s) + for t, ss in byT2.items(): + ss.sort(key=lambda s: (len(placed[s]), s)) + require(all(contains(placed[p], placed[q_]) for p, q_ in zip(ss, ss[1:])), 'target chain %d' % t) + + # ------------------------------------------------------------ E. one-child histogram + z = Counter() + for s in range(Rr): + ds = chain_dims[s] + for a, b in zip(ds[:-1], ds[1:-1]): + if b > a: z[b - a] += 2 * v + lastd = ds[-2] + if s in role_root and kind[role_root[s]]: z[h - 1] += 2 * v # copied centre transform + z[h - lastd] += 2 * v # final growth to F + z[m - h + ds[0]] += 2 * v # exterior, gauged by sigma + levels = defaultdict(set) + for s in deferred: + for t in reach[s]: levels[t].add(len(placed[s])) + for t in range(v): + ds = sorted(levels[t] | {0, h - 1}) + for a, b in zip(ds, ds[1:]): z[b - a] += 2 * v # target fronts + z[h - 1] += 2 * N # data-wire fronts + z[(h - 1) ** 2] += 2 * N # data macros + z[1] += N # endpoint copies + z.pop(0, None) + W = 2 * N + 2 * v * R; L = 2 * v * h * (h - 1); s_ = W * m - N + L + require(sum(t * c for t, c in z.items()) == s_, 'complex rank mass') + require(all(0 < t < m for t in z), 'children below m') + out = dict(h=h, v=v, additions=c_add, roots=q, links=len(links), R=R, m=m, N=N, W=W, L=L, total_rank=s_, + deficit=N - L, maxchild=max(z), phase_one_ops=len(Anc), phase_one_roles=len(touched), + deferred_roles=len(deferred), + deferred_dims=dict(sorted(Counter(len(X) for X in placed.values()).items())), + lifted_additions=sum(1 for x in U if args[x][0] and dimU[x] > ranks[x]), + replay=dict(seeds=[1, 2], scratch_restored=True, y_plus_x=True, field='Z/(2^61-1)'), + child_multiplicities=dict(sorted(z.items()))) + (HERE / 'complex-profile.json').write_text(json.dumps(out, indent=1) + '\n') + print('PASS complex: R=%d, deferred roles %d, maxchild %d, rank mass %d' % (R, len(deferred), max(z), s_)) + + +if __name__ == '__main__': + main() diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/controls/pr114-complex-profile.json b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/controls/pr114-complex-profile.json new file mode 100644 index 0000000000..90a44f18a8 --- /dev/null +++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/controls/pr114-complex-profile.json @@ -0,0 +1,85 @@ +{ + "h": 24, + "v": 2024, + "additions": 91770, + "roots": 8120, + "links": 71185, + "R": 28705, + "m": 576, + "N": 4096576, + "W": 124390992, + "L": 2234496, + "total_rank": 71647349312, + "deficit": 1862080, + "maxchild": 574, + "phase_one_ops": 18844, + "phase_one_roles": 13555, + "deferred_roles": 4706, + "deferred_dims": { + "2": 863, + "4": 357, + "6": 573, + "8": 144, + "10": 25, + "12": 323, + "14": 241, + "16": 337, + "17": 1, + "18": 900, + "19": 603, + "20": 208, + "21": 11, + "22": 120 + }, + "lifted_additions": 39989, + "replay": { + "seeds": [ + 1, + 2 + ], + "scratch_restored": true, + "y_plus_x": true, + "field": "Z/(2^61-1)" + }, + "child_multiplicities": { + "1": 339934848, + "2": 358859248, + "3": 36626304, + "4": 66512688, + "5": 30258800, + "6": 17062320, + "7": 14240864, + "8": 23757712, + "9": 6290592, + "10": 9500656, + "11": 9456128, + "12": 15430976, + "13": 10949840, + "14": 1384416, + "15": 1275120, + "16": 793408, + "17": 506000, + "18": 2902416, + "19": 2092816, + "20": 817696, + "21": 1230592, + "22": 64768, + "23": 8363168, + "529": 8193152, + "552": 97147952, + "554": 3493424, + "556": 1445136, + "558": 2319504, + "560": 582912, + "562": 101200, + "564": 1307504, + "566": 975568, + "568": 1364176, + "569": 4048, + "570": 3643200, + "571": 2440944, + "572": 841984, + "573": 44528, + "574": 485760 + } +} diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/inputs/complex-dag.json.gz 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for t in after: + if t:formula[t]+=2*v + packet_types[sig,M[w['target'][j]],first]+=1 + actual=Counter({int(t):c for t,c in new['child_multiplicities'].items()}) + actual.subtract({int(t):c for t,c in old['child_multiplicities'].items()}) + actual[m]+=old['W']-new['W'] + assert all(actual[t]==formula[t] for t in actual.keys()|formula.keys()) + assert sum(t*c for t,c in actual.items())==0 + hinges=[sum(min(t,k)*c for t,c in actual.items()) for k in range(1,m+1)] + assert max(hinges)==0 and min(hinges)<0 + # Exhaustive small parameter controls for the general packet lemma. + checked=0 + for hh in range(2,17): + mm=hh*hh + for sig in range(hh): + for MM in range(sig,hh): + for f in range(MM,hh): + B=[mm-hh+sig,1,f-sig,hh-1-MM];A=[mm,f-MM,0,0] + assert sum(A)==sum(B) and max(B)=sum(sorted(B,reverse=True)[:k]) for k in range(1,5)) + checked+=1 + a.output.write_text(json.dumps(dict(status='PASS independent exact all-concave terminal gain',roles=len(e['removed']), + packet_types={str(k):c for k,c in sorted(packet_types.items())},hinge_min=min(hinges),hinge_max=max(hinges), + full_augmented_delta={t:c for t,c in sorted(actual.items()) if c},small_parameter_cases=checked, + theorem='For h>=2 and 0<=sigma<=M<=F<=h-1, [h^2,F-M,0,0] strictly majorizes [h^2-h+sigma,1,F-sigma,h-1-M]. Hence the physically verified distinct-target elimination strictly decreases sum(child^p)-W*(h^2)^p for every 0= v else HALF', '-21 if j >= v else 21') + new = once(new, '(p + q_) % P for p, q_ in zip(cvec[dst], cvec[src])', + '(p + q_) for p, q_ in zip(cvec[dst], cvec[src])') + new = once(new, '(dpart[dst].get(t, 0) + c) % P', '(dpart[dst].get(t, 0) + c)') + new = once(new, '(I21 - (HALF if i in trip[t] else 0)) % P', '(2 - 21*(i in trip[t]))') + new = once(new, 'f = sign * ci * value % P', 'f = sign * ci * value * I42 % P') + new = once(new, 'y[t] + sign * c * value) % P', 'y[t] + sign * c * value * I42) % P') + marker = " (HERE / 'complex-profile.json').write_text" + extra = ''' # Exact clean support replay, separate from modular dirty-state tests. + clean=[0]*Rr + for o in ops: + if o[0]=='src': + require(clean[o[1]]==0,'fresh input role') + clean[o[1]]=1<<(o[2]-1) + elif o[0]=='add': + require(not(clean[o[1]]&clean[o[2]]),'clean support overlap') + clean[o[1]] |= clean[o[2]] + else: + require(o[0]=='copy' and clean[o[2]]==0,'fresh scalar copy role') + clean[o[2]]=clean[o[1]] + dag=[0]*n + for x in order: + if not args[x][0]:dag[x]=1<<(x-1) + else: + aa,bb=args[x] + require(not(dag[aa]&dag[bb]),'input DAG disjoint support') + dag[x]=dag[aa]|dag[bb] + require(all(clean[s]==dag[roots[j]] for s,j in role_root.items()),'exact all-input clean root supports') + # These conservative finite constants charge the literal centre/dpart + # readout loops, or dominate offline-combined coefficient evaluation. + read_terms=sum(v*sum(c!=0 for c in (cv or []))+len(dp) + for cv,dp in zip(cvec,dpart)) + direct_ops=2*sum(o[0] in ('add','copy') for o in ops)+2*len(leaf_of) + numerator_bound=max((19*sum(abs(c) for c in (cv or []))+ + max((abs(c) for c in dp.values()),default=0)) + for cv,dp in zip(cvec,dpart)) + max_bits=max(1,numerator_bound.bit_length()) + literal_scalar_terms=read_terms+direct_ops+q+h*v+4*h*h+8*h+8 + # Expanding each fixed coefficient into unit/dyadic operations followed + # by at most one21-division gives this deliberately generous count. + safe_scalar_groups=(4*max_bits+16)*literal_scalar_terms + out.update(exact_clean_roots=True,adjoint_denominator=42, + adjoint_numerator_bound=numerator_bound,max_coefficient_bits=max_bits, + literal_readout_terms=read_terms,literal_scalar_terms=literal_scalar_terms, + safe_one_axis_scalar_groups=safe_scalar_groups, + second_stage_scope='Written complement-inverse and translated-gauge lemma required; this producer replays stage1.') + witness=dict(h=h,v=v,n=n,q=q,R=R,args=args,active=list(active), + roots=list(roots),kind=list(kind),target=target,centre_of=centre_of, + links={x:list(r) for x,r in links.items()},ops=ops,holds=holds, + first_node=first_node,role_root=role_root,frames=U,sigma=placed, + phase_one=phase1,deferred=deferred,reach=[sorted(t) for t in reach], + leaf_of=leaf_of,root_frames=root_frame,chain_dims=chain_dims, + adjoint_centre=cvec,adjoint_ordinary=dpart) + data=json.dumps(witness,separators=(',',':')).encode() + (HERE/'word.json.gz').write_bytes(gzip.compress(data,mtime=0)) +''' + new = once(new, marker, extra + marker) + derived = out / 'producer.py' + derived.write_text(new) + (out / 'producer.patch').write_text(''.join(difflib.unified_diff( + original.splitlines(True), new.splitlines(True), + fromfile='PR110/complex_deferred.py', tofile='adapted/producer.py'))) + (out / 'adapter-source.py').write_bytes(Path(__file__).read_bytes()) + paths = [source, case/'graph.bin', case/'graph.labels', case/'matched.json', Path(__file__)] + (out / 'SOURCE.json').write_text(json.dumps(dict( + compiler_pin='09775e9f3fbf1900175010bcd0c3d6d1dbf65ffe', + order=a.order, input_sha256={str(p):hashlib.sha256(p.read_bytes()).hexdigest() for p in paths}, + derived_sha256=hashlib.sha256(new.encode()).hexdigest()),indent=2)+'\n') + print('Running explicit deferred compile; log', out/'run.log', flush=True) + with (out/'run.log').open('w') as log: + subprocess.run([sys.executable,str(derived)],stdout=log,stderr=subprocess.STDOUT,check=True) + print((out/'run.log').read_text(), flush=True) + + +if __name__ == '__main__': + main() diff --git a/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/defer_exact_only.py b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/defer_exact_only.py new file mode 100644 index 0000000000..2fc9ae2e47 --- /dev/null +++ b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/defer_exact_only.py @@ -0,0 +1,43 @@ +#!