{ "what": "The self-audit of cert-machine, Phase 3 — the mutation campaign (M1 and M5 of the pre-registration): for every register row of a built family, mutants derived from the row's pinned record entry by one named transformation of the class table, each FALSE one witnessed by a standard-library script that shares no code with the decider, each decided by the row's own decider and by a double-precision checker at three tolerances; outcomes derived from (truth, witness, word); every mutant pinned by the sha256 of its canonical JSON, regenerable from the pinned record by its class. Written by tools/run-selfaudit-mutations.js; --check re-derives every outcome and total from the stored fields.", "name": "selfaudit", "phase": 3, "generated": "2026-10-21T17:33:07.956Z", "git": "2311ac2c", "machine": { "os": "Darwin 27.0.0", "cpu": "Apple M2", "node": "v24.14.1", "python": "Python 3.9.6" }, "seconds": 1015.7, "preregistration": { "path": "notes/selfaudit-preregistration-2026-10-20.md", "sha256": "b799715c0f840d2a201b7a7907025137e70653095319ad8c97a3b7f8be7b23c2" }, "inventory": { "path": "certs/selfaudit-inventory.json", "sha256": "b5f226e1eff7d9810a0a95b59039de184316f589ee8f0de0d6b9b2734a015b8e" }, "inputs": { "register": { "path": "certs/claims-ledger.json", "sha256": "270094aa3c9218fa000654ae3020d388e3821b845e76647da9d429f095cd77ff", "rows": 132 }, "recordPins": { "certs/strassen-certificate.json": "0e400efeb8a4bba99fba620dd77c6e6d4aa6eff9b8016834f0c4aa9071f8b008", "certs/mc100-alphatensor-q.json": "753485444a3e4498c15cfa47e8e1a48ff40d66ca2cebd5d55349216f3902d9f7", "certs/mc100-alphatensor-f2.json": "0222c5552b7c24f38f1231508bce613876eafce4e161325ef1b0bf3817d90a77", "certs/mc100-alphaevolve-nb-matmul.json": "50183f3ffba87bd2964ae6c0e32a8d985c8f0176f420728f8b19d826df4ea12a", "certs/kissing-ledger.json": "5c823b21ac43b5bdb3ad4b91a46e909cbf86a192e4cf382e2d8c5be2b29f611f", "certs/easota-ledger.json": "57f46876a7c79b0c6f7f236f0cb133e0ce896f9773cc85b36cf9d8e7fa3f627b", "certs/mc100-einstein-arena.json": "5d05c32da7e1d4788a2bff1af3f3d2ff45056bb02c69d54fc142fe0e24060226", "certs/erdos852-certificate.json": "13cfc7fa212a4355139a45cba78450ed371db78d2c980b3faec09a121c024ad1", "certs/polymaps-ledger.json": "c3f99c9398ef410e402d4422286dfdd2ab0085ddad933bf9bcdd5c18eef6c3f3", "certs/mc100-station-v2.json": "b526305ff85bbb353a51f5ae2183d06f2e071c2e4a889a9e9025622c41a04431", "certs/countex-ledger.json": "948f6c633e5142746a7fa952700f39f18b806129effa2eaf622b7133400701dc", "certs/sumdiff-ledger.json": "bf8857db9f64b6508da042b5f0d4e4b30fe452f47fb14a64b701482e7ab94ac4", "certs/fei-ledger.json": "ad853dabf838029896747144ee765fd418830311dc7c4b133575119d08bcf59e", "certs/turan-ledger.json": "f0b9c2b48a5b32654f0cdeab9389464549c64d5fd10c075dd928ba0a5e9a38ef", "certs/horizonmath-ledger.json": "78adab0aa528381db4e8a49e4ba7e0a57224f536d1ea984472fa402a2ee1f03a", "certs/gnnw-certificate.json": "b7127457078d064ed8b6e7cd4f26110f8949c7a384b322a0d22de575a9875273", "certs/sumproduct-ledger.json": "61cc3c57f7a6567c55f7850551e8ca92543e988b7eb57645d4afa5bc66673ea0" } }, "required": { "FALSE": "REFUTED", "TRUE": "CERTIFIED", "MALFORMED": "REFUSED" }, "taus": [ "1e-6", "1e-9", "1e-12" ], "partial": false, "dryRun": false, "built": [ "tensor", "kissing", "shapes", "erdos852", "polymaps", "countex", "entropy", "turan", "horizonmath", "gnnw", "sumproduct" ], "pending": [], "totals": { "tensor": { "rows": 45, "originalsAsRequired": 45, "mutants": 315, "excluded": 10, "byTruth": { "FALSE": 180, "TRUE": 90, "MALFORMED": 45 }, "byOutcome": { "as required": 312, "refused": 3 }, "falseCertifications": 0, "falseRefutations": 0, "refusalsOnFalse": 3, "refusalsOnTrue": 0, "discards": 0, "malformedNotRefused": 0, "rowsWithWitnessedFalse": 45, "float": { "1e-6": { "witnessedFalseAccepted": 35, "witnessedFalse": 180, "originalsAccepted": 45, "originals": 45, "trueAccepted": 90, "trueMutants": 90, "witnessedFalseAcceptRate": 0.1944 }, "1e-9": { "witnessedFalseAccepted": 11, "witnessedFalse": 180, "originalsAccepted": 45, "originals": 45, "trueAccepted": 90, "trueMutants": 90, "witnessedFalseAcceptRate": 0.0611 }, "1e-12": { "witnessedFalseAccepted": 0, "witnessedFalse": 180, "originalsAccepted": 45, "originals": 45, "trueAccepted": 90, "trueMutants": 90, "witnessedFalseAcceptRate": 0 } } }, "kissing": { "rows": 11, "originalsAsRequired": 10, "mutants": 69, "excluded": 1, "byTruth": { "FALSE": 39, "TRUE": 20, "MALFORMED": 10 }, "byOutcome": { "as required": 69 }, "falseCertifications": 0, "falseRefutations": 0, "refusalsOnFalse": 0, "refusalsOnTrue": 0, "discards": 0, "malformedNotRefused": 0, "rowsWithWitnessedFalse": 10, "float": { "1e-6": { "witnessedFalseAccepted": 0, "witnessedFalse": 39, "originalsAccepted": 10, "originals": 10, "trueAccepted": 20, "trueMutants": 20, "witnessedFalseAcceptRate": 0 }, "1e-9": { "witnessedFalseAccepted": 0, "witnessedFalse": 39, "originalsAccepted": 10, "originals": 10, "trueAccepted": 20, "trueMutants": 20, "witnessedFalseAcceptRate": 0 }, "1e-12": { "witnessedFalseAccepted": 0, "witnessedFalse": 39, "originalsAccepted": 10, "originals": 10, "trueAccepted": 20, "trueMutants": 20, "witnessedFalseAcceptRate": 0 } }, "rowsWithoutObject": 1 }, "shapes": { "rows": 28, "originalsAsRequired": 28, "mutants": 136, "excluded": 4, "byTruth": { "FALSE": 80, "TRUE": 28, "MALFORMED": 28 }, "byOutcome": { "as required": 88, "DISCARDED": 27, "not as required (REPAIRED)": 17, "not as required (UNWITNESSED)": 1, "refused": 3 }, "falseCertifications": 0, "falseRefutations": 0, "refusalsOnFalse": 3, "refusalsOnTrue": 0, "discards": 27, "malformedNotRefused": 0, "rowsWithWitnessedFalse": 25, "float": { "1e-6": { "witnessedFalseAccepted": 41, "witnessedFalse": 53, "originalsAccepted": 28, "originals": 28, "trueAccepted": 28, "trueMutants": 28, "witnessedFalseAcceptRate": 0.7736 }, "1e-9": { "witnessedFalseAccepted": 16, "witnessedFalse": 53, "originalsAccepted": 15, "originals": 28, "trueAccepted": 15, "trueMutants": 28, "witnessedFalseAcceptRate": 0.3019 }, "1e-12": { "witnessedFalseAccepted": 1, "witnessedFalse": 53, "originalsAccepted": 7, "originals": 28, "trueAccepted": 7, "trueMutants": 28, "witnessedFalseAcceptRate": 0.0189 } } }, "erdos852": { "rows": 1, "originalsAsRequired": 1, "mutants": 5, "excluded": 0, "byTruth": { "FALSE": 2, "TRUE": 2, "MALFORMED": 1 }, "byOutcome": { "as required": 5 }, "falseCertifications": 0, "falseRefutations": 0, "refusalsOnFalse": 0, "refusalsOnTrue": 0, "discards": 0, "malformedNotRefused": 0, "rowsWithWitnessedFalse": 1, "float": { "1e-6": { "witnessedFalseAccepted": 2, "witnessedFalse": 2, "originalsAccepted": 1, "originals": 1, "trueAccepted": 2, "trueMutants": 2, "witnessedFalseAcceptRate": 1 }, "1e-9": { "witnessedFalseAccepted": 2, "witnessedFalse": 2, "originalsAccepted": 1, "originals": 1, "trueAccepted": 2, "trueMutants": 2, "witnessedFalseAcceptRate": 1 }, "1e-12": { "witnessedFalseAccepted": 2, "witnessedFalse": 2, "originalsAccepted": 1, "originals": 1, "trueAccepted": 1, "trueMutants": 2, "witnessedFalseAcceptRate": 1 } } }, "polymaps": { "rows": 9, "originalsAsRequired": 9, "mutants": 35, "excluded": 1, "byTruth": { "FALSE": 17, "TRUE": 9, "MALFORMED": 9 }, "byOutcome": { "as required": 34, "not as required (PARTIAL)": 1 }, "falseCertifications": 0, "falseRefutations": 0, "refusalsOnFalse": 0, "refusalsOnTrue": 0, "discards": 0, "malformedNotRefused": 1, "rowsWithWitnessedFalse": 9, "float": { "1e-6": { "witnessedFalseAccepted": 0, "witnessedFalse": 17, "originalsAccepted": 6, "originals": 9, "trueAccepted": 5, "trueMutants": 9, "witnessedFalseAcceptRate": 0 }, "1e-9": { "witnessedFalseAccepted": 0, "witnessedFalse": 17, "originalsAccepted": 6, "originals": 9, "trueAccepted": 5, "trueMutants": 9, "witnessedFalseAcceptRate": 0 }, "1e-12": { "witnessedFalseAccepted": 0, "witnessedFalse": 17, "originalsAccepted": 5, "originals": 9, "trueAccepted": 5, "trueMutants": 9, "witnessedFalseAcceptRate": 0 } } }, "countex": { "rows": 14, "originalsAsRequired": 0, "mutants": 0, "excluded": 0, "byTruth": {}, "byOutcome": {}, "falseCertifications": 0, "falseRefutations": 0, "refusalsOnFalse": 0, "refusalsOnTrue": 0, "discards": 0, "malformedNotRefused": 0, "rowsWithWitnessedFalse": 0, "float": { "1e-6": { "witnessedFalseAccepted": 0, "witnessedFalse": 0, "originalsAccepted": 0, "originals": 0, "trueAccepted": 0, "trueMutants": 0, "witnessedFalseAcceptRate": null }, "1e-9": { "witnessedFalseAccepted": 0, "witnessedFalse": 0, "originalsAccepted": 0, "originals": 0, "trueAccepted": 0, "trueMutants": 0, "witnessedFalseAcceptRate": null }, "1e-12": { "witnessedFalseAccepted": 0, "witnessedFalse": 0, "originalsAccepted": 0, "originals": 0, "trueAccepted": 0, "trueMutants": 0, "witnessedFalseAcceptRate": null } }, "rowsWithoutObject": 14 }, "entropy": { "rows": 4, "originalsAsRequired": 4, "mutants": 12, "excluded": 0, "byTruth": { "FALSE": 4, "TRUE": 4, "MALFORMED": 4 }, "byOutcome": { "as required": 12 }, "falseCertifications": 0, "falseRefutations": 0, "refusalsOnFalse": 0, "refusalsOnTrue": 0, "discards": 0, "malformedNotRefused": 0, "rowsWithWitnessedFalse": 4, "float": { "1e-6": { "witnessedFalseAccepted": 4, "witnessedFalse": 4, "originalsAccepted": 4, "originals": 4, "trueAccepted": 4, "trueMutants": 4, "witnessedFalseAcceptRate": 1 }, "1e-9": { "witnessedFalseAccepted": 4, "witnessedFalse": 4, "originalsAccepted": 4, "originals": 4, "trueAccepted": 4, "trueMutants": 4, "witnessedFalseAcceptRate": 1 }, "1e-12": { "witnessedFalseAccepted": 4, "witnessedFalse": 4, "originalsAccepted": 4, "originals": 4, "trueAccepted": 4, "trueMutants": 4, "witnessedFalseAcceptRate": 1 } } }, "turan": { "rows": 2, "originalsAsRequired": 0, "mutants": 0, "excluded": 0, "byTruth": {}, "byOutcome": {}, "falseCertifications": 0, "falseRefutations": 0, "refusalsOnFalse": 0, "refusalsOnTrue": 0, "discards": 0, "malformedNotRefused": 0, "rowsWithWitnessedFalse": 0, "float": { "1e-6": { "witnessedFalseAccepted": 0, "witnessedFalse": 0, "originalsAccepted": 0, "originals": 0, "trueAccepted": 0, "trueMutants": 0, "witnessedFalseAcceptRate": null }, "1e-9": { "witnessedFalseAccepted": 0, "witnessedFalse": 0, "originalsAccepted": 0, "originals": 0, "trueAccepted": 0, "trueMutants": 0, "witnessedFalseAcceptRate": null }, "1e-12": { "witnessedFalseAccepted": 0, "witnessedFalse": 0, "originalsAccepted": 0, "originals": 0, "trueAccepted": 0, "trueMutants": 0, "witnessedFalseAcceptRate": null } }, "rowsWithoutObject": 2 }, "horizonmath": { "rows": 3, "originalsAsRequired": 0, "mutants": 0, "excluded": 0, "byTruth": {}, "byOutcome": {}, "falseCertifications": 0, "falseRefutations": 0, "refusalsOnFalse": 0, "refusalsOnTrue": 0, "discards": 0, "malformedNotRefused": 0, "rowsWithWitnessedFalse": 0, "float": { "1e-6": { "witnessedFalseAccepted": 0, "witnessedFalse": 0, "originalsAccepted": 0, "originals": 0, "trueAccepted": 0, "trueMutants": 0, "witnessedFalseAcceptRate": null }, "1e-9": { "witnessedFalseAccepted": 0, "witnessedFalse": 0, "originalsAccepted": 0, "originals": 0, "trueAccepted": 0, "trueMutants": 0, "witnessedFalseAcceptRate": null }, "1e-12": { "witnessedFalseAccepted": 0, "witnessedFalse": 0, "originalsAccepted": 0, "originals": 0, "trueAccepted": 0, "trueMutants": 0, "witnessedFalseAcceptRate": null } }, "rowsWithoutObject": 3 }, "gnnw": { "rows": 1, "originalsAsRequired": 0, "mutants": 0, "excluded": 0, "byTruth": {}, "byOutcome": {}, "falseCertifications": 0, "falseRefutations": 0, "refusalsOnFalse": 0, "refusalsOnTrue": 0, "discards": 0, "malformedNotRefused": 0, "rowsWithWitnessedFalse": 0, "float": { "1e-6": { "witnessedFalseAccepted": 0, "witnessedFalse": 0, "originalsAccepted": 0, "originals": 0, "trueAccepted": 0, "trueMutants": 0, "witnessedFalseAcceptRate": null }, "1e-9": { "witnessedFalseAccepted": 0, "witnessedFalse": 0, "originalsAccepted": 0, "originals": 0, "trueAccepted": 0, "trueMutants": 0, "witnessedFalseAcceptRate": null }, "1e-12": { "witnessedFalseAccepted": 0, "witnessedFalse": 0, "originalsAccepted": 0, "originals": 0, "trueAccepted": 0, "trueMutants": 0, "witnessedFalseAcceptRate": null } }, "rowsWithoutObject": 1 }, "sumproduct": { "rows": 1, "originalsAsRequired": 0, "mutants": 0, "excluded": 0, "byTruth": {}, "byOutcome": {}, "falseCertifications": 0, "falseRefutations": 0, "refusalsOnFalse": 0, "refusalsOnTrue": 0, "discards": 0, "malformedNotRefused": 0, "rowsWithWitnessedFalse": 0, "float": { "1e-6": { "witnessedFalseAccepted": 0, "witnessedFalse": 0, "originalsAccepted": 0, "originals": 0, "trueAccepted": 0, "trueMutants": 0, "witnessedFalseAcceptRate": null }, "1e-9": { "witnessedFalseAccepted": 0, "witnessedFalse": 0, "originalsAccepted": 0, "originals": 0, "trueAccepted": 0, "trueMutants": 0, "witnessedFalseAcceptRate": null }, "1e-12": { "witnessedFalseAccepted": 0, "witnessedFalse": 0, "originalsAccepted": 0, "originals": 0, "trueAccepted": 0, "trueMutants": 0, "witnessedFalseAcceptRate": null } }, "rowsWithoutObject": 1 } }, "all": { "rows": 119, "originalsAsRequired": 97, "mutants": 572, "excluded": 16, "byTruth": { "FALSE": 322, "TRUE": 153, "MALFORMED": 97 }, "byOutcome": { "as required": 520, "refused": 6, "DISCARDED": 27, "not as required (REPAIRED)": 17, "not as required (UNWITNESSED)": 1, "not as required (PARTIAL)": 1 }, "falseCertifications": 0, "falseRefutations": 0, "refusalsOnFalse": 6, "refusalsOnTrue": 0, "discards": 27, "malformedNotRefused": 1, "rowsWithWitnessedFalse": 94, "float": { "1e-6": { "witnessedFalseAccepted": 82, "witnessedFalse": 295, "originalsAccepted": 94, "originals": 97, "trueAccepted": 149, "trueMutants": 153, "witnessedFalseAcceptRate": 0.278 }, "1e-9": { "witnessedFalseAccepted": 33, "witnessedFalse": 295, "originalsAccepted": 81, "originals": 97, "trueAccepted": 136, "trueMutants": 153, "witnessedFalseAcceptRate": 0.1119 }, "1e-12": { "witnessedFalseAccepted": 7, "witnessedFalse": 295, "originalsAccepted": 72, "originals": 97, "trueAccepted": 127, "trueMutants": 153, "witnessedFalseAcceptRate": 0.0237 } } }, "killSwitch": { "mutableRows": 119, "half": 60, "rowsWithWitnessedFalse": 94, "tripped": false, "note": "decided: every family built or its exclusion recorded" }, "findings": [ { "family": "tensor", "class": "coefficient-times-one-plus-1e-9", "truth": "FALSE", "outcome": "refused", "count": 3, "rows": [ "mm-alphaevolve-48-4x4x4", "mc100-ae-nb-3x4x7-r63", "mc100-ae-nb-4x4x8-r96" ], "example": "Gaussian coefficient bound too large for exact double summation" }, { "family": "shapes", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "outcome": "DISCARDED", "count": 13, "rows": [ "ea-circles-alphaevolve_2025", "ea-heilbronn-alphaevolve_2025", "ea-heilbronn-ours_2026", "ea-mindist-alphaevolve_2025", "ea-mindist-ours_2026", "ea-edges-alphaevolve_2025" ], "example": "Σr = 2.3658321334167631, 0 overlapping pairs, box slack 0.0000000319647749; printed 2.3658321334 agrees (rounding)" }, { "family": "shapes", "class": "printed-plus-one-unit", "truth": "FALSE", "outcome": "not as required (REPAIRED)", "count": 5, "rows": [ "ea-circles-ours_2026", "ea-overlap-alphaevolve_2025", "ea-overlap-ttt_discover_2026", "ea-overlap-together_ai_2026", "mc100-ea-best-erdos-min-overlap" ], "example": "Σr = 2.3658323759185154, 44 overlapping pairs, box slack -0.0000000000000420; printed 2.3658323760 DOES NOT agree (rounding)" }, { "family": "shapes", "class": "printed-minus-one-unit", "truth": "FALSE", "outcome": "not as required (REPAIRED)", "count": 5, "rows": [ "ea-circles-ours_2026", "ea-overlap-alphaevolve_2025", "ea-overlap-ttt_discover_2026", "ea-overlap-together_ai_2026", "mc100-ea-best-erdos-min-overlap" ], "example": "Σr = 2.3658323759185154, 44 overlapping pairs, box slack -0.0000000000000420; printed 2.3658323758 agrees (rounding)" }, { "family": "shapes", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "outcome": "not as required (REPAIRED)", "count": 7, "rows": [ "ea-circles-ours_2026", "ea-overlap-haugland_2016", "ea-overlap-alphaevolve_2025", "ea-overlap-ttt_discover_2026", "ea-overlap-together_ai_2026", "mc100-ea-best-erdos-min-overlap" ], "example": "Σr = 2.3658323759185154, 43 overlapping pairs, box slack -0.0000000000000420; printed 2.3658323759 DOES NOT agree (rounding)" }, { "family": "shapes", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "outcome": "not as required (UNWITNESSED)", "count": 1, "rows": [ "ea-autocorr-alphaevolve_2025" ], "example": "a negative value; printed 1.50529397 DOES NOT agree (ceiling)" }, { "family": "shapes", "class": "printed-plus-one-unit", "truth": "FALSE", "outcome": "DISCARDED", "count": 8, "rows": [ "ea-flat-alphaevolve_2025", "ea-flat-ours_2026", "mc100-ea-best-first-autocorrelation-inequality", "mc100-ea-best-flat-polynomials", "mc100-ea-best-edges-vs-triangles", "mc100-ea-best-circles-rectangle" ], "example": "C⁺ ∈ [1.3409252804007615, 1.3409252804007616]; printed 1.340926 DOES NOT agree (rounding)" }, { "family": "shapes", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "outcome": "refused", "count": 3, "rows": [ "ea-flat-alphaevolve_2025", "ea-flat-ours_2026", "mc100-ea-best-flat-polynomials" ], "example": "the decider threw: a coefficient that is not an integer literal" }, { "family": "shapes", "class": "printed-minus-one-unit", "truth": "FALSE", "outcome": "DISCARDED", "count": 6, "rows": [ "mc100-ea-best-first-autocorrelation-inequality", "mc100-ea-best-flat-polynomials", "mc100-ea-best-edges-vs-triangles", "mc100-ea-best-circles-rectangle", "mc100-ea-best-kissing-number-d11-605", "mc100-ea-best-kissing-number-d12-842" ], "example": "f ≥ 0 at all 65536 values, exactly: C1 ≤ 1.50274364923261637372… exactly (the maximum of the autoconvolution decided at 16684 candidate indexes the float screen could not separate; the printed 1.5027436492326164 agrees, above)" }, { "family": "polymaps", "class": "exponent-missing", "truth": "MALFORMED", "outcome": "not as required (PARTIAL)", "count": 1, "rows": [ "polymaps-gao-f7" ], "example": "2 distinct rational points with one image: ok · det J constant: rests on the paper's lemma: rests on the lemma" } ], "fixes": [ { "id": "easota-word", "finding": "the easota ledger's word (WITNESSED → the register's CERTIFIED) was about the bytes witnessing a value; the printed digits were a field beside it (printedAgrees), gated only by the easota page build and the paper numbers. A printed value moved one unit in its last digit past the bytes stayed CERTIFIED on the 15 easota rows with a printed value and a WITNESSED decision, while tools/run-mc100-einstein.js refutes the same for the mc100 rows.", "found": { "record": "certs/selfaudit-mutations.json", "commit": "d961cda2", "date": "2026-10-21", "outcome": "FALSE CERTIFICATION", "count": 28 }, "fix": { "date": "2026-10-21", "what": "instruments/easota/word.js composes the word in one place: WITNESSED with a printed value the exact value does not reproduce → MISPRINTED → the register's REFUTED, kind not-from-the-published-data, the exact value certified beside it; tools/run-easota-ledger.js and instruments/selfaudit/shapes.js both call it; tools/run-claims-ledger.js maps MISPRINTED; the easota page and battery know the word. No row of the pinned records changes word; the ledger record's grammar string gains MISPRINTED at the next re-pin (Phase 5).", "files": [ "instruments/easota/word.js", "tools/run-easota-ledger.js", "tools/run-claims-ledger.js", "tools/build-report-easota.js", "instruments/easota/battery.js", "instruments/selfaudit/shapes.js" ] }, "mutants": 28, "asRequiredNow": 28, "notAsRequired": [], "notInThisRun": 0 }, { "id": "malformed-word", "finding": "a malformed input — a factor matrix with a short row (the rank claim no longer matching the columns), an object that is not n vectors in R^d, a weight row without 20 weights — was answered REFUTED (the tensor instrument's shape checks; the mc100-einstein decider's shape checks, kind not-from-the-published-data) where the vocabulary of instruments/verdict.js and the pre-registration say REFUSED: a claim the instrument cannot decide, not a false one.", "found": { "record": "certs/selfaudit-mutations.json", "commit": "d961cda2", "date": "2026-10-21", "outcome": "not as required (REFUTED)", "count": 49 }, "fix": { "date": "2026-10-21", "what": "instruments/strassen/tensor.js: the four shape checks of audit() and of auditZi() answer REFUSED with the same reason (the identity failing under both layouts stays REFUTED); families/strassen-audit.js and tools/run-mc100-tensors.js already map the instrument's REFUSED to the register's; tools/run-mc100-einstein.js: an object that is not n vectors in R^d and a weight row without 20 weights are REFUSED, kind none. The strassen battery's forged-rank red control expects REFUSED with its reason. No row of the pinned records changes word.", "files": [ "instruments/strassen/tensor.js", "instruments/strassen/battery.js", "tools/run-mc100-einstein.js" ] }, "mutants": 49, "asRequiredNow": 49, "notAsRequired": [], "notInThisRun": 0 } ], "fixesTable": { "path": "instruments/selfaudit/fixes.json", "sha256": "8072ab6d5523385866145d3660a05769404024c271fa6bd6028ccb5c8606d31f" }, "families": { "tensor": { "decider": "families/strassen-audit.js certify → instruments/strassen/tensor.js audit/auditZi (both layouts; F₂ rows also over Q; rank < naive), the path of tools/export-strassen-certificate.js and the audit tools/run-mc100-tensors.js decide calls; its BigInt cross-check recorded beside it", "witness": "instruments/selfaudit/witness_tensor.py", "floatcheck": "instruments/selfaudit/floatcheck_tensor.py", "redControl": "coefficient-plus-one", "records": [ "certs/strassen-certificate.json", "certs/mc100-alphatensor-q.json", "certs/mc100-alphatensor-f2.json", 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false, "transformation": "column 3 of U, V and W appended again; rank claimed 8", "sha256": "881f9248ff7639f6cc23c24c7d4f09984be7b56b6bfb30e49928de208640b041", "bytes": 281, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": { "ab": 1, "bc": 2, "k": 0, "sum": 2, "target": 1, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphatensor-q-2x2x2/term-duplicated does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=1, bc=2, k=0): sum 2, target 1", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphatensor-q-2x2x2/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 7", "sha256": "db8d94fd0c34f87c36e41d0807699d72c96b6dae944cf5a410da8d8538f6304d", "bytes": 256, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "alphatensor-q-2x2x2/columns-permuted: 2x2 times 2x2 in 7 multiplications VERIFIED over Q — all 64 tensor-identity equations hold exactly (layout CA); rank 7 < 8 naive", "ms": 0, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mm-alphatensor-q-2x2x2/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 3 of U and of V negated (the product u·v·w unchanged)", "sha256": "aef6366f149af964f8d4b4dc6c0202ea1d1687e0bcfca9df0b3df71909ee7727", "bytes": 258, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "alphatensor-q-2x2x2/uv-signs-flipped: 2x2 times 2x2 in 7 multiplications VERIFIED over Q — all 64 tensor-identity equations hold exactly (layout CA); rank 7 < 8 naive", "ms": 0, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mm-alphatensor-q-2x2x2/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 6 entries", "sha256": "e990de0d612edc352e8b98f2c86c866ced720a6bd22757f0601cad5f340bcc77", "bytes": 254, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", 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< 27 naive", "ms": 0, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mm-alphatensor-q-3x3x3/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 11 of U and of V negated (the product u·v·w unchanged)", "sha256": "02770d78815debe1d8776d08ae3e4038e06890e5222f9285f4626ba9f377f63d", "bytes": 1408, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "alphatensor-q-3x3x3/uv-signs-flipped: 3x3 times 3x3 in 23 multiplications VERIFIED over Q — all 729 tensor-identity equations hold exactly (layout CA); rank 23 < 27 naive", "ms": 0, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mm-alphatensor-q-3x3x3/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 22 entries", "sha256": "ef37e25235d68bbd3a2b4e878736001be78b95a71541357122194fdb835b3c77", "bytes": 1407, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "a factor row does not have rank-many entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "claimed rank 23 but the factors have 22 columns", "ms": 0, "bigInt": { "verdict": "not run (the exact-double audit refused)", "agrees": null } }, "required": "REFUSED", "outcome": "as required", "float": { "error": "list index out of range", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [], "ms": 154 }, { "rowId": "mm-alphatensor-q-4x4x4", "record": "certs/strassen-certificate.json", "entryId": "alphatensor-q-4x4x4", "verdict": "CERTIFIED", "object": "<4,4,4> rank 49 over Q", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "alphatensor-q-4x4x4: 4x4 times 4x4 in 49 multiplications VERIFIED over Q — all 4096 tensor-identity equations hold exactly (layout CA); rank 49 < 64 naive", "ms": 0.2, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "06abbc6e288fa65198ea48a72bdcfbe40c190861b41ac53d2c165350e81d3938" }, "mutants": [ { "id": "mm-alphatensor-q-4x4x4/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][0] += 1", "sha256": "ce11d4ac5f59b0f40928ce13f44188d0b5f59b966378014f180b837a7126ba35", 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"sha256": "667e74c8fe75f9f55bc19efec20937c8336461c11dafc9937c9a41aced5d0819", "bytes": 6887, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 0, "k": 0, "sum": 1000000001, "target": 1000000000, "mod": null }, "CA": { "ab": 0, "bc": 0, "k": 0, "sum": 1000000001, "target": 1000000000, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphatensor-q-4x4x4/coefficient-times-one-plus-1e-9 does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=0, k=0): sum 1000000001, target 1000000000", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1.000000082740371e-9, "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphatensor-q-4x4x4/term-dropped", "class": "term-dropped", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 24 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claimed 50", "sha256": "93a76dc4d548eb8a996280f48ded0e0f8db7afd9ede8fe65a0e427778258d22b", "bytes": 5221, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": { "ab": 1, "bc": 9, "k": 3, "sum": 1, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphatensor-q-4x4x4/term-duplicated does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=1, bc=9, k=3): sum 1, target 0", "ms": 0.1, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphatensor-q-4x4x4/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 49", "sha256": "9955c6c5416c39bb016014d1f6dabfa8b3a0b5c28dfa1c80d4702db383866b2e", "bytes": 5122, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "alphatensor-q-4x4x4/columns-permuted: 4x4 times 4x4 in 49 multiplications VERIFIED over Q — all 4096 tensor-identity equations hold exactly (layout CA); rank 49 < 64 naive", "ms": 0.2, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mm-alphatensor-q-4x4x4/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 24 of U and of V negated (the product u·v·w unchanged)", "sha256": "f4fb8fdc89dd653bec904cd21e6d6bbde114ec665275789905260f8e00e1db18", "bytes": 5126, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "alphatensor-q-4x4x4/uv-signs-flipped: 4x4 times 4x4 in 49 multiplications VERIFIED over Q — all 4096 tensor-identity equations hold exactly (layout CA); rank 49 < 64 naive", "ms": 0.3, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mm-alphatensor-q-4x4x4/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 48 entries", "sha256": "555d7e818691f5645c559a2869305ec834a40c2ed167a42590c68d9c6ab336fb", "bytes": 5120, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "a 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true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphatensor-q-3x4x5/coefficient-times-one-plus-1e-9", "class": "coefficient-times-one-plus-1e-9", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][3] × 1.000000001 exactly: U scaled by 10⁹ with that entry × 1000000001, the identity's scale × 10⁹ (scale 1000000000)", "sha256": "1eab9ff707c942abc357a8a3d9c052f362fbe556812f1d9f2cb88f727997697b", "bytes": 6090, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1000000000, "mod": null }, "CA": { "ab": 0, "bc": 4, "k": 6, "sum": -1, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphatensor-q-3x4x5/coefficient-times-one-plus-1e-9 does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: 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"verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphatensor-q-3x4x5/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 47", "sha256": "712fa3d8c37c074ef0defa4575ae18ac1e743c9a552774d997181ba6be0d0429", "bytes": 4775, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "alphatensor-q-3x4x5/columns-permuted: 3x4 times 4x5 in 47 multiplications VERIFIED over Q — all 3600 tensor-identity equations hold exactly (layout CA); rank 47 < 60 naive", "ms": 0.2, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { 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"mm-alphatensor-q-3x4x5/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 46 entries", "sha256": "3a7e7c550b244dc8a1d3053e9281ba59ab31aabfd59280ca73060b18819b50df", "bytes": 4773, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "a factor row does not have rank-many entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "claimed rank 47 but the factors have 46 columns", "ms": 0, "bigInt": { "verdict": "not run (the exact-double audit refused)", "agrees": null } }, "required": "REFUSED", "outcome": "as required", "float": { "error": "list index out of range", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [], "ms": 334 }, { "rowId": "mm-alphatensor-q-4x5x5", "record": "certs/strassen-certificate.json", "entryId": "alphatensor-q-4x5x5", 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null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": { "ab": 3, "bc": 0, "k": 2, "sum": 1, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphatensor-q-4x5x5/term-duplicated does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=3, bc=0, k=2): sum 1, target 0", "ms": 0.2, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphatensor-q-4x5x5/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 76", "sha256": "f5c7f241b3b15c3c94fc13bb246ef12bb8e8e2c08feca2d08bc2e37a4237b8ca", "bytes": 10429, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "alphatensor-q-4x5x5/columns-permuted: 4x5 times 5x5 in 76 multiplications VERIFIED over Q — all 10000 tensor-identity equations hold exactly (layout CA); rank 76 < 100 naive", "ms": 1.3, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mm-alphatensor-q-4x5x5/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 38 of U and of V negated (the product u·v·w unchanged)", "sha256": "3af0d872bd8fa4f317cb704bf33805e7ce2001bcd90fc5fef6b7720c75d26b4e", "bytes": 10427, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "alphatensor-q-4x5x5/uv-signs-flipped: 4x5 times 5x5 in 76 multiplications VERIFIED over Q — all 10000 tensor-identity equations hold exactly (layout CA); rank 76 < 100 naive", "ms": 0.8, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mm-alphatensor-q-4x5x5/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 75 entries", "sha256": "dde83e82af89e325202829a2c472f4d68761c67e565c252608dbf8c78125aff0", "bytes": 10426, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "a factor row does not have rank-many entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "claimed rank 76 but the factors have 75 columns", "ms": 0, "bigInt": { "verdict": "not run (the exact-double audit refused)", "agrees": null } }, "required": "REFUSED", "outcome": "as required", "float": { "error": "list index out of range", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [], "ms": 935 }, { "rowId": "mm-alphatensor-f2-4x4x4", "record": "certs/strassen-certificate.json", "entryId": "alphatensor-f2-4x4x4", "verdict": "CERTIFIED", "object": "<4,4,4> rank 47 over F2", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "alphatensor-f2-4x4x4: 4x4 times 4x4 in 47 multiplications VERIFIED over F2 — all 4096 tensor-identity equations hold exactly (layout CA); rank 47 < 64 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 2.8, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "356ed53498ba4bf6f6c3127323f1c8f6acbbb21a0e89f5f10a5e710ad2efd43b" }, "mutants": [ { "id": "mm-alphatensor-f2-4x4x4/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][4] += 1", "sha256": "a6c0bafb1e3083d58e765ba01aeafdad944061c10f13e2663f166f884c71a998", "bytes": 4664, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 0, "k": 0, "sum": 2, "target": 1, "mod": 2 }, "CA": { "ab": 0, "bc": 0, "k": 0, "sum": 2, "target": 1, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphatensor-f2-4x4x4/coefficient-plus-one does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=0, k=0): sum 2, target 1 (mod 2)", "ms": 0.1, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphatensor-f2-4x4x4/term-dropped", "class": "term-dropped", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 23 removed from U, V and W; rank claimed 46", "sha256": "302c5d8a51e32b9afec1a34fa1fddc0ff6e23635f1eb81481f24905b071e120e", "bytes": 4568, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 3, "bc": 10, "k": 5, "sum": 3, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphatensor-f2-4x4x4/term-dropped does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=3, bc=10, k=5): sum 3, target 0 (mod 2)", "ms": 