/usr/bin/env python3 +"""Exact-certificate exporter; random scalar sampling deliberately omitted. + +This adapter preserves the original matching, scalar operations, integer +adjoint, exact clean-support replay, every F2 incidence check and full rank +accounting. It replaces two costly random scalar evaluations with a required +separate all-input certificate (verify_deferred_word.py). An exported profile +alone is not acceptance. The original sampled exporter is preserved unchanged. +""" +from pathlib import Path +import sys + + +def main(): + original=Path(__file__).with_name('defer_complex_graph.py') + text=original.read_text() + def once(old,new): + nonlocal text + assert text.count(old)==1,old + text=text.replace(old,new) + once("choices=('ascending', 'reversed')","choices=('ascending', 'reversed', 'numeric')") + once(" # Use exact integer adjoint coordinates with common denominator42.", + " if a.order == 'numeric':\n" + " new = once(new, 'key=lambda i: ((i ^ 1) in (a, b), i)', 'key=lambda i: i')\n" + " # Use exact integer adjoint coordinates with common denominator42.") + once(" marker = \" (HERE / 'complex-profile.json').write_text\"", + " new = once(new, ' rep = [replay(seed) for seed in (1, 2)]',\n" + " ' # Random scalar sampling omitted; separate exact all-input audit REQUIRED.')\n" + " new = once(new, \" require(all(r == (True, True) for r in rep), 'replay %s' % rep)\",\n" + " \" print('Exact-only export: random dirty scalar replay not run', flush=True)\")\n" + " new = once(new, \"replay=dict(seeds=[1, 2], scratch_restored=True, y_plus_x=True, field='Z/(2^61-1)')\",\n" + " \"replay=dict(random_tests_run=False, exact_all_input_audit_required=True)\")\n" + " marker = \" (HERE / 'complex-profile.json').write_text\"") + # Keep the base adapter and this wrapper in the generated source closure. + once(" paths = [source, case/'graph.bin', case/'graph.labels', case/'matched.json', Path(__file__)]", + " (out/'base-adapter-source.py').write_bytes(Path(__file__).with_name('defer_complex_graph.py').read_bytes())\n" + " paths = [source, case/'graph.bin', case/'graph.labels', case/'matched.json', Path(__file__), Path(__file__).with_name('defer_complex_graph.py')]") + namespace={'__file__':str(Path(__file__).resolve()),'__name__':'exact_only_adapter'} + exec(compile(text,str(original),'exec'),namespace) + namespace['main']() + + +if __name__=='__main__':main() diff --git a/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/eliminate_terminal_roles.py b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/eliminate_terminal_roles.py new file mode 100644 index 0000000000..8adc29ac9b --- /dev/null +++ b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/eliminate_terminal_roles.py @@ -0,0 +1,194 @@ +#!/usr/bin/env python3 +"""Explicit terminal-role deletion, retaining old garbage/front schedules. + +Input is an exported deferred word and its complete one-child profile. +The literal stage-one event word keeps every retained auxiliary update at +its old time; it redirects only destination-only terminal roles into Y. +""" +import argparse +from collections import Counter +import gzip +import hashlib +import json +from pathlib import Path +import random +import sys +from frame_extension import basis, contains +from inventory_terminal_schedule import inspect + + +def need(ok, msg): + if not ok: raise ValueError(msg) + + +def main(): + if sys.flags.optimize: raise ValueError('Assertions required') + p=argparse.ArgumentParser(description=__doc__) + p.add_argument('--word',type=Path,required=True);p.add_argument('--profile',type=Path,required=True) + p.add_argument('--inventory',type=Path,required=True);p.add_argument('--out',type=Path,required=True) + a=p.parse_args();a.out.mkdir(parents=True,exist_ok=False) + w=json.loads(gzip.decompress(a.word.read_bytes()));oldprof=json.loads(a.profile.read_text()) + inv=json.loads(a.inventory.read_text()) + need(hashlib.sha256(a.word.read_bytes()).hexdigest()==inv['word_sha256'],'inventory word hash') + schedule=inspect(w,set(inv['terminal_roles'])) + removed=set(schedule['accepted']) + need(removed and not schedule['rejected'],'prescribed simultaneous candidates') + frames={int(k):v for k,v in w['frames'].items()};sigma={int(k):v for k,v in w['sigma'].items()} + roots={int(k):v for k,v in w['role_root'].items()};leaves={int(k):v for k,v in w['leaf_of'].items()} + rootframes={int(k):v for k,v in w['root_frames'].items()} + phase1=set(w['phase_one']);dset=set(w['deferred']);v,h=w['v'],w['h'];m=h*h + active=[s for s in range(w['R']) if s not in removed] + # Each event stores its original source index, making temporal claims + # independently inspectable. A target_front executes even if its old + # associated garbage readout was removed. + events=[];current=[[] for _ in range(v)];target_paths=[[[]] for _ in range(v)] + def front(t,F,why): + need(contains(current[t],F),'target frame reversal') + if basis(current[t])!=basis(F): + events.append(['target_front',t,F,why]);target_paths[t].append(F) + current[t]=F + def redirect(s,src,frame,index,data=False): + j=roots[s];t=w['target'][j];coeff=21 if jx:new_target[y-x]+=2*v + for s in removed: + ds=w['chain_dims'][s] + for x,y in zip(ds[:-1],ds[1:-1]): + if y>x:deleted_hist[y-x]+=2*v + deleted_hist[h-ds[-2]]+=2*v + deleted_hist[m-h+ds[0]]+=2*v + deleted_hist.pop(0,None) + need(sum(t*c for t,c in deleted_hist.items())==2*v*len(removed)*m,'deleted role mass') + z=Counter({int(t):c for t,c in oldprof['child_multiplicities'].items()}) + z.subtract(deleted_hist);z.subtract(old_target);z.update(new_target) + need(all(c>=0 for c in z.values()),'negative child multiplicity') + z=Counter({t:c for t,c in z.items() if c}) + newR=w['R']-len(removed);newW=2*v*v+2*v*newR;rank=sum(t*c for t,c in z.items()) + need(newW*m-rank==oldprof['deficit'],'complete deficit changed') + incoming=sum(e[0] in ('direct_aux','direct_input') for e in events) + oldscalar=oldprof['literal_scalar_terms'] + # Each removed role had one ordinary adjoint read and one final read. + # An incoming gate/injection and its inverse cost two old operations; + # replacing those by one ±1/2 output update costs at most one of the + # same generously expanded fixed-coefficient scalar groups. + newscalar=oldscalar-2*len(removed)-incoming + need(newscalar<=oldscalar,'local scalar bound increase') + prof=dict(oldprof);prof.update(pre_elimination_R=w['R'],R=newR,W=newW,total_rank=rank, + terminal_elimination_count=len(removed),terminal_direct_updates=incoming, + child_multiplicities=dict(sorted(z.items())),maxchild=max(z), + literal_scalar_terms=newscalar, + safe_one_axis_scalar_groups=(4*oldprof['max_coefficient_bits']+16)*newscalar, + deferred_roles=oldprof['deferred_roles']-len(removed), + role_count_scope='Explicit terminal-elided word; old DAG c+q-links is pre-elimination only.') + dd=Counter({int(k):c for k,c in oldprof['deferred_dims'].items()}) + for s in removed:dd[len(basis(sigma[s]))]-=1 + prof['deferred_dims']={k:c for k,c in sorted(dd.items()) if c} + receipt=dict(removed=sorted(removed),active_roles=active,events=events, + target_paths=target_paths,deleted_child_multiplicities=dict(sorted(deleted_hist.items())), + old_target_histogram=dict(sorted(old_target.items())), + new_target_histogram=dict(sorted(new_target.items())), + target_delta={t:new_target[t]-old_target[t] for t in sorted(old_target.keys()|new_target.keys()) + if new_target[t]!=old_target[t]}, + input_word_sha256=hashlib.sha256(a.word.read_bytes()).hexdigest()) + # Scalar replay is separate from the exact structural/adjoint proof. + P=(1<<61)-1;inv42=pow(42,P-2,P) + trip=[tuple(i for i in range(h) if mask>>i&1) for mask in []] + from itertools import combinations + trip=list(combinations(range(h),3)) + scatter=[[2-21*(i in T) for T in trip] for i in range(h)] + def replay(seed): + rng=random.Random(seed);x=[rng.randrange(P) for _ in range(v)] + z0={s:rng.randrange(P) for s in active};aux=dict(z0) + y0=[rng.randrange(P) for _ in range(v)];y=list(y0) + # Batched centers change only evaluator work, not exported word. + center_pending=[0]*h + def read(s,sign,seeded): + if seeded: + j=roots[s] + if w['kind'][j]:cv=[0]*h;cv[int(w['centre_of'][str(j)])]=1;dp={} + else:cv=None;dp={w['target'][j]:21 if j p and (pivots[q] >> p) & 1: + pivots[q] ^= pivots[p] + return [pivots[p] for p in sorted(pivots, reverse=True)] + + +def contains(small, large): + return len(basis(list(small) + list(large))) == len(basis(large)) + + +def gram_rank(rows): + rows = basis(rows) + return len(basis(sum(dot(x, y) << j for j, y in enumerate(rows)) for x in rows)) + + +def kernel(functionals, h): + rows = basis(functionals) + pivots = {x.bit_length() - 1 for x in rows} + return basis((1 << c) | sum(((x >> c) & 1) << (x.bit_length() - 1) for x in rows) + for c in range(h) if c not in pivots) + + +def restrict(rows, functionals): + rows = basis(rows) + for f in functionals: + indices = [i for i, x in enumerate(rows) if dot(x, f)] + if indices: + i = indices[0] + pivot = rows[i] + rows = basis(x ^ (pivot if dot(x, f) else 0) + for j, x in enumerate(rows) if j != i) + return rows + + +def extend(E, B): + """Return nondegenerate U with E⊆U⊆B and dim U=rank Gram(B).""" + E, B = basis(E), basis(B) + require(contains(E, B), 'baseline frame outside feasible intersection') + require(gram_rank(E) == len(E), 'baseline frame degenerate') + rest = restrict(B, E) + chosen = list(E) + while rest: + i = next((i for i, x in enumerate(rest) if dot(x, x)), None) + if i is not None: + p = rest[i] + chosen.append(p) + rest = basis(x ^ (p if dot(x, p) else 0) + for j, x in enumerate(rest) if j != i) + continue + pair = next(((i, j) for i in range(len(rest)) for j in range(i + 1, len(rest)) + if dot(rest[i], rest[j])), None) + if pair is None: + break # precisely the remaining radical + i, j = pair + p, q = rest[i], rest[j] + chosen.extend((p, q)) + rest = basis(x ^ (p if dot(x, q) else 0) ^ (q if dot(x, p) else 0) + for k, x in enumerate(rest) if k not in (i, j)) + U = basis(chosen) + require(contains(E, U) and contains(U, B), 'extension containment') + require(gram_rank(U) == len(U), 'extension degeneracy') + require(len(U) == gram_rank(B), 'extension not maximal dimension') + return U + + +def enlarge_frames(h, old, order_desc, args, K, successors): + """One reverse-topological pass; leaves remain their original lines.""" + U = {x: list(rows) for x, rows in old.items()} + inverse_cache = {} + def perpendicular(rows): + key = tuple(basis(rows)) + if key not in inverse_cache: + inverse_cache[key] = kernel(key, h) + return inverse_cache[key] + visited = set() + changes = Counter() + witness = {} + for x in order_desc: + require(all(t in visited for t in successors[x]), 'not reverse successor order') + visited.add(x) + if not args[x][0]: + continue + # Intersect ker K with every updated successor frame by adding + # their annihilators. Baseline E is retained, never reselected. + constraints = list(K[x]) + for t in sorted(successors[x]): + constraints.extend(perpendicular(U[t])) + B = kernel(constraints, h) + E = U[x] + U[x] = extend(E, B) + changes[len(E), len(U[x])] += 1 + if len(U[x]) != len(E): + witness[x] = dict(old=basis(E), feasible=B, enlarged=U[x]) + for x in U: + require(contains(old[x], U[x]), 'old frame lost') + require(gram_rank(U[x]) == len(U[x]), 'nondegeneracy final') + require(all(not dot(u, f) for u in U[x] for f in K[x]), 'root annihilator final') + require(all(contains(U[x], U[t]) for t in successors[x]), 'nesting final') + if not args[x][0]: + require(basis(old[x]) == basis(U[x]), 'leaf frame changed') + receipt = dict(policy='reverse-successor maximal nondegenerate completion retaining baseline', + changed_nodes=len(witness), + dimension_counts={f'{a}->{b}': c for (a, b), c in sorted(changes.items())}, + changed_frames=witness) + return U, receipt diff --git a/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/inventory_deferred_roles.py b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/inventory_deferred_roles.py new file mode 100644 index 0000000000..dd6ec00164 --- /dev/null +++ b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/inventory_deferred_roles.py @@ -0,0 +1,90 @@ +#!/usr/bin/env python3 +"""Read-only structural elimination inventory of an exported deferred word. + +No word is changed. Terminal candidates additionally require all current +target readout frames to fit their earliest replaced gate frame. +""" +import argparse +from collections import Counter +import gzip +import hashlib +import json +from pathlib import Path +from frame_extension import basis, contains + + +def main(): + p = argparse.ArgumentParser(description=__doc__) + p.add_argument('--word', type=Path, required=True) + p.add_argument('--out', type=Path, required=True) + a = p.parse_args() + w = json.loads(gzip.decompress(a.word.read_bytes())) + frames = {int(k): v for k, v in w['frames'].items()} + sigma = {int(k): v for k, v in w['sigma'].items()} + leaves = {int(k): v for k, v in w['leaf_of'].items()} + roots = {int(k): v for k, v in w['role_root'].items()} + dest, source = [Counter() for _ in range(2)] + gate_frames = [[] for _ in range(w['R'])] + for op in w['ops']: + if op[0] == 'add': + dst, src = op[1], op[2] + elif op[0] == 'copy': + src, dst = op[1], op[2] + else: + continue + dest[dst] += 1 + source[src] += 1 + gate_frames[dst].append(frames[op[3]]) + bytarget = [[] for _ in range(w['v'])] + for s in w['deferred']: + for t in w['reach'][s]: + bytarget[t].append(sigma[s]) + pure = [] + terminal = [] + terminal_blocked = Counter() + for s in range(w['R']): + if s in leaves and dest[s] == 0 and s in sigma: + assert basis(sigma[s]) == basis(frames[w['first_node'][s]]) + assert w['adjoint_centre'][s] is None + pure.append(s) + if s not in roots or w['kind'][roots[s]] or source[s]: + continue + if s not in sigma: + terminal_blocked['not_deferred'] += 1 + continue + t = w['target'][roots[s]] + birth_frame = frames[w['first_node'][s]] + update_frames = ([birth_frame] if s in leaves else []) + gate_frames[s] + if not update_frames: + terminal_blocked['no_updates'] += 1 + continue + if not all(contains(B, F) for B in bytarget[t] for F in update_frames): + terminal_blocked['target_past_update_frame'] += 1 + continue + terminal.append(s) + removed = set(pure) | set(terminal) + hist = Counter() + for s in removed: + ds = w['chain_dims'][s] + for lo, hi in zip(ds[:-1], ds[1:-1]): + if hi > lo: + hist[hi-lo] += 2*w['v'] + hist[w['h']-ds[-2]] += 2*w['v'] + hist[w['h']*w['h']-w['h']+ds[0]] += 2*w['v'] + hist.pop(0, None) + assert sum(k*v for k, v in hist.items()) == 2*w['v']*len(removed)*w['h']**2 + out = dict(word_sha256=hashlib.sha256(a.word.read_bytes()).hexdigest(), + scope='Read-only candidate inventory; combined deletion conflicts and a literal replacement word remain unchecked.', + R=w['R'], deferred_count=len(w['deferred']), + pure_leaf_count=len(pure), pure_leaf_roles=pure, + terminal_count=len(terminal), terminal_roles=terminal, + terminal_blocked=dict(terminal_blocked), union=len(removed), + hypothetical_removed_child_multiplicities=dict(sorted(hist.items())), + source_histogram=dict(sorted(Counter(source[s] for s in pure).items())), + terminal_types={str(k):v for k,v in Counter((s in leaves,dest[s],len(basis(sigma[s]))) for s in terminal).items()}) + a.out.write_text(json.dumps(out,indent=2)+'\n') + print(json.dumps({k:v for k,v in out.items() if not k.endswith('_roles')},indent=2)) + + +if __name__ == '__main__': + main() diff --git a/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/inventory_terminal_schedule.py b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/inventory_terminal_schedule.py new file mode 100644 index 0000000000..1f46f770c2 --- /dev/null +++ b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/inventory_terminal_schedule.py @@ -0,0 +1,61 @@ +"""Exact simultaneous output-chain check for terminal-role candidates.""" +import argparse +from collections import defaultdict +import gzip +import json +from pathlib import Path +from frame_extension import basis, contains + + +def inspect(w, candidates): + frames = {int(k): v for k, v in w['frames'].items()} + sigma = {int(k): v for k, v in w['sigma'].items()} + roots = {int(k): v for k, v in w['role_root'].items()} + leaves = {int(k): v for k, v in w['leaf_of'].items()} + initial = [[] for _ in range(w['v'])] + for s in w['deferred']: + for t in w['reach'][s]: + assert contains(initial[t], sigma[s]) + initial[t] = sigma[s] + bytarget = defaultdict(list) + for s in sorted(set(candidates)): + j = roots[s] + t = w['target'][j] + assert not w['kind'][j] and w['adjoint_centre'][s] is None + assert {int(k):v for k,v in w['adjoint_ordinary'][s].items()} == {t:(21 if j=1 + lo,hi=Q(),Q();terms={} + for t,count in sorted(rows.items()): + assert type(t) is int and type(count) is int and 00 + 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 log_interval(x): + assert x>=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> p & 1: vec ^= r + if vec: + p = vec.bit_length() - 1 + for i in range(len(rows)): + if rows[i] >> p & 1: rows[i] ^= vec + rows.append(vec); piv.append(p) + return rows + + +def kernel(funcs, h): + K = reduce(funcs); piv = [r.bit_length() - 1 for r in K] + out = [] + for c in (i for i in range(h) if i not in piv): + vec = 1 << c + for r, p in zip(K, piv): + if r >> c & 1: vec |= 1 << p + out.append(vec) + return out + + +def restrict(basis, funcs): + B = reduce(basis) + for f in funcs: + if not B: break + vals = [dot(b, f) for b in B] + if not any(vals): continue + k = vals.index(1); pv = B[k] + B = [b ^ pv if val else b for b, val in zip(B, vals)]; B.pop(k) + return reduce(B) + + +def contains(A, B): + RB = reduce(B) + return len(reduce(RB + list(A))) == len(RB) + + +def cap(A, B): + A = reduce(A); B = reduce(B) + if not A or not B: return [] + ker = []; red = [] + for i, vec in enumerate(A + B): + tag = 1 << i + for rv, rt in red: + if vec >> (rv.bit_length() - 1) & 1: vec ^= rv; tag ^= rt + if vec: red.append((vec, tag)) + else: + comb_ = 0 + for k in range(len(A)): + if tag >> k & 1: comb_ ^= A[k] + ker.append(comb_) + return reduce(ker) + + +def nondeg(B): + B = reduce(B); k = len(B) + if not k: return True + M = [sum(dot(B[i], B[j]) << j for j in range(k)) for i in range(k)] + return len(reduce(M)) == k + + +def hopcroft_karp(left, adj): + """maximum bipartite matching; adj[x] = sorted list of right vertices.""" + INF = 1 << 60 + mate_l = {x: None for x in left}; mate_r = {} + while True: + dist = {}; queue = [] + for x in left: + if mate_l[x] is None: dist[x] = 0; queue.append(x) + else: dist[x] = INF + found = INF; head = 0 + while head < len(queue): + x = queue[head]; head += 1 + if dist[x] >= found: continue + for r in adj[x]: + y = mate_r.get(r) + if y is None: found = min(found, dist[x] + 1) + elif dist[y] == INF: dist[y] = dist[x] + 1; queue.append(y) + if found == INF: break + gained = 0 + for x0 in left: + if mate_l[x0] is not None: continue + stack = [(x0, iter(adj[x0]))]; path = [] + while stack: + x, it = stack[-1] + advanced = False + for r in it: + y = mate_r.get(r) + if (y is None and dist[x] + 1 == found) or (y is not None and dist[y] == dist[x] + 1): + path.append((x, r)) + if y is None: + for xx, rr in path: mate_l[xx] = rr; mate_r[rr] = xx + gained += 1; stack = []; break + stack.append((y, iter(adj[y]))); advanced = True; break + else: + dist[x] = INF; stack.pop() + if path: path.pop() + continue + if not advanced: break + if not gained: break + return mate_l + + +from functools import lru_cache +from fractions import Fraction + +def sat_basis(vectors): + piv = {} + for x in vectors: + for p in sorted(piv, reverse=True): + if x >> p & 1: + x ^= piv[p] + if x: + p = x.bit_length() - 1 + for q in piv: + if piv[q] >> p & 1: + piv[q] ^= x + piv[p] = x + return tuple((piv[p] for p in sorted(piv, reverse=True))) + +def sat_dot(a, b): + return (a & b).bit_count() & 1 + +@lru_cache(None) +def sat_contained(A, B): + for x in A: + for r in B: + if x >> r.bit_length() - 1 & 1: + x ^= r + if x: + return False + return True + +@lru_cache(None) +def sat_cap(A, B): + if not A or not B: + return () + red = {} + out = [] + for i, x in enumerate(A + B): + tag = 1 << i + for p in sorted(red, reverse=True): + if x >> p & 1: + r, t = red[p] + x ^= r + tag ^= t + if x: + red[x.bit_length() - 1] = (x, tag) + else: + y = 0 + for j, r in enumerate(A): + if tag >> j & 1: + y ^= r + if y: + out.append(y) + return sat_basis(out) + +@lru_cache(None) +def sat_nondeg(B): + return len(sat_basis((sum((sat_dot(a, b) << j for j, b in enumerate(B))) for a in B))) == len(B) + +@lru_cache(None) +def sat_nonsingular_part(B): + rows = list(B) + out = [] + while rows: + i = next((i for i, x in enumerate(rows) if sat_dot(x, x)), None) + if i is not None: + a = rows.pop(i) + out.append(a) + rows = [x ^ a if sat_dot(x, a) else x for x in rows] + continue + pair = next(((i, j) for i in range(len(rows)) for j in range(i + 1, len(rows)) if sat_dot(rows[i], rows[j])), None) + if pair is None: + break + i, j = pair + a, b = (rows[i], rows[j]) + out.extend((a, b)) + rows = [x ^ (a if sat_dot(x, b) else 0) ^ (b if sat_dot(x, a) else 0) for k, x in enumerate(rows) if k not in (i, j)] + return sat_basis(out) + +def saturated_placement(cand, reach): + # Each extracted block is orthogonal to previously selected blocks. + # A diagonal-one pivot contributes a nondegenerate line; when all + # remaining diagonals vanish, a dot-one pair contributes a hyperbolic + # plane. The residual radical is discarded, not counted as a frame. + cand = {s: sat_basis(B) for s, B in cand.items()} + order = sorted(cand, key=lambda s: (Fraction(-len(cand[s])**2, max(1, len(reach[s]))), -len(cand[s]), s)) + byT = defaultdict(list); placed = {} + for s in order: + X = cand[s]; changed = True + while changed and X: + changed = False + for t in sorted(reach[s]): + for w in byT[t]: + B = placed[w] + if (len(B) >= len(X) and not sat_contained(X, B)) or (len(B) < len(X) and not sat_contained(B, X)): + X = sat_cap(X, B); changed = True + if not X: break + if not X: break + if X and not sat_nondeg(X): + before = X; X = sat_nonsingular_part(X) + assert sat_contained(X, before) and sat_nondeg(X) + assert len(X) < len(before) + changed = True # Extraction can break containment of a smaller target frame. + if X: + assert sat_nondeg(X) and sat_contained(X, cand[s]) + placed[s] = X + for t in reach[s]: byT[t].append(s) + for t, ss in byT.items(): + ss.sort(key=lambda s: (len(placed[s]), s)) + assert all(sat_contained(placed[a], placed[b]) for a, b in zip(ss, ss[1:])) + return placed + +def main(): + with tempfile.TemporaryDirectory(prefix='deferred-stopped-') as work: + prefix = Path(work) / 'complex' + build(24, prefix, central_disjoint=24) + h, v, n, q, args, core, cover, roots, kind, active, ranks, types = load(prefix) + trip = list(combinations(range(h), 3)); require(len(trip) == v, 'triple count') + m = h * h; N = v * v; FULL = (1 << h) - 1 + tmask = [sum(1 << p for p in T) for T in trip] + tid = {T: i for i, T in enumerate(trip)} + + # ------------------------------------------------------------ uses and matching (inherited adjacency) + degree = [0] * n; uses = defaultdict(list); c_add = 0 + for x in range(1, n): + if active[x] and args[x][0]: + c_add += 1 + for pos, y in enumerate(args[x]): degree[y] += 1; uses[y].append(('gate', x, pos)) + for j, x in enumerate(roots): degree[x] += 1; uses[x].append(('root', j)) + def unode(u): return roots[u[1]] if u[0] == 'root' else u[1] + def before(x, u): + y = unode(u) + return (ranks[x], x) < (ranks[y], (n + u[1]) if u[0] == 'root' else y) + def incl(x, y): + tx, ty = types[x], types[y] + if tx == 1 and ty == 1: return not (core[y] & ~core[x]) and not (cover[x] & ~cover[y]) + if tx in (1, 2) and ty == 2: return not (cover[x] & ~cover[y]) + if tx == 1 and ty == 3: return bool(core[x] & core[y]) + if tx == 2 and ty == 3: return not (cover[x] & ~core[y]) + if tx == 3 and ty == 2: return cover[y] == FULL + if tx == 3 and ty == 3: return core[x] == core[y] + return False + left = []; adj = {} + for x in range(1, n): + if not (active[x] and args[x][0]): continue + rs = sorted({(y, k) for y in args[x] for k, u in enumerate(uses[y]) if before(x, u) and incl(x, unode(u))}) + if rs: left.append(x); adj[x] = rs + mate = hopcroft_karp(left, adj) + links = {x: r for x, r in mate.items() if r is not None} + R = c_add + q - len(links) + require((c_add, q, len(links), R) == (68800, 8120, 39061, 37859), 'selected graph size') + linked_use = {(y, k): x for x, (y, k) in links.items()} + + # ------------------------------------------------------------ root targets, read coefficients, root functionals + target = [None] * q + for j in range(v): target[j] = j + idx = v + for a, b in combinations(range(h), 2): + others = sorted((i for i in range(h) if i not in (a, b)), key=lambda i: ((i ^ 1) in (a, b), i)) + for i in others: target[idx] = tid[tuple(sorted((a, b, i)))]; idx += 1 + centre_of = {} + for j in range(q): + if kind[j]: + miss = FULL & ~cover[roots[j]]; require(bin(miss).count('1') == 1, 'centre cover') + centre_of[j] = miss.bit_length() - 1 + require(idx + len(centre_of) == q, 'root order') + rootfun = [(1 << centre_of[j]) if kind[j] else tmask[target[j]] for j in range(q)] + + # ------------------------------------------------------------ lifted binary frames, monotone + succ = defaultdict(set); droot = defaultdict(set) + for x in range(1, n): + if not active[x]: continue + for k, u in enumerate(uses[x]): + if (x, k) in linked_use: continue + (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1])) + for x, (y, k) in links.items(): + u = uses[y][k]; (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1])) + order_desc = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x), reverse=True) + K = {} + for x in order_desc: + rows = [rootfun[j] for j in droot[x]] + for t in succ[x]: rows += K[t] + K[x] = reduce(rows) + def envelope(x): + if not args[x][0]: return [tmask[x - 1]] + if types[x] == 2: return [1 << i for i in range(h) if cover[x] >> i & 1] + require(types[x] == 1, 'only ordinary and common-pair labels occur') + ks = [i for i in range(h) if (cover[x] & ~core[x]) >> i & 1] + require(len(ks) == ranks[x], 'common-pair support') + return [core[x] | (1 << k) for k in ks] + U = {} + for x in range(1, n): + if not active[x]: continue + if not args[x][0]: U[x] = envelope(x); continue + B = kernel(K[x], h) + require(contains(envelope(x), B), 'label outside lifted frame') + U[x] = B if nondeg(B) else envelope(x) + changed = True + while changed: + changed = False + for x in order_desc: + if args[x][0] and any(not contains(U[x], U[t]) for t in succ[x]): + env = envelope(x) + if len(reduce(U[x])) != len(reduce(env)) or not contains(U[x], env): U[x] = env; changed = True + dimU = {x: len(reduce(B)) for x, B in U.items()} + + # ------------------------------------------------------------ explicit role compile + order = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x)) + holds = []; first_node = []; ops = []; edge_key = {}; role_root = {} + def new_role(node): holds.append([node]); first_node.append(node); return len(holds) - 1 + def serve(s, y, k): + u = uses[y][k] + if u[0] == 'gate': edge_key[(y, k)] = s + else: role_root[s] = u[1] + for x in order: + free = [k for k in range(len(uses[x])) if (x, k) not in linked_use] + if not args[x][0]: + for k in free: + s = new_role(x); ops.append(('src', s, x)); serve(s, x, k) + continue + a, b = args[x] + ka = next(k for k, u in enumerate(uses[a]) if u == ('gate', x, 0)) + kb = next(k for k, u in enumerate(uses[b]) if u == ('gate', x, 1)) + sa, sb = edge_key.pop((a, ka)), edge_key.pop((b, kb)) + if x in links and links[x][0] == a: sa, sb = sb, sa + piv, oth = sa, sb + ops.append(('add', piv, oth, x)); holds[piv].append(x); holds[oth].append(x) + if x in links: serve(oth, *links[x]) + require(free, 'every use linked at node %d' % x) + serve(piv, x, free[0]) + for k in free[1:]: + f = new_role(x); ops.append(('copy', piv, f, x)); serve(f, x, k) + require(not edge_key and len(holds) == R, 'compile') + Rr = R + + # ------------------------------------------------------------ B. the word computes every root value + rng = random.Random(20261008) + xs = [rng.randrange(P) for _ in range(v)] + val = [0] * n + for i in range(v): val[i + 1] = xs[i] + for x in order: + if args[x][0]: val[x] = (val[args[x][0]] + val[args[x][1]]) % P + leaf_of = {s: first_node[s] for s in range(Rr) if not args[first_node[s]][0]} + a_ = [0] * Rr + for s, leaf in leaf_of.items(): a_[s] = xs[leaf - 1] + for o in ops: + if o[0] == 'add': a_[o[1]] = (a_[o[1]] + a_[o[2]]) % P + elif o[0] == 'copy': a_[o[2]] = (a_[o[2]] + a_[o[1]]) % P + require(all(a_[s] == val[roots[j]] for s, j in role_root.items()), 'root values') + + # ------------------------------------------------------------ phase one and garbage reach + def touch(o): return [o[1], o[2]] if o[0] in ('add', 'copy') else [] + prev = {}; pred = defaultdict(list); last = {} + for i, o in enumerate(ops): + for s in touch(o): + if s in prev: pred[i].append(prev[s]) + prev[s] = i; last[s] = i + centre_roles = [s for s, j in role_root.items() if kind[j]] + Anc = set(); st = [last[s] for s in centre_roles] + while st: + i = st.pop() + if i not in Anc: Anc.add(i); st.extend(pred[i]) + touched = set(centre_roles) + for i in Anc: touched.update(touch(ops[i])) + require(all(last[s] in Anc for s in centre_roles), 'centres complete in phase one') + reach = [set() for _ in range(Rr)]; reach_all = [False] * Rr + for s, j in role_root.items(): + if kind[j]: reach_all[s] = True + else: reach[s].add(target[j]) + for o in reversed(ops): + if o[0] == 'add': reach[o[2]] |= reach[o[1]]; reach_all[o[2]] = reach_all[o[2]] or reach_all[o[1]] + elif o[0] == 'copy': reach[o[1]] |= reach[o[2]]; reach_all[o[1]] = reach_all[o[1]] or reach_all[o[2]] + + # ------------------------------------------------------------ deferral frames, insertion nesting + def F0(s): return U[first_node[s]] + cand = {} + for s in range(Rr): + if s in touched or reach_all[s]: continue + S_ = restrict(F0(s), [tmask[t] for t in reach[s]]) + if S_ and nondeg(S_): cand[s] = S_ + placed = saturated_placement(cand, reach) + deferred = sorted(placed, key=lambda s: (len(placed[s]), s)); dset = set(deferred) + + # ------------------------------------------------------------ C. replay with arbitrary scratch and data + inv = lambda a: pow(a % P, P - 2, P); HALF = inv(2); I21 = inv(21) + cvec = [None] * Rr; dpart = [dict() for _ in range(Rr)] + for s, j in role_root.items(): + if kind[j]: c = [0] * h; c[centre_of[j]] = 1; cvec[s] = c + else: dpart[s][target[j]] = (P - HALF) if j >= v else HALF + seed_c = {s: (None if cvec[s] is None else list(cvec[s])) for s in role_root} + seed_d = {s: dict(dpart[s]) for s in role_root} + def addc(dst, src): + if cvec[src] is not None: + cvec[dst] = list(cvec[src]) if cvec[dst] is None else [(p + q_) % P for p, q_ in zip(cvec[dst], cvec[src])] + for t, c in dpart[src].items(): dpart[dst][t] = (dpart[dst].get(t, 0) + c) % P + for o in reversed(ops): + if o[0] == 'add': addc(o[2], o[1]) + elif o[0] == 'copy': addc(o[1], o[2]) + scatter = [[(I21 - (HALF if i in trip[t] else 0)) % P for t in range(v)] for i in range(h)] + def readout(y, s, value, sign, seed=False): + cv = seed_c[s] if seed else cvec[s]; dp = seed_d[s] if seed else dpart[s] + if cv is not None: + for i, ci in enumerate(cv): + if ci: + f = sign * ci * value % P; row = scatter[i] + for t in range(v): y[t] = (y[t] + f * row[t]) % P + for t, c in dp.items(): y[t] = (y[t] + sign * c * value) % P + phase1 = sorted(Anc); rest = [i for i in range(len(ops)) if i not in Anc] + def replay(seed): + rng = random.Random(seed) + x = [rng.randrange(P) for _ in range(v)]; z = [rng.randrange(P) for _ in range(Rr)] + y0 = [rng.randrange(P) for _ in range(v)]; a = list(z); y = list(y0) + for s in range(Rr): + if s not in dset: readout(y, s, a[s], -1) + for s, leaf in leaf_of.items(): + if s not in dset: a[s] = (a[s] + x[leaf - 1]) % P + def run(i, sign=1): + o = ops[i] + if o[0] == 'add': a[o[1]] = (a[o[1]] + sign * a[o[2]]) % P + elif o[0] == 'copy': a[o[2]] = (a[o[2]] + sign * a[o[1]]) % P + for i in phase1: run(i) + for s in centre_roles: readout(y, s, a[s], +1, True) + for s in deferred: readout(y, s, a[s], -1) + for s in deferred: + if s in leaf_of: a[s] = (a[s] + x[leaf_of[s] - 1]) % P + for i in rest: run(i) + for s, j in role_root.items(): + if not kind[j]: readout(y, s, a[s], +1, True) + for i in reversed(range(len(ops))): run(i, -1) + for s, leaf in leaf_of.items(): a[s] = (a[s] - x[leaf - 1]) % P + return a == z, all((y[t] - y0[t] - x[t]) % P == 0 for t in range(v)) + rep = [replay(seed) for seed in (1, 2)] + require(all(r == (True, True) for r in rep), 'replay %s' % rep) + + # ------------------------------------------------------------ D. exact F2 frame facts + root_frame = {} + for s, j in role_root.items(): + root_frame[s] = [1 << i for i in range(h) if i != centre_of[j]] if kind[j] else kernel([tmask[target[j]]], h) + FULLB = [1 << i for i in range(h)] + chain_dims = [] + for s in range(Rr): + seq = [placed.get(s, []), F0(s)] + [U[x] for x in holds[s][1:]] + if s in root_frame: seq.append(root_frame[s]) + seq.append(FULLB) + require(all(contains(A, B) for A, B in zip(seq, seq[1:])), 'role chain nesting %d' % s) + require(all(nondeg(B) for B in seq[1:-1] if B), 'degenerate frame on role %d' % s) + chain_dims.append([len(reduce(B)) for B in seq]) + for s, X in placed.items(): + require(contains(X, F0(s)) and nondeg(X), 'deferral frame %d' % s) + require(all(not any(dot(xv, tmask[t]) for xv in X) for t in reach[s]), 'target frame %d' % s) + byT2 = defaultdict(list) + for s in deferred: + for t in reach[s]: byT2[t].append(s) + for t, ss in byT2.items(): + ss.sort(key=lambda s: (len(placed[s]), s)) + require(all(contains(placed[p], placed[q_]) for p, q_ in zip(ss, ss[1:])), 'target chain %d' % t) + + # ------------------------------------------------------------ E. one-child histogram + z = Counter() + for s in range(Rr): + ds = chain_dims[s] + for a, b in zip(ds[:-1], ds[1:-1]): + if b > a: z[b - a] += 2 * v + lastd = ds[-2] + if s in role_root and kind[role_root[s]]: z[h - 1] += 2 * v # copied centre transform + z[h - lastd] += 2 * v # final growth to F + z[m - h + ds[0]] += 2 * v # exterior, gauged by sigma + levels = defaultdict(set) + for s in deferred: + for t in reach[s]: levels[t].add(len(placed[s])) + for t in range(v): + ds = sorted(levels[t] | {0, h - 1}) + for a, b in zip(ds, ds[1:]): z[b - a] += 2 * v # target fronts + z[h - 1] += 2 * N # data-wire fronts + z[(h - 1) ** 2] += 2 * N # data macros + z[1] += N # endpoint copies + z.pop(0, None) + W = 2 * N + 2 * v * R; L = 2 * v * h * (h - 1); s_ = W * m - N + L + require(sum(t * c for t, c in z.items()) == s_, 'complex rank mass') + require(all(0 < t < m for t in z), 'children below m') + out = dict(h=h, v=v, additions=c_add, roots=q, links=len(links), R=R, m=m, N=N, W=W, L=L, total_rank=s_, + deficit=N - L, maxchild=max(z), phase_one_ops=len(Anc), phase_one_roles=len(touched), + deferred_roles=len(deferred), + deferred_dims=dict(sorted(Counter(len(X) for X in placed.values()).items())), + lifted_additions=sum(1 for x in U if args[x][0] and dimU[x] > ranks[x]), + replay=dict(seeds=[1, 2], scratch_restored=True, y_plus_x=True, field='Z/(2^61-1)'), + child_multiplicities=dict(sorted(z.items()))) + (HERE / 'complex-profile.json').write_text(json.dumps(out, indent=1) + '\n') + print('PASS complex: R=%d, deferred roles %d, maxchild %d, rank mass %d' % (R, len(deferred), max(z), s_)) + + +if __name__ == '__main__': + main() diff --git a/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/regenerate_graph_118.py b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/regenerate_graph_118.py new file mode 100644 index 0000000000..195d73db4a --- /dev/null +++ b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/regenerate_graph_118.py @@ -0,0 +1,54 @@ +#!/usr/bin/env python3 +"""Regenerate only the pinned PR118 scalar graph and matched physical profile.""" +import argparse +from hashlib import sha256 +import importlib.util +import json +import os +from pathlib import Path +import shlex +import subprocess +import sys +from pr118_sources import check_base,PACKAGE + +sys.dont_write_bytecode=True +if not __debug__:raise SystemExit('Assertions required') +EXPECTED={ + 'graph.bin':'4ef7308feb5cbe0da4f35f8fe69eba89ec8f4cc7de174bc5468843e4e89f9a44', + 'graph.labels':'8d5133c205191ad80f19deae946a51ebcb546fd8a0302c8e8f0c5575f122bfc0', + 'graph.json':'1a1b287daccb0929f6e24e3648f57a9b2835ef4779df051eb8441e1b89b34c03', + 'matched.json':'1f633cae6f1eee1a0fbe3c7af30fa041553ca47417c83fb3b591230dbcdff586', +} + + +def generate(repo,output): + repo=repo.resolve();binding=check_base(repo) + output.mkdir(parents=True,exist_ok=False) + source=repo/PACKAGE/'producer.py' + spec=importlib.util.spec_from_file_location('checked_replayed_producer',source) + producer=importlib.util.module_from_spec(spec);spec.loader.exec_module(producer) + producer.build(24,output/'graph',24) + compiler=shlex.split(os.environ.get('CXX','c++')) + binary=output/'matcher' + subprocess.run([*compiler,'-O3','-std=c++17',str(repo/'scripts/endpoint_gauge/match_complex_general.cpp'),'-o',str(binary)],check=True) + row=json.loads(subprocess.check_output([str(binary),str(output/'graph.bin'),str(output/'graph.labels')],text=True)) + assert (row['h'],row['v'],row['c'],row['q'],row['matched'],row['R'])==(24,2024,91770,8120,71185,28705) + (output/'matched.json').write_text(json.dumps(row,indent=2,sort_keys=True)+'\n') + observed={name:sha256((output/name).read_bytes()).hexdigest() for name in EXPECTED} + assert observed==EXPECTED + receipt=dict(source_binding=binding,generated_hashes=observed, + pair_root_order='numeric i, not aligned parity order', + scope='Exact scalar support/center/scatter/frame replay plus matching; deferred word and assembly not rerun here') + (output/'receipt.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n') + return receipt + + +def main(): + ap=argparse.ArgumentParser(description=__doc__) + ap.add_argument('--repo',type=Path,required=True) + ap.add_argument('--output',type=Path,required=True) + a=ap.parse_args();generate(a.repo,a.output) + print('PASS pinned PR118 scalar graph and matching',flush=True) + + +if __name__=='__main__':main() diff --git a/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/reselect_deferrals.py b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/reselect_deferrals.py new file mode 100644 index 0000000000..527c5d8788 --- /dev/null +++ b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/reselect_deferrals.py @@ -0,0 +1,95 @@ +#!/usr/bin/env python3 +"""Apply pinned PR114's refined placement to a frozen explicit scalar word. + +This is a credited composition experiment, not a new claim for radical +extraction or dim-squared/reach priority. Every old scalar operation, frame, +and exact adjoint is retained. A separate checker must verify the new schedule. +""" +import argparse +import ast +from collections import Counter,defaultdict +import gzip +import hashlib +import importlib.util +import json +from pathlib import Path +import shutil +import sys +from functools import lru_cache +from fractions import Fraction +from types import SimpleNamespace + + +def main(): + ap=argparse.ArgumentParser(description=__doc__) + ap.add_argument('--source',type=Path,required=True) + ap.add_argument('--placement-repo',type=Path) + ap.add_argument('--output',type=Path,required=True) + a=ap.parse_args();assert __debug__ + a.output.mkdir(parents=True,exist_ok=False) + path=(a.placement_repo.resolve()/'research/cyclic-deferred/complex_deferred.py' + if a.placement_repo else Path(__file__).with_name('references')/'placement_5633a2.py') + assert hashlib.sha256(path.read_bytes()).hexdigest()=='910f86649f72dab4490562f1fa0ea7f887ee5849f888fa37dd4f8e832d3eb47d' + # Extract the exact pure functions without executing upstream producer + # imports or main. The entire unmodified, credited source is retained. + names={'dot','reduce','kernel','restrict','contains','cap','nondeg', + 'sat_basis','sat_dot','sat_contained','sat_cap','sat_nondeg', + 'sat_nonsingular_part','saturated_placement'} + tree=ast.parse(path.read_text()) + selected=[node for node in tree.body if isinstance(node,ast.FunctionDef) and node.name in names] + assert {node.name for node in selected}==names + ns={'defaultdict':defaultdict,'lru_cache':lru_cache,'Fraction':Fraction} + exec(compile(ast.Module(body=selected,type_ignores=[]),str(path),'exec'),ns) + lib=SimpleNamespace(**ns) + w=json.loads(gzip.decompress((a.source/'word.json.gz').read_bytes())) + p=json.loads((a.source/'complex-profile.json').read_text()) + h,v,R=w['h'],w['v'],w['R'];m=h*h;N=v*v + U={int(x):b for x,b in w['frames'].items()} + rr={int(s):j for s,j in w['role_root'].items()} + touched={s for s,j in rr.items() if w['kind'][j]} + for i in w['phase_one']: + o=w['ops'][i] + if o[0] in ('add','copy'):touched.update(o[1:3]) + masks=[U[i+1][0] for i in range(v)] + cand={} + for s in range(R): + if s in touched or any(w['adjoint_centre'][s] or []):continue + X=lib.restrict(U[w['first_node'][s]],[masks[t] for t in w['reach'][s]]) + if X and lib.nondeg(X):cand[s]=X + placed=lib.saturated_placement(cand,w['reach']) + w['sigma']=placed;w['deferred']=sorted(placed,key=lambda s:(len(placed[s]),s)) + z=Counter();levels=defaultdict(set) + for s,ds in enumerate(w['chain_dims']): + ds[0]=len(placed.get(s,())) + for x,y in zip(ds[:-1],ds[1:-1]): + assert y>=x + if y>x:z[y-x]+=2*v + if s in rr and w['kind'][rr[s]]:z[h-1]+=2*v + z[h-ds[-2]]+=2*v;z[m-h+ds[0]]+=2*v + for s,X in placed.items(): + assert lib.nondeg(X) and lib.contains(X,U[w['first_node'][s]]) + for t in w['reach'][s]: + assert all(not lib.dot(x,masks[t]) for x in X) + levels[t].add(len(X)) + for t in range(v): + ds=sorted(levels[t]|{0,h-1}) + for x,y in zip(ds,ds[1:]):z[y-x]+=2*v + z[h-1]+=2*N;z[(h-1)**2]+=2*N;z[1]+=N;z.pop(0,None) + assert sum(t*c for t,c in z.items())==p['total_rank'] + p.update(deferred_roles=len(placed),deferred_dims=dict(sorted(Counter(map(len,placed.values())).items())), + child_multiplicities=dict(sorted(z.items())),maxchild=max(z), + replay={'scope':'Changed placement; independent exact verifier required, no inherited random replay claim'}, + placement='Unchanged saturated_placement from PR114 pin5633a22443940f424dc2a09f44b2f447890e0074') + (a.output/'word.json.gz').write_bytes(gzip.compress(json.dumps(w,separators=(',',':')).encode(),mtime=0)) + (a.output/'complex-profile.json').write_text(json.dumps(p,indent=2)+'\n') + # This frozen original producer is provided solely as the same F2 helper + # library consumed by salvage_deferrals.py, not the new placement entrypoint. + shutil.copyfile(a.source/'producer.py',a.output/'producer.py') + (a.output/'REPRODUCE.txt').write_text('Use reselect_deferrals.py, not producer.py, to regenerate this changed placement.\n') + paths=[a.source/'word.json.gz',a.source/'complex-profile.json',a.source/'producer.py',path,Path(__file__)] + (a.output/'SOURCE.json').write_text(json.dumps({str(p.resolve()):hashlib.sha256(p.read_bytes()).hexdigest() for p in paths},indent=2)+'\n') + (a.output/'reselection-source.py').write_bytes(Path(__file__).read_bytes()) + print('PASS credited reselect; candidates',len(cand),'placed',len(placed),flush=True) + + +if __name__=='__main__':main() diff --git a/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/run_deferred_mutants.py b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/run_deferred_mutants.py new file mode 100644 index 0000000000..b4be9c5ce4 --- /dev/null +++ b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/run_deferred_mutants.py @@ -0,0 +1,67 @@ +#!/usr/bin/env python3 +"""Run malformed real-witness files through the actual independent checkers.""" +import argparse +import copy +import gzip +import json +from pathlib import Path +import subprocess +import sys + + +def main(): + p=argparse.ArgumentParser();p.add_argument('--parent',type=Path,required=True) + p.add_argument('--parent-audit',type=Path) + p.add_argument('--terminal',type=Path);p.add_argument('--out',type=Path,required=True) + a=p.parse_args();a.out.mkdir(parents=True,exist_ok=False) + here=Path(__file__).resolve().parent + w=json.loads(gzip.decompress((a.parent/'word.json.gz').read_bytes())) + pr=json.loads((a.parent/'complex-profile.json').read_text()) + if a.terminal: + assert a.parent_audit + ew=json.loads(gzip.decompress((a.terminal/'word.json.gz').read_bytes())) + ep=json.loads((a.terminal/'complex-profile.json').read_text()) + results=[] + def run(name,W,P,terminal=False): + folder=a.out/name;folder.mkdir() + (folder/'word.json.gz').write_bytes(gzip.compress(json.dumps(W,separators=(',',':')).encode(),mtime=0)) + (folder/'complex-profile.json').write_text(json.dumps(P,indent=2)+'\n') + command=[sys.executable,str(here/('verify_terminal_word.py' if terminal else 'verify_deferred_word.py')), + '--case',str(folder),'--output',str(folder/'audit')] + if terminal:command+=['--parent',str(a.parent),'--parent-audit',str(a.parent_audit)] + q=subprocess.run(command,text=True,capture_output=True,timeout=240) + (folder/'stdout.log').write_text(q.stdout);(folder/'stderr.log').write_text(q.stderr) + assert q.returncode!=0 and 'AssertionError' in q.stderr,(name,q.returncode,q.stderr) + results.append(dict(name=name,rejected=True,returncode=q.returncode,command=command, + last_error=q.stderr.strip().splitlines()[-1])) + print('REJECTED',name,flush=True) + z=copy.deepcopy(w) + s=next(i for i,row in enumerate(z['adjoint_ordinary']) if row) + t=next(iter(z['adjoint_ordinary'][s]));z['adjoint_ordinary'][s][t]+=1 + run('adjoint-coefficient',z,pr) + z=copy.deepcopy(w);centres={int(s) for s,j in z['role_root'].items() if z['kind'][j]} + last=max(i for i,o in enumerate(z['ops']) if o[0]!='src' and centres.intersection(o[1:3])) + assert last in z['phase_one'];z['phase_one'].remove(last) + run('center-phase-omission',z,pr) + z=copy.deepcopy(w) + s=next(s for s,B in z['sigma'].items() if B and z['reach'][int(s)]) + target=z['reach'][int(s)][0];mask=z['frames'][str(target+1)][0] + dim=len(z['sigma'][s]);bad=mask&-mask + # Preserve dimension/order and nondegeneracy, but deliberately include + # one norm-one vector outside the required target hyperplane. + coordinates=[bad]+[1<>p&1:b[q]^=b[p] + return tuple(b[p] for p in sorted(b,reverse=True)) + + +@lru_cache(None) +def inside(A,B): + for x in A: + for b in B: + if x>>(b.bit_length()-1)&1:x^=b + if x:return False + return True + + +@lru_cache(None) +def gram_ok(B): + return len(canon(tuple(sum(((x&y).bit_count()&1)<>j&1:v|=1<<(x.bit_length()-1) + rows.append(v) + return canon(tuple(rows)) + + +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--case',type=Path,required=True) + ap.add_argument('--output',type=Path,required=True);a=ap.parse_args() + out=a.output.resolve();out.mkdir(parents=True,exist_ok=False) + wp=a.case/'word.json.gz';w=json.loads(gzip.decompress(wp.read_bytes())) + profile=json.loads((a.case/'complex-profile.json').read_text()) + h,v,n,q,R=(w[k] for k in ('h','v','n','q','R'));m=h*h;N=v*v + trip=list(combinations(range(h),3));assert len(trip)==v + tv=[sum(1<0 + ranks[rank]+=1;events.append(('move',reg,old,f));current[reg]=f + def gate(t,s,c): + nonlocal gate_count + assert t!=s and current[t]==current[s] + events.append(('gate',t,s,c));gate_count+=1 + nondeferred=tuple(s for s in range(R) if s not in ds) + assert all(current[2*v+s]==zero for s in nondeferred) and all(current[v+t]==zero for t in range(v)) + events.append(('old',-1)) + def inject(s,j,c): + move(2*v+s,current[j-1]);gate(2*v+s,j-1,c) + for s,j in leaves.items(): + if s not in ds:inject(s,j,1) + def operation(i,sign=1): + o=ops[i] + if o[0]=='src':return + if sign>0: + f=uf[o[3]] + move(2*v+o[1],f);move(2*v+o[2],f) + if o[0]=='add':gate(2*v+o[1],2*v+o[2],sign) + else:gate(2*v+o[2],2*v+o[1],sign) + for i in phase:operation(i) + for s in sorted(centres): + move(2*v+s,rf[s]);assert all(current[v+t]==zero for t in range(v)) + events.append(('center',s,rf[s],zero,1));ranks[h-1]+=1 + for s in deferred: + f=sf[s];assert current[2*v+s]==f and inside(frames[f],frames[uf[w['first_node'][s]]]) + for t in w['reach'][s]: + assert all((x&tv[t]).bit_count()%2==0 for x in frames[f]);move(v+t,f) + events.append(('deferred',s,-1)) + for s in deferred: + if s in leaves:inject(s,leaves[s],1) + for i in range(len(ops)): + if i not in ps:operation(i) + for s,j in rr.items(): + if not kind[j]: + t=target[j];move(2*v+s,rf[s]);move(v+t,rf[s]) + events.append(('root',s,j,1)) + for s in range(R):move(2*v+s,fullf) + for t in range(v):move(t,fullf) + for i in range(len(ops)-1,-1,-1):operation(i,-1) + for s,j in leaves.items():inject(s,j,-1) + final=current[:] + assert all(current[v+t]==frame(perpendicular(canon((tv[t],)),h)) for t in range(v)) + print('PASS literal grouped stage1 frame trace',len(events),'events',flush=True) + + # Actual reverse-complement trace, not just a doubled histogram. + complement={i:frame(perpendicular(B,h)) for i,B in enumerate(frames[:])} + bank=lambda s:s+v if s full, with C_U rather than C_U^-1. + assert inside(frames[complement[old]],frames[complement[tar]]) + rranks[h-1]+=1 + assert rranks==ranks + assert all(reflected[bank(s)]==complement[f] for s,f in enumerate(initial)) + print('PASS explicit reverse-complement frame trace and fresh-copy ranks',flush=True) + H=Counter({t:2*v*c for t,c in ranks.items()}) + for s in range(R):H[m-h+len(sigma.get(s,()))]+=2*v + H[(h-1)**2]+=2*N;H[1]+=N + claimed={int(t):c for t,c in profile['child_multiplicities'].items()} + assert dict(H)==claimed + W=2*N+2*v*R;mass=sum(t*c for t,c in H.items()) + assert mass==profile['total_rank']==W*m-N+2*v*h*(h-1) + read_terms=sum(v*sum(c!