0.2, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphatensor-f2-4x4x4/term-duplicated", "class": "term-duplicated", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 23 of U, V and W appended again; rank claimed 48", "sha256": "726b74f0721ebf017880f9c614971487a309a70932c53c50abb4030b47faa227", "bytes": 4760, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 3, "bc": 10, "k": 5, "sum": 5, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphatensor-f2-4x4x4/term-duplicated does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=3, bc=10, k=5): sum 5, target 0 (mod 2)", "ms": 0.2, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphatensor-f2-4x4x4/f2-asserted-over-q", "class": "f2-asserted-over-q", "truth": "FALSE", "preservesOriginal": false, "transformation": "ring F2 → Q, the factors unchanged (FALSE only when the witness finds a violated entry over Z, else DISCARDED)", "sha256": "60e6ef91dd4eeaf42afbb9be679c386416e8e8c48297a1e9115f04bd9edbf7a5", "bytes": 4663, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 0, "k": 2, "sum": 2, "target": 0, "mod": null }, "CA": { "ab": 0, "bc": 0, "k": 2, "sum": 2, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphatensor-f2-4x4x4/f2-asserted-over-q does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=0, k=2): sum 2, target 0", "ms": 0.1, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 8, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphatensor-f2-4x4x4/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 47", "sha256": "0509ad8536048659a1ae06b69aaf81672f442169365b71ce1dc51557ba9f1fa2", "bytes": 4664, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "alphatensor-f2-4x4x4/columns-permuted: 4x4 times 4x4 in 47 multiplications VERIFIED over F2 — all 4096 tensor-identity equations hold exactly (layout CA); rank 47 < 64 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0.5, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mm-alphatensor-f2-4x4x4/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 23 of U and of V negated (the product u·v·w unchanged); over F₂ this is the identity, the mutant equals the original", "sha256": "868b3ea5159a420835a7d0cc075ade36184a9a43ab3c493dfc4bc979e6e3b889", "bytes": 4670, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "alphatensor-f2-4x4x4/uv-signs-flipped: 4x4 times 4x4 in 47 multiplications VERIFIED over F2 — all 4096 tensor-identity equations hold exactly (layout CA); rank 47 < 64 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0.4, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mm-alphatensor-f2-4x4x4/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 46 entries", "sha256": "61aed05900949b93d120fe7c23d613f0cd6c421e873a30b1347a557b2d384a72", "bytes": 4662, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "a factor row does not have rank-many entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "claimed rank 47 but the factors have 46 columns", "ms": 0, "bigInt": { "verdict": "not run (the exact-double audit refused)", "agrees": null } }, "required": "REFUSED", "outcome": "as required", "float": { "error": "list index out of range", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [ { "class": "coefficient-times-one-plus-1e-9", "reason": "no meaning over F₂: 1 + 10⁻⁹ is not an element of the field; the class is stated for Q and Z[i]" } ], "controlsFired": [], "ms": 416 }, { "rowId": "mm-alphatensor-f2-5x5x5", "record": "certs/strassen-certificate.json", "entryId": "alphatensor-f2-5x5x5", "verdict": "CERTIFIED", "object": "<5,5,5> rank 96 over F2", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "alphatensor-f2-5x5x5: 5x5 times 5x5 in 96 multiplications VERIFIED over F2 — all 15625 tensor-identity equations hold exactly (layout CA); rank 96 < 125 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 2.1, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "f5e0ca873437440f2dc8bc2765dcbda843dd0ee78607d1fd81b82c634ee5f41f" }, "mutants": [ { "id": "mm-alphatensor-f2-5x5x5/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][8] += 1", "sha256": "365558dbd4398c17cb1605c5baa6b6964e5248852c821d5c27cf6450ae00ab33", "bytes": 14606, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 0, "bc": 3, "k": 15, "sum": 2, "target": 1, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphatensor-f2-5x5x5/coefficient-plus-one does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=3, k=15): sum 2, target 1 (mod 2)", "ms": 0.1, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphatensor-f2-5x5x5/term-dropped", "class": "term-dropped", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 48 removed from U, V and W; rank claimed 95", "sha256": "abc14ccb2358ae6863c7dac0e6c8e4a5c4c64360ee52421508013290630a167a", "bytes": 14456, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 16, "bc": 7, "k": 3, "sum": 1, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphatensor-f2-5x5x5/term-dropped does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=16, bc=7, k=3): sum 1, target 0 (mod 2)", "ms": 1.2, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphatensor-f2-5x5x5/term-duplicated", "class": "term-duplicated", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 48 of U, V and W appended again; rank claimed 97", "sha256": "85382b3762dcdee0be63b64f8e878544f115fba1a3a8c267c03cad9baed1190a", "bytes": 14756, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 16, "bc": 7, "k": 3, "sum": 3, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphatensor-f2-5x5x5/term-duplicated does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=16, bc=7, k=3): sum 3, target 0 (mod 2)", "ms": 1.1, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphatensor-f2-5x5x5/f2-asserted-over-q", "class": "f2-asserted-over-q", "truth": "FALSE", "preservesOriginal": false, "transformation": "ring F2 → Q, the factors unchanged (FALSE only when the witness finds a violated entry over Z, else DISCARDED)", "sha256": "6bd327318e2c91d14d80f32abc90506372b70b18a52c944c8ee143cd0f2d73e3", "bytes": 14605, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 0, "k": 2, "sum": 2, "target": 0, "mod": null }, "CA": { "ab": 0, "bc": 0, "k": 2, "sum": 2, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphatensor-f2-5x5x5/f2-asserted-over-q does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=0, k=2): sum 2, target 0", "ms": 0.1, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 8, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphatensor-f2-5x5x5/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 96", "sha256": "257ac4db7b2e09082edf7630339d39c5b798a63aac570e0a1b9086df7f1b4a46", "bytes": 14606, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "alphatensor-f2-5x5x5/columns-permuted: 5x5 times 5x5 in 96 multiplications VERIFIED over F2 — all 15625 tensor-identity equations hold exactly (layout CA); rank 96 < 125 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 1.7, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mm-alphatensor-f2-5x5x5/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 48 of U and of V negated (the product u·v·w unchanged); over F₂ this is the identity, the mutant equals the original", "sha256": "145a18abd6f6641729e2a285cf32c2597fb54c568f6270111f9ce48b422420d5", "bytes": 14611, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "alphatensor-f2-5x5x5/uv-signs-flipped: 5x5 times 5x5 in 96 multiplications VERIFIED over F2 — all 15625 tensor-identity equations hold exactly (layout CA); rank 96 < 125 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 1.8, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mm-alphatensor-f2-5x5x5/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 95 entries", "sha256": "cfcfabfbe2d7eda9238a692446b9aa68bae1bc39051e55fdf60da68957d34ede", "bytes": 14604, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "a factor row does not have rank-many entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "claimed rank 96 but the factors have 95 columns", "ms": 0, "bigInt": { "verdict": "not run (the exact-double audit refused)", "agrees": null } }, "required": "REFUSED", "outcome": "as required", "float": { "error": "list index out of range", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [ { "class": "coefficient-times-one-plus-1e-9", "reason": "no meaning over F₂: 1 + 10⁻⁹ is not an element of the field; the class is stated for Q and Z[i]" } ], "controlsFired": [], "ms": 1840 }, { "rowId": "mm-alphaevolve-48-4x4x4", "record": "certs/strassen-certificate.json", "entryId": "alphaevolve-48-4x4x4", "verdict": "CERTIFIED", "object": "<4,4,4> rank 48 over Zi (scale 8)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "alphaevolve-48-4x4x4: 4x4 times 4x4 in 48 multiplications VERIFIED over Z[i] (doubled half-Gaussian factors; identity = 8*T, denominators cleared) — all 4096 tensor-identity equations hold exactly (layout CA); rank 48 < 64 naive", "ms": 5.5, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "be88866a7defef418f8050018cfb39976332eaa2afb0f16c29e026f4e006564e" }, "mutants": [ { "id": "mm-alphaevolve-48-4x4x4/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][0].re += 1", "sha256": "e08cbd56770623bf0dab6a7cf5781c4e92908949f08d879c487e1f0d48ad6920", "bytes": 14814, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 0, "k": 0, "sum": [ 8, -1 ], "target": [ 8, 0 ] }, "CA": { "ab": 0, "bc": 0, "k": 0, "sum": [ 8, -1 ], "target": [ 8, 0 ] } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphaevolve-48-4x4x4/coefficient-plus-one does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=0, k=0): sum 8-1i, target 8", "ms": 0.6, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 0.125, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphaevolve-48-4x4x4/coefficient-times-one-plus-1e-9", "class": "coefficient-times-one-plus-1e-9", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][0] × 1.000000001 exactly: U scaled by 10⁹ with that entry × 1000000001, the identity's scale × 10⁹ (scale 8000000000)", "sha256": "21a68414befb289e4d4e1ed9da7009e29585ac19d00fcafc432afd618eb4964b", "bytes": 21591, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 0, "k": 0, "sum": [ 8000000001, -1 ], "target": [ 8000000000, 0 ] }, "CA": { "ab": 0, "bc": 0, "k": 0, "sum": [ 8000000001, -1 ], "target": [ 8000000000, 0 ] } } }, "decided": { "verdict": "REFUSED", "why": "Gaussian coefficient bound too large for exact double summation", "ms": 0.4, "bigInt": { "verdict": "not run (the exact-double audit refused)", "agrees": null } }, "required": "REFUTED", "outcome": "refused", "float": { "maxResidual": 1.767767026099217e-10, "accept": { "1e-6": true, "1e-9": true, "1e-12": false } } }, { "id": "mm-alphaevolve-48-4x4x4/term-dropped", "class": "term-dropped", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 24 removed from U, V and W; rank claimed 47", "sha256": "4d2c3b2d9fe60e69372000b17a9c052197c7039c2fbda8d436707789205d212b", "bytes": 14504, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 0, "sum": [ 1, 0 ], "target": [ 0, 0 ] }, "CA": { "ab": 0, "bc": 1, "k": 0, "sum": [ 1, 0 ], "target": [ 0, 0 ] } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphaevolve-48-4x4x4/term-dropped does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=1, k=0): sum 1+0i, target 0", "ms": 0.5, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 