=0 for c in (row or []))+len(d) for row,d in zip(cv,dp)) + nb=max(19*sum(abs(c) for c in (row or []))+max((abs(c) for c in d.values()),default=0) for row,d in zip(cv,dp)) + terms=read_terms+2*sum(o[0]!='src' for o in ops)+2*len(leaves)+q+h*v+4*h*h+8*h+8 + safe=(4*max(1,nb.bit_length())+16)*terms + assert read_terms==profile['literal_readout_terms'] and nb==profile['adjoint_numerator_bound'] + assert safe==profile['safe_one_axis_scalar_groups'] + # Targeted negative controls of the normalized proof and full paid profile. + s=next(s for s,row in enumerate(dp) if row);t=next(iter(dp[s])) + assert dp[s][t]+1!=stored_dp[s][t] # leaves an exact z_s/42 residual + assert touched and next(iter(touched)) not in ds + unpaid=H.copy();unpaid[h-1]-=2*v*h + assert sum(t*c for t,c in unpaid.items())!=mass + receipt=dict(status='PASS independent exact normalized dirty proof and both frame traces', + word_sha256=sha256(wp.read_bytes()).hexdigest(),R=R,W=W,total_rank=mass, + deficit=W*m-mass,forward_grouped_events=len(events),scalar_gate_events=gate_count, + reflected_inverse_signs=inverse_signs,deferred_roles=len(ds), + exact_all_input_clean_transfer=True,exact_integer_adjoint_denominator=42, + exact_all_dirty_normalization=True,reflected_frame_trace=True, + fresh_reflected_center_copies=h,safe_one_axis_scalar_groups=safe, + adjoint_numerator_bound=nb,negative_controls=dict(adjoint_perturbation_detected=True, + touched_role_cannot_defer=True,unpaid_copy_rejected=True), + scope='Finite graph/word/frames, exact normalized dirty algebra, reflected-template implementation and complete child list checked; inherited Gauss normal form, streaming/tape and analytic multiplication interfaces remain dependencies') + (out/'receipt.json').write_text(json.dumps(receipt,indent=2)+'\n') + data=json.dumps(events,separators=(',',':')).encode() + (out/'stage1-grouped-events.json.gz').write_bytes(gzip.compress(data,mtime=0)) + (out/'frames.json.gz').write_bytes(gzip.compress(json.dumps(frames,separators=(',',':')).encode(),mtime=0)) + print(json.dumps(receipt,indent=2)) + + +if __name__=='__main__':main() diff --git a/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/verify_portable_118.py b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/verify_portable_118.py new file mode 100644 index 0000000000..a2addfd1d0 --- /dev/null +++ b/research/shrunk-birth-terminal/references/pr122/research/terminal-elision/verify_portable_118.py @@ -0,0 +1,157 @@ +#!/usr/bin/env python3 +"""Portable exact arithmetic for a changed PR118 deferred complex profile. + +Only the published PR118 bit supplier is used. The pr118_sources helper pins +the complete reused source closure before imports. This verifies arithmetic, not +the generator's scalar/frame/gauge claims. Requires this file, moments.py, +pr118_sources.py and +an unchanged PR118 source closure; the repository may have additive commits. +""" +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys +import moments +import pr118_sources + +sys.dont_write_bytecode=True +if not __debug__:raise SystemExit('Assertions required; optimized Python is forbidden') +PIN='ec862a5af51537495c745d9f2323e8a5736ee265' +MANIFEST='9c5cc05d04537e6604a2dfa0e5f19295599df2fd6f7b72e4822eca51b854b583' +CGRID=10**14;KGRID=10**17;BACKOFF=Q(1,10**14) + + +def module(name,path): + spec=importlib.util.spec_from_file_location(name,path) + value=importlib.util.module_from_spec(spec);spec.loader.exec_module(value) + return value + + +def load(repo): + pr118_sources.check_base(repo) + package=repo/pr118_sources.PACKAGE + api=module('portable_pinned_arithmetic',package/'certificate.py') + old=api.exact() + assert api.js(old)==json.loads((package/'certificate.json').read_text()) + moments.configure(repo) + return api,old + + +def profile(p): + p=dict(p);p['child_multiplicities']={int(t):n for t,n in p['child_multiplicities'].items()} + assert (p['h'],p['v'],p['m'],p['N'])==(24,2024,576,2024**2) + assert p['W']==2*p['N']+2*p['v']*p['R'] + assert p['L']==2*p['v']*24*23 + assert p['total_rank']==p['W']*p['m']-p['N']+p['L'] + assert p['deficit']==p['N']-p['L']==1862080 + z=p['child_multiplicities'] + assert all(type(t) is int and 00 for t,n in z.items()) + assert max(z)==p['maxchild'] and sum(t*n for t,n in z.items())==p['total_rank'] + return p + + +def enclose(api,p,a): + first=moments.exact_moment(p['m'],p['W'],p['child_multiplicities'],a) + lo,hi=moments.independent_moment(p,a,api.js(first['terms'])) + return dict(primary=first,independent=dict(lower=lo,upper=hi)) + + +def root(api,p): + lo,hi=1,CGRID//1000 + while hi-lo>1: + middle=(lo+hi)//2 + interval=moments.exact_moment(p['m'],p['W'],p['child_multiplicities'],Q(middle,CGRID)) + if interval['upper']<1:lo=middle + elif interval['lower']>1:hi=middle + else:raise ArithmeticError('Insufficient interval precision') + a,b=Q(lo,CGRID),Q(hi,CGRID) + yes,no=enclose(api,p,a),enclose(api,p,b) + assert yes['primary']['upper']<1 and yes['independent']['upper']<1 + assert no['primary']['lower']>1 and no['independent']['lower']>1 + return dict(saving=a,next_saving=b,accepted=yes,rejected=no) + + +def changed_bridge(api,bit,p): + row=dict(h=24,v=2024,c=p['additions'],central_disjoint=24) + bridge=api.copied_bridge(bit,p,[row,row]) + local=p['safe_one_axis_scalar_groups'] + assert type(local) is int and local>0 and p['exact_clean_roots'] + assert p['adjoint_denominator']==42 + assert local==(4*p['max_coefficient_bits']+16)*p['literal_scalar_terms'] + sparse=bridge['complex']['scalar_group_upper'];G=max(sparse,4*p['v']*local) + W,m,s=p['W'],p['m'],p['total_rank'];L=W+m+G+1 + E=64*L**3;charge=2*G*W*W+8*s+4*W+4+32*m;B=s+E;C0=32*m*B*B + assert charge<=50*L**3=s+E and 2*B+18=sum(before[:k]) for k in range(1,5)),'majorization') + check(after!=before,'strict majorization') + for z in before: + if z:formula[z]-=2*v + for z in after: + if z:formula[z]+=2*v + rows.append(dict(role=s,target=t,sigma=sig,first=f,last_old_target=M[t],before=before,after=after)) + actual=Counter({int(t):c for t,c in new['child_multiplicities'].items()}) + actual.subtract({int(t):c for t,c in old['child_multiplicities'].items()}) + actual[m]+=old['W']-new['W'] + check(all(actual[t]==formula[t] for t in actual.keys()|formula.keys()),'full-profile linkage') + hinges=[sum(min(t,k)*c for t,c in actual.items()) for k in range(1,m+1)] + check(max(hinges)==0 and min(hinges)<0,'all-concave full profile') + check(old['deficit']==new['deficit'],'deficit') + out=dict(passed=True,roles=len(rows),packet_rows=rows,full_hinge_differences=hinges, + complete_padded_delta={t:c for t,c in sorted(actual.items()) if c}, + statement='New profile plus (W_old−W_new) width-m dummy children strictly improves every power t^p for 00:move(('a',dst),U[o[3]]);move(('a',src),U[o[3]]) + scalar(('a',dst),('a',src),sign) + elif mode=='input': + _,s,j,sign=row;move(('a',s),current[('x',j-1)]) + scalar(('a',s),('x',j-1),sign) + elif mode in ('direct_aux','direct_input'): + _,t,src,num,F,i,s=row;F=canon(tuple(F));directs+=1 + reg=('a',src) if mode=='direct_aux' else ('x',src-1) + if mode=='direct_aux':move(reg,F) + assert current[reg]==F and current[('y',t)]==F + scalar(('y',t),reg,num,42) + else: + assert mode=='readout';_,s,sign,seeded,tag=row + assert s in active + if tag=='center': + assert seeded and sign==1;move(('a',s),rf[s]) + assert all(current[('y',j)]==zero for j in range(v)) + trace.append(('copy_read',s,rf[s],zero,sign));ranks[h-1]+=1 + elif tag=='ordinary': + j=roots[s];t=w['target'][j];move(('a',s),rf[s]) + assert current[('y',t)]==rf[s] and sign==1 and seeded + 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