0.125, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphaevolve-48-4x4x4/term-duplicated", "class": "term-duplicated", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 24 of U, V and W appended again; rank claimed 49", "sha256": "5af98819cd67b5fafbdcd86ef750326ca61a642abe2e0427d8f02f7f38936cdc", "bytes": 15124, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 0, "sum": [ -1, 0 ], "target": [ 0, 0 ] }, "CA": { "ab": 0, "bc": 1, "k": 0, "sum": [ -1, 0 ], "target": [ 0, 0 ] } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: alphaevolve-48-4x4x4/term-duplicated does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=1, k=0): sum -1+0i, target 0", "ms": 0.1, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 0.125, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mm-alphaevolve-48-4x4x4/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 48", "sha256": "af585bd132cc8176c687e7a849a1a8252a520cdc3268d2a0f7cbdd93ea322dff", "bytes": 14814, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": [ 0, 0 ], "target": [ 8, 0 ] }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "alphaevolve-48-4x4x4/columns-permuted: 4x4 times 4x4 in 48 multiplications VERIFIED over Z[i] (doubled half-Gaussian factors; identity = 8*T, denominators cleared) — all 4096 tensor-identity equations hold exactly (layout CA); rank 48 < 64 naive", "ms": 0.9, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mm-alphaevolve-48-4x4x4/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 24 of U and of V negated (the product u·v·w unchanged)", "sha256": "d438252a92899e55cc694bd550327bc0898b90801c067f535248dee93123975f", "bytes": 14812, "witness": { "violated": false, 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false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-q-2x4x5/uv-signs-flipped: 2x4 times 4x5 in 33 multiplications VERIFIED over Q — all 1600 tensor-identity equations hold exactly (layout CA); rank 33 < 40 naive", "ms": 0.1, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-q-2x4x5/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 32 entries", "sha256": "e0ce82aa5c19e9792737fb2a50bae4d489e1643d9a725b0103241be47ef0c208", "bytes": 2785, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "a factor row does not have 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required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x2x3/term-duplicated", "class": "term-duplicated", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 5 of U, V and W appended again; rank claimed 12", "sha256": "023b95e066b2a67723970ab98b3408520ed1a5ee0e700320d9b34697d6fe4eb8", "bytes": 472, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 1, "bc": 0, "k": 0, "sum": 3, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x2x3/term-duplicated does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=1, bc=0, k=0): sum 3, target 0 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, 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"maxResidual": 2, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x2x3/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 11", "sha256": "8c3f97f571f0ba04a992f3cc5407bdf03d4c61f9edce8fd257cfdb00f68ad80a", "bytes": 440, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x2x3/columns-permuted: 2x2 times 2x3 in 11 multiplications VERIFIED over F2 — all 144 tensor-identity equations hold exactly (layout CA); rank 11 < 12 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-2x2x3/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 5 of U and of V negated (the product u·v·w unchanged); over F₂ this is the identity, the mutant equals the original", "sha256": "4922a205ac79edfdce25bfe43b11423ff3615a26d3a5d3a3eda89429475af60f", "bytes": 444, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x2x3/uv-signs-flipped: 2x2 times 2x3 in 11 multiplications VERIFIED over F2 — all 144 tensor-identity equations hold exactly (layout CA); rank 11 < 12 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-2x2x3/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 10 entries", "sha256": "69cd916e441aec8d30faedc3fb439924f067761e340f44bb716b1ee6c1b6d9f2", "bytes": 438, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "a factor row does not have rank-many entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "claimed rank 11 but the factors have 10 columns", "ms": 0, "bigInt": { "verdict": "not run (the exact-double audit refused)", "agrees": null } }, "required": "REFUSED", "outcome": "as required", "float": { "error": "list index out of range", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [ { "class": "coefficient-times-one-plus-1e-9", "reason": "no meaning over F₂: 1 + 10⁻⁹ is not an element of the field; the class is stated for Q and Z[i]" } ], "controlsFired": [], "ms": 137 }, { "rowId": "mc100-at-f2-2x2x4", "record": "certs/mc100-alphatensor-f2.json", "entryId": "at-f2-2x2x4", "verdict": "CERTIFIED", "object": "<2,2,4> rank 14 over F2", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x2x4: 2x2 times 2x4 in 14 multiplications VERIFIED over F2 — all 256 tensor-identity equations hold exactly (layout CA); rank 14 < 16 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "995bce5039daa942478fdf2e0fa01b703c5c8049df11eea95cc66863ec6c5479" }, "mutants": [ { "id": "mc100-at-f2-2x2x4/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][3] += 1", "sha256": "2d9f6e9e052eb69413702e5f2a4a5c3a37e2c483474f1b4a14875903c3839c13", "bytes": 656, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 0, "bc": 2, "k": 4, "sum": 2, "target": 1, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x2x4/coefficient-plus-one does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=2, k=4): sum 2, target 1 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x2x4/term-dropped", "class": "term-dropped", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 7 removed from U, V and W; rank claimed 13", "sha256": "869688d72291e11182433b94703b904461c5a9c23a9363d7dce47e7f5d0443c5", "bytes": 616, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 0, "bc": 2, "k": 6, "sum": 1, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x2x4/term-dropped does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=2, k=6): sum 1, target 0 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x2x4/term-duplicated", "class": "term-duplicated", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 7 of U, V and W appended again; rank claimed 15", "sha256": "8db34c7792cce55d98f61808828bfc4d157abdec265ca15c7db2e4a3ff63a9bd", "bytes": 696, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 0, "bc": 2, "k": 6, "sum": 3, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x2x4/term-duplicated does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=2, k=6): sum 3, target 0 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x2x4/f2-asserted-over-q", "class": "f2-asserted-over-q", "truth": "FALSE", "preservesOriginal": false, "transformation": "ring F2 → Q, the factors unchanged (FALSE only when the witness finds a violated entry over Z, else DISCARDED)", "sha256": "b1b227191e1b07f5c1339a9386d7f2adda89694ea3de8553968b1fc9a3ef93a2", "bytes": 655, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": { "ab": 0, "bc": 2, "k": 6, "sum": 2, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x2x4/f2-asserted-over-q does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=2, k=6): sum 2, target 0", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 4, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x2x4/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 14", "sha256": "65696bcb777af640c918da52f54ef5ae8babe48c1fe62c88648a714b9531acec", "bytes": 656, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x2x4/columns-permuted: 2x2 times 2x4 in 14 multiplications VERIFIED over F2 — all 256 tensor-identity equations hold exactly (layout CA); rank 14 < 16 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-2x2x4/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 7 of U and of V negated (the product u·v·w unchanged); over F₂ this is the identity, the mutant equals the original", "sha256": "d65bf9bf899e01375daf31dddd97f529ebeef9dd6c2875a4f404946e06b52577", "bytes": 662, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x2x4/uv-signs-flipped: 2x2 times 2x4 in 14 multiplications VERIFIED over F2 — all 256 tensor-identity equations hold exactly (layout CA); rank 14 < 16 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-2x2x4/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 13 entries", "sha256": "312a30fcdfa24bed75a48a13fe4ee9d555e260c525936861e2170870b62d7f45", "bytes": 654, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "a factor row does not have rank-many entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "claimed rank 14 but the factors have 13 columns", "ms": 0, "bigInt": { "verdict": "not run (the exact-double audit refused)", "agrees": null } }, "required": "REFUSED", "outcome": "as required", "float": { "error": "list index out of range", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [ { "class": "coefficient-times-one-plus-1e-9", "reason": "no meaning over F₂: 1 + 10⁻⁹ is not an element of the field; the class is stated for Q and Z[i]" } ], "controlsFired": [], "ms": 139 }, { "rowId": "mc100-at-f2-2x3x3", "record": "certs/mc100-alphatensor-f2.json", "entryId": "at-f2-2x3x3", "verdict": "CERTIFIED", "object": "<2,3,3> rank 15 over F2", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x3x3: 2x3 times 3x3 in 15 multiplications VERIFIED over F2 — all 324 tensor-identity equations hold exactly (layout CA); rank 15 < 18 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "d910af5a6863163abde21e31d73288028a255d621f515404f86f998a5071a3b6" }, "mutants": [ { "id": "mc100-at-f2-2x3x3/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][2] += 1", "sha256": "bb9f1839c63779d1007efb87eda67084f45c7cea0cceae45921fc6c4e27d38e4", "bytes": 728, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 0, "bc": 1, "k": 2, "sum": 2, "target": 1, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x3x3/coefficient-plus-one does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=1, k=2): sum 2, target 1 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x3x3/term-dropped", "class": "term-dropped", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 7 removed from U, V and W; rank claimed 14", "sha256": "787a00ea8b1a37e8448cb5f53268ed3334fb64e2b8af8a9d7d7de286a4b28660", "bytes": 686, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 0, "bc": 5, "k": 4, "sum": 1, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x3x3/term-dropped does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=5, k=4): sum 1, target 0 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x3x3/term-duplicated", "class": "term-duplicated", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 7 of U, V and W appended again; rank claimed 16", "sha256": "88d2c8ad6bb8077e2ae3746c208618fa7d5ec6b325fda0ac4c5b48a57844acf7", "bytes": 770, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 0, "bc": 5, "k": 4, "sum": 3, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x3x3/term-duplicated does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=5, k=4): sum 3, target 0 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x3x3/f2-asserted-over-q", "class": "f2-asserted-over-q", "truth": "FALSE", "preservesOriginal": false, "transformation": "ring F2 → Q, the factors unchanged (FALSE only when the witness finds a violated entry over Z, else DISCARDED)", "sha256": "e8fc57781c89fa659364dbb9f5a4392668cc124a2bd627cbc726547c66c24469", "bytes": 727, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 0, "k": 2, "sum": 2, "target": 0, "mod": null }, "CA": { "ab": 0, "bc": 0, "k": 2, "sum": 2, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x3x3/f2-asserted-over-q does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=0, k=2): sum 2, target 0", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 2, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x3x3/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 15", "sha256": "242c93824a6b8e5812a246d15859f5c0d2b164be7ae5e50ecf3ab3d80c31af01", "bytes": 728, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x3x3/columns-permuted: 2x3 times 3x3 in 15 multiplications VERIFIED over F2 — all 324 tensor-identity equations hold exactly (layout CA); rank 15 < 18 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-2x3x3/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 7 of U and of V negated (the product u·v·w unchanged); over F₂ this is the identity, the mutant equals the original", "sha256": "d94285ec180b1a917346b3afeb371b288f49c66ad21cca4e97b01e0226ae2b3c", "bytes": 731, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x3x3/uv-signs-flipped: 2x3 times 3x3 in 15 multiplications VERIFIED over F2 — all 324 tensor-identity equations hold exactly (layout CA); rank 15 < 18 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-2x3x3/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 14 entries", "sha256": "6d7deb73a91e3faeaaaed2bbb9c228889e4d6777dcd1dbe456692731981c8f6f", "bytes": 726, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "a factor row does not have rank-many entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "claimed rank 15 but the factors have 14 columns", "ms": 0, "bigInt": { "verdict": "not run (the exact-double audit refused)", "agrees": null } }, "required": "REFUSED", "outcome": "as required", "float": { "error": "list index out of range", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [ { "class": "coefficient-times-one-plus-1e-9", "reason": "no meaning over F₂: 1 + 10⁻⁹ is not an element of the field; the class is stated for Q and Z[i]" } ], "controlsFired": [], "ms": 141 }, { "rowId": "mc100-at-f2-2x2x5", "record": "certs/mc100-alphatensor-f2.json", "entryId": "at-f2-2x2x5", "verdict": "CERTIFIED", "object": "<2,2,5> rank 18 over F2", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x2x5: 2x2 times 2x5 in 18 multiplications VERIFIED over F2 — all 400 tensor-identity equations hold exactly (layout CA); rank 18 < 20 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0.1, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "f59280aa25091044758aabe8444fd870ddd2acdd1ff2d3d607eaaa0e548c3401" }, "mutants": [ { "id": "mc100-at-f2-2x2x5/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][3] += 1", "sha256": "a5ed59e32fb189502a097bddd5958349ba82671c2956e36d036f20742ebde613", "bytes": 968, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 0, "bc": 3, "k": 6, "sum": 2, "target": 1, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x2x5/coefficient-plus-one does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=3, k=6): sum 2, target 1 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x2x5/term-dropped", "class": "term-dropped", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 9 removed from U, V and W; rank claimed 17", "sha256": "46cc5267aab643fbf3115320d037e188f90c138933752fadc865baa92d629b4d", "bytes": 920, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 3, "bc": 2, "k": 5, "sum": 1, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x2x5/term-dropped does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=3, bc=2, k=5): sum 1, target 0 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x2x5/term-duplicated", "class": "term-duplicated", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 9 of U, V and W appended again; rank claimed 19", "sha256": "84f3dc69a6a18fd6b6847abb14b364d5e729b7e2ad0bcea909306efb2b9df6f2", "bytes": 1016, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 3, "bc": 2, "k": 5, "sum": 3, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x2x5/term-duplicated does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=3, bc=2, k=5): sum 3, target 0 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x2x5/f2-asserted-over-q", "class": "f2-asserted-over-q", "truth": "FALSE", "preservesOriginal": false, "transformation": "ring F2 → Q, the factors unchanged (FALSE only when the witness finds a violated entry over Z, else DISCARDED)", "sha256": "9380e5f904b4b6170b9e09329f92d6c4219a7cf5b29a152014bd358a58cf0199", "bytes": 967, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": { "ab": 1, "bc": 0, "k": 0, "sum": 2, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x2x5/f2-asserted-over-q does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=1, bc=0, k=0): sum 2, target 0", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 2, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x2x5/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 18", "sha256": "09cc81327615908f67b0eb65fd67eae79e2104e68c42969d5e465ef170a3a5d4", "bytes": 968, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x2x5/columns-permuted: 2x2 times 2x5 in 18 multiplications VERIFIED over F2 — all 400 tensor-identity equations hold exactly (layout CA); rank 18 < 20 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-2x2x5/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 9 of U and of V negated (the product u·v·w unchanged); over F₂ this is the identity, the mutant equals the original", "sha256": "7f82ccf5f293370d58857ecf2b5c793dd5144ce5c1b2faa083e0de209ab33e6f", "bytes": 971, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x2x5/uv-signs-flipped: 2x2 times 2x5 in 18 multiplications VERIFIED over F2 — all 400 tensor-identity equations hold exactly (layout CA); rank 18 < 20 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-2x2x5/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 17 entries", "sha256": "06ec8c8271144b4001bfcb55c16ef0d3e3855385db207712ee2f76458e563173", "bytes": 966, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "a factor row does not have rank-many entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "claimed rank 18 but the factors have 17 columns", "ms": 0, "bigInt": { "verdict": "not run (the exact-double audit refused)", "agrees": null } }, "required": "REFUSED", "outcome": "as required", "float": { "error": "list index out of range", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [ { "class": "coefficient-times-one-plus-1e-9", "reason": "no meaning over F₂: 1 + 10⁻⁹ is not an element of the field; the class is stated for Q and Z[i]" } ], "controlsFired": [], "ms": 150 }, { "rowId": "mc100-at-f2-2x3x4", "record": "certs/mc100-alphatensor-f2.json", "entryId": "at-f2-2x3x4", "verdict": "CERTIFIED", "object": "<2,3,4> rank 20 over F2", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x3x4: 2x3 times 3x4 in 20 multiplications VERIFIED over F2 — all 576 tensor-identity equations hold exactly (layout CA); rank 20 < 24 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0.1, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "b8db97439219cf1ad8f217eeb6c2135404a55ea46232e423d7fb3bf2a2605ace" }, "mutants": [ { "id": "mc100-at-f2-2x3x4/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][2] += 1", "sha256": "8a5f842f9c1a77b565b87fc45feb517f5ab5b75c0e707c3fc6979d5d0ca0bc47", "bytes": 1148, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 0, "bc": 3, "k": 2, "sum": 3, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x3x4/coefficient-plus-one does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=3, k=2): sum 3, target 0 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x3x4/term-dropped", "class": "term-dropped", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 10 removed from U, V and W; rank claimed 19", "sha256": "febc83a434263574771304f5a74b7a41e27edf6f5e62c5836dd06a9c46e06dce", "bytes": 1096, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 5, "bc": 5, "k": 3, "sum": 1, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x3x4/term-dropped does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=5, bc=5, k=3): sum 1, target 0 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x3x4/term-duplicated", "class": "term-duplicated", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 10 of U, V and W appended again; rank claimed 21", "sha256": "f00f383ed23dd0a647d652078b9c1512eee7dbb8d0eb515a7e39be99528512b8", "bytes": 1200, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 5, "bc": 5, "k": 3, "sum": 3, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x3x4/term-duplicated does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=5, bc=5, k=3): sum 3, target 0 (mod 2)", "ms": 0.2, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x3x4/f2-asserted-over-q", "class": "f2-asserted-over-q", "truth": "FALSE", "preservesOriginal": false, "transformation": "ring F2 → Q, the factors unchanged (FALSE only when the witness finds a violated entry over Z, else DISCARDED)", "sha256": "eeec2246393af39a7c263792f603f53612005d2486b86825300c5dc474a8f7f9", "bytes": 1147, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 0, "k": 5, "sum": 2, "target": 0, "mod": null }, "CA": { "ab": 0, "bc": 0, "k": 5, "sum": 2, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x3x4/f2-asserted-over-q does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=0, k=5): sum 2, target 0", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 4, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x3x4/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 20", "sha256": "4e607f59f96bd1df2d7c966b5c482a3be9b61088b45d0040e4b0eb92c85fbc4b", "bytes": 1148, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x3x4/columns-permuted: 2x3 times 3x4 in 20 multiplications VERIFIED over F2 — all 576 tensor-identity equations hold exactly (layout CA); rank 20 < 24 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0.1, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-2x3x4/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 10 of U and of V negated (the product u·v·w unchanged); over F₂ this is the identity, the mutant equals the original", "sha256": "b52ba3765a8d8c98ed6319d4923dbe88bc5b80ed9d966c8c9c58ca21b492c5e4", "bytes": 1151, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x3x4/uv-signs-flipped: 2x3 times 3x4 in 20 multiplications VERIFIED over F2 — all 576 tensor-identity equations hold exactly (layout CA); rank 20 < 24 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0.1, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-2x3x4/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 19 entries", "sha256": "1cdef21d3c512c7837203cca0cad883008cdebec115106d2306c9a5c03d07e2f", "bytes": 1146, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "a factor row does not have rank-many entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "claimed rank 20 but the factors have 19 columns", "ms": 0, "bigInt": { "verdict": "not run (the exact-double audit refused)", "agrees": null } }, "required": "REFUSED", "outcome": "as required", "float": { "error": "list index out of range", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [ { "class": "coefficient-times-one-plus-1e-9", "reason": "no meaning over F₂: 1 + 10⁻⁹ is not an element of the field; the class is stated for Q and Z[i]" } ], "controlsFired": [], "ms": 157 }, { "rowId": "mc100-at-f2-2x3x5", "record": "certs/mc100-alphatensor-f2.json", "entryId": "at-f2-2x3x5", "verdict": "CERTIFIED", "object": "<2,3,5> rank 25 over F2", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x3x5: 2x3 times 3x5 in 25 multiplications VERIFIED over F2 — all 900 tensor-identity equations hold exactly (layout CA); rank 25 < 30 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0.1, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "a59c1de22fde0e77fa2a0e70045b08948b15d33e77fbe13175d06d5e49367d7b" }, "mutants": [ { "id": "mc100-at-f2-2x3x5/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][6] += 1", "sha256": "90d225ada12ee4e1dc577a36005550907ffbb247ae229634bf144cf78f30c3ee", "bytes": 1668, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 0, "bc": 2, "k": 0, "sum": 3, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x3x5/coefficient-plus-one does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=2, k=0): sum 3, target 0 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x3x5/term-dropped", "class": "term-dropped", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 12 removed from U, V and W; rank claimed 24", "sha256": "e48659558b7d99609dad74ce3cf79918c0d1a0bb9bb972c38a13eb1e5c5daab3", "bytes": 1606, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 1, "bc": 1, "k": 6, "sum": 1, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x3x5/term-dropped does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=1, bc=1, k=6): sum 1, target 0 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x3x5/term-duplicated", "class": "term-duplicated", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 12 of U, V and W appended again; rank claimed 26", "sha256": "a4bfea15d03e6955e21febe340d6e31c8ae1fad11ab5d1dccd7a8764f6c2e1ca", "bytes": 1730, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 1, "bc": 1, "k": 6, "sum": 3, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x3x5/term-duplicated does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=1, bc=1, k=6): sum 3, target 0 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x3x5/f2-asserted-over-q", "class": "f2-asserted-over-q", "truth": "FALSE", "preservesOriginal": false, "transformation": "ring F2 → Q, the factors unchanged (FALSE only when the witness finds a violated entry over Z, else DISCARDED)", "sha256": "fdbffe0dcd9e03ba6c24c4b31cdd1b7959958230df72d877e26921ab30ebcf8a", "bytes": 1667, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": { "ab": 0, "bc": 1, "k": 3, "sum": 2, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x3x5/f2-asserted-over-q does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=1, k=3): sum 2, target 0", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 4, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x3x5/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 25", "sha256": "d9170ec575b3d72616aaee4cb895bf6ef6aceaa7ff3d1db0d61a69ccdcbdb606", "bytes": 1668, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x3x5/columns-permuted: 2x3 times 3x5 in 25 multiplications VERIFIED over F2 — all 900 tensor-identity equations hold exactly (layout CA); rank 25 < 30 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0.1, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-2x3x5/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 12 of U and of V negated (the product u·v·w unchanged); over F₂ this is the identity, the mutant equals the original", "sha256": "830f25e16a388228f23333cc3275dcd4ded0b8ead2929068136eca8274a594db", "bytes": 1678, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x3x5/uv-signs-flipped: 2x3 times 3x5 in 25 multiplications VERIFIED over F2 — all 900 tensor-identity equations hold exactly (layout CA); rank 25 < 30 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0.1, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-2x3x5/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 24 entries", "sha256": "0451b9f17b9b0a9d7844be513df4398f61a4a207b25f28f032bc815c2c44157a", "bytes": 1666, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "a factor row does not have rank-many entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "claimed rank 25 but the factors have 24 columns", "ms": 0, "bigInt": { "verdict": "not run (the exact-double audit refused)", "agrees": null } }, "required": "REFUSED", "outcome": "as required", "float": { "error": "list index out of range", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [ { "class": "coefficient-times-one-plus-1e-9", "reason": "no meaning over F₂: 1 + 10⁻⁹ is not an element of the field; the class is stated for Q and Z[i]" } ], "controlsFired": [], "ms": 175 }, { "rowId": "mc100-at-f2-2x4x4", "record": "certs/mc100-alphatensor-f2.json", "entryId": "at-f2-2x4x4", "verdict": "CERTIFIED", "object": "<2,4,4> rank 26 over F2", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x4x4: 2x4 times 4x4 in 26 multiplications VERIFIED over F2 — all 1024 tensor-identity equations hold exactly (layout CA); rank 26 < 32 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0.1, 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"verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x4x4/term-duplicated", "class": "term-duplicated", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 13 of U, V and W appended again; rank claimed 27", "sha256": "525791283b523e97a525304f565db750dbff46e97e67673ec17b797dd9e50344", "bytes": 1848, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 5, "bc": 4, "k": 1, "sum": 2, "target": 1, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x4x4/term-duplicated does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=5, bc=4, k=1): sum 2, target 1 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x4x4/f2-asserted-over-q", "class": "f2-asserted-over-q", "truth": "FALSE", "preservesOriginal": false, "transformation": "ring F2 → Q, the factors unchanged (FALSE only when the witness finds a violated entry over Z, else DISCARDED)", "sha256": "1e45037b0b8c25b05d10b8143b0c36f72d59cd6959333e82093e4d51a6e34a64", "bytes": 1783, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 0, "k": 1, "sum": 2, "target": 0, "mod": null }, "CA": { "ab": 0, "bc": 0, "k": 1, "sum": 2, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-2x4x4/f2-asserted-over-q does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=0, k=1): sum 2, target 0", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 2, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-2x4x4/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 26", "sha256": "3074182017227e4f44f64cc7f016fdaeba90d3f0ddfff4f811116375e9c2f5ec", "bytes": 1784, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x4x4/columns-permuted: 2x4 times 4x4 in 26 multiplications VERIFIED over F2 — all 1024 tensor-identity equations hold exactly (layout CA); rank 26 < 32 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0.1, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-2x4x4/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 13 of U and of V negated (the product u·v·w unchanged); over F₂ this is the identity, the mutant equals the original", "sha256": "efc11f7e8d9fc67aaabc2e44105863da40095dd3de38a6c4ff299335a30a0ecf", "bytes": 1789, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-2x4x4/uv-signs-flipped: 2x4 times 4x4 in 26 multiplications VERIFIED over F2 — all 1024 tensor-identity equations hold exactly (layout CA); rank 26 < 32 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0.1, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-2x4x4/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 25 entries", "sha256": "d3033c2fe2e6ebf83ef0343219b36bc4b2196f6bfaaa614e978b1d043e90887e", "bytes": 1782, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "a factor row does not have rank-many entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "claimed rank 26 but the factors have 25 columns", "ms": 0, "bigInt": { "verdict": "not run (the exact-double audit refused)", "agrees": null } }, "required": "REFUSED", "outcome": "as required", "float": { "error": "list index out of range", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [ { "class": "coefficient-times-one-plus-1e-9", "reason": "no meaning over F₂: 1 + 10⁻⁹ is not an element of the field; the class is stated for Q and Z[i]" } ], "controlsFired": [], "ms": 182 }, { "rowId": "mc100-at-f2-3x3x4", "record": "certs/mc100-alphatensor-f2.json", "entryId": "at-f2-3x3x4", "verdict": "CERTIFIED", "object": "<3,3,4> rank 29 over F2", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "at-f2-3x3x4: 3x3 times 3x4 in 29 multiplications VERIFIED over F2 — all 1296 tensor-identity equations hold exactly (layout CA); rank 29 < 36 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0.1, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "6c6b9bce7bac065934ec2dd9224496c57afba4a03a61ca4f1f59cb03129d1fa6" }, "mutants": [ { "id": "mc100-at-f2-3x3x4/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][0] += 1", "sha256": "19676d264744f4cb3e881db48fe22da336ca20b922c2d6a4cfc1599b89f2d025", "bytes": 2036, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 0, "bc": 1, "k": 3, "sum": 2, "target": 1, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-3x3x4/coefficient-plus-one does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=1, k=3): sum 2, target 1 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-3x3x4/term-dropped", "class": "term-dropped", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 14 removed from U, V and W; rank claimed 28", "sha256": "a585fd79902487593adb8373aaad17c23b7f8080d49fca08a945305a8d53f6ee", "bytes": 1970, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 0, "bc": 2, "k": 1, "sum": 1, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-3x3x4/term-dropped does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=2, k=1): sum 1, target 0 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-3x3x4/term-duplicated", "class": "term-duplicated", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 14 of U, V and W appended again; rank claimed 30", "sha256": "4f327ccf49120747bed810f6b059fba814a4495e8f9826e15afa5c8e7e749ce9", "bytes": 2102, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": { "ab": 0, "bc": 2, "k": 1, "sum": 3, "target": 0, "mod": 2 } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-3x3x4/term-duplicated does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=2, k=1): sum 3, target 0 (mod 2)", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-3x3x4/f2-asserted-over-q", "class": "f2-asserted-over-q", "truth": "FALSE", "preservesOriginal": false, "transformation": "ring F2 → Q, the factors unchanged (FALSE only when the witness finds a violated entry over Z, else DISCARDED)", "sha256": "8b29b0f33f3c4372e94becf958c2c2a3691855f54ac2c239dbb04a833743e116", "bytes": 2035, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 0, "sum": 2, "target": 0, "mod": null }, "CA": { "ab": 0, "bc": 1, "k": 0, "sum": 2, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: at-f2-3x3x4/f2-asserted-over-q does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=1, k=0): sum 2, target 0", "ms": 0, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 2, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-at-f2-3x3x4/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 29", "sha256": "a37ca18d3d2ce9b97c11e9682ed996dc9208711a05fc64bf784ac92ddba4a765", "bytes": 2036, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-3x3x4/columns-permuted: 3x3 times 3x4 in 29 multiplications VERIFIED over F2 — all 1296 tensor-identity equations hold exactly (layout CA); rank 29 < 36 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0.1, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-3x3x4/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 14 of U and of V negated (the product u·v·w unchanged); over F₂ this is the identity, the mutant equals the original", "sha256": "b01b1ccdef6777c3036071ed11a3eaa11c8b194138ffd8ab1c493f397eb90919", "bytes": 2041, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": 2 }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "at-f2-3x3x4/uv-signs-flipped: 3x3 times 3x4 in 29 multiplications VERIFIED over F2 — all 1296 tensor-identity equations hold exactly (layout CA); rank 29 < 36 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2", "ms": 0.1, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-at-f2-3x3x4/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 28 entries", "sha256": "c998b4b7802446bedf184e7898f07a88ebb566b3b6c139715ca28cb6e1e03990", "bytes": 2034, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "a factor row does not have rank-many entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "claimed rank 29 but the factors have 28 columns", "ms": 0, "bigInt": { "verdict": "not run (the exact-double audit refused)", "agrees": null } }, "required": "REFUSED", "outcome": "as required", "float": { "error": "list index out of range", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [ { "class": "coefficient-times-one-plus-1e-9", "reason": "no meaning over F₂: 1 + 10⁻⁹ is not an element of the field; the class is stated for Q and Z[i]" } ], "controlsFired": [], "ms": 189 }, { "rowId": "mc100-ae-nb-2x4x5-r32", "record": "certs/mc100-alphaevolve-nb-matmul.json", "entryId": "ae-nb-2x4x5-r32", "verdict": "CERTIFIED", "object": "<2,4,5> rank 32 over Q (scale 8)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "ae-nb-2x4x5-r32: 2x4 times 4x5 in 32 multiplications VERIFIED over Q — all 1600 tensor-identity equations hold exactly (layout CA); rank 32 < 40 naive", "ms": 1.5, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "727d58fe12d82b16f80833197fb7331bf12573c9f95cf2f3272e54feabe0f811" }, "mutants": [ { "id": "mc100-ae-nb-2x4x5-r32/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][1] += 1", "sha256": "a343d6f98c46fb3402de6fe3af14cdb3512beffaa4c64747f837d9b6ef35e676", "bytes": 2832, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 8, "mod": null }, "CA": { "ab": 0, "bc": 5, "k": 0, "sum": -4, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: ae-nb-2x4x5-r32/coefficient-plus-one does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=5, k=0): sum -4, target 0", "ms": 0.1, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 0.5, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-ae-nb-2x4x5-r32/coefficient-times-one-plus-1e-9", "class": "coefficient-times-one-plus-1e-9", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][1] × 1.000000001 exactly: U scaled by 10⁹ with that entry × 1000000001, the identity's scale × 10⁹ (scale 8000000000)", "sha256": "23217f4122ff7966338c978fa8fdd3a1d861525c0a31eefd732a726bb8f339f6", "bytes": 3813, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 8000000000, "mod": null }, "CA": { "ab": 0, "bc": 5, "k": 0, "sum": -4, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: ae-nb-2x4x5-r32/coefficient-times-one-plus-1e-9 does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=5, k=0): sum -4, target 0", "ms": 0.1, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 5e-10, "accept": { "1e-6": true, "1e-9": true, "1e-12": false } } }, { "id": "mc100-ae-nb-2x4x5-r32/term-dropped", "class": "term-dropped", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 16 removed from U, V and W; rank claimed 31", "sha256": "4576ff73d12b602ec0e5993facad74a3e0cd2d7bc64186cb0d942b425d093911", "bytes": 2745, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 8, "mod": null }, "CA": { "ab": 0, "bc": 2, "k": 4, "sum": 4, "target": 8, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: ae-nb-2x4x5-r32/term-dropped does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=2, k=4): sum 4, target 8", "ms": 0.1, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 0.5, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-ae-nb-2x4x5-r32/term-duplicated", "class": "term-duplicated", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 16 of U, V and W appended again; rank claimed 33", "sha256": "4b7eed201418c46829ee76f89930619517a95dbe05e1d59d242cfa1e501bfc5e", "bytes": 2919, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { 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"target": 8, "mod": null }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "ae-nb-2x4x5-r32/columns-permuted: 2x4 times 4x5 in 32 multiplications VERIFIED over Q — all 1600 tensor-identity equations hold exactly (layout CA); rank 32 < 40 naive", "ms": 0.2, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ae-nb-2x4x5-r32/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 16 of U and of V negated (the product u·v·w unchanged)", "sha256": "fdff379c7e7f32d4e2261ee1601c2e8176b6476c1e7b8a675e42fb25e51e27fc", "bytes": 2832, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 8, "mod": null }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": 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exact-double audit refused)", "agrees": null } }, "required": "REFUSED", "outcome": "as required", "float": { "error": "list index out of range", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [], "ms": 209 }, { "rowId": "mc100-ae-nb-2x4x7-r45", "record": "certs/mc100-alphaevolve-nb-matmul.json", "entryId": "ae-nb-2x4x7-r45", "verdict": "CERTIFIED", "object": "<2,4,7> rank 45 over Q", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "ae-nb-2x4x7-r45: 2x4 times 4x7 in 45 multiplications VERIFIED over Q — all 3136 tensor-identity equations hold exactly (layout CA); rank 45 < 56 naive", "ms": 0.3, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "939f97c7610d061b8e0a8465b895ecf5212669c3926b614886ffe4cdb133b2e1" }, "mutants": [ { "id": "mc100-ae-nb-2x4x7-r45/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][1] += 1", "sha256": "901e2ad628203f5cac45517b2fdee452bf8d15e8c008dd4e456a9aa77ab3ed19", "bytes": 4863, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": { "ab": 0, "bc": 1, "k": 9, "sum": 1, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: ae-nb-2x4x7-r45/coefficient-plus-one does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=1, k=9): sum 1, target 0", "ms": 0.1, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-ae-nb-2x4x7-r45/coefficient-times-one-plus-1e-9", "class": "coefficient-times-one-plus-1e-9", "truth": "FALSE", "preservesOriginal": false, "transformation": "U[0][1] × 1.000000001 exactly: U scaled by 10⁹ with that entry × 1000000001, the identity's scale × 10⁹ (scale 1000000000)", "sha256": "1e726c80c72840b98eee6870bcf2b0106a21ba9674e26b3f463c4265fe58b3ad", "bytes": 5936, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1000000000, "mod": null }, "CA": { "ab": 0, "bc": 1, "k": 9, "sum": -1, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: ae-nb-2x4x7-r45/coefficient-times-one-plus-1e-9 does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=1, k=9): sum -1, target 0", "ms": 0.1, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1e-9, "accept": { "1e-6": true, "1e-9": 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"why": "ae-nb-4x5x6-r90/columns-permuted: 4x5 times 5x6 in 90 multiplications VERIFIED over Q — all 14400 tensor-identity equations hold exactly (layout CA); rank 90 < 120 naive", "ms": 1.5, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ae-nb-4x5x6-r90/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 45 of U and of V negated (the product u·v·w unchanged)", "sha256": "725daa7e497e65bc0204274265967cca74500bf1dceb21c4ecfa1eca8d5e684c", "bytes": 14038, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "ae-nb-4x5x6-r90/uv-signs-flipped: 4x5 times 5x6 in 90 multiplications VERIFIED over Q — all 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false, "transformation": "U[0][3] × 1.000000001 exactly: U scaled by 10⁹ with that entry × 1000000001, the identity's scale × 10⁹ (scale 1000000000)", "sha256": "0c60d30bd7ec1072fd15a74f520e661752e72e1a42369894c67aac3b2265eb68", "bytes": 17883, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1000000000, "mod": null }, "CA": { "ab": 0, "bc": 1, "k": 24, "sum": -1, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: ae-nb-5x5x5-r93/coefficient-times-one-plus-1e-9 does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=1, k=24): sum -1, target 0", "ms": 0.1, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1e-9, "accept": { "1e-6": true, "1e-9": true, "1e-12": false } } }, { "id": "mc100-ae-nb-5x5x5-r93/term-dropped", "class": "term-dropped", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 46 removed from U, V and W; rank claimed 92", "sha256": "52ef0a9539148b722a55a2a00d0cac875249c3c0c53dc3d2da09959d47420931", "bytes": 14529, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": { "ab": 1, "bc": 0, "k": 12, "sum": 1, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: ae-nb-5x5x5-r93/term-dropped does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=1, bc=0, k=12): sum 1, target 0", "ms": 0.2, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-ae-nb-5x5x5-r93/term-duplicated", "class": "term-duplicated", "truth": "FALSE", "preservesOriginal": false, "transformation": "column 46 of U, V and W appended again; rank claimed 94", "sha256": "62c7dba157e398480e14c2f5ade0030f35bdccf128ce3a8e9ebf530e8e924131", "bytes": 14845, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": { "ab": 1, "bc": 0, "k": 12, "sum": -1, "target": 0, "mod": null } } }, "decided": { "verdict": "REFUTED", "why": "DISCOVERY-CLASS REFUTATION: ae-nb-5x5x5-r93/term-duplicated does NOT multiply matrices — identity fails under BOTH C-layouts; last failure: equation (ab=1, bc=0, k=12): sum -1, target 0", "ms": 0.2, "bigInt": { "verdict": "REFUTED", "agrees": true } }, "required": "REFUTED", "outcome": "as required", "float": { "maxResidual": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-ae-nb-5x5x5-r93/columns-permuted", "class": "columns-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "columns of U, V and W permuted by t → t+1 mod 93", "sha256": "c66c77832fe255eb738a1c3e4b10d4cdbcc8722c22f322af3e088bac8ebd3d5b", "bytes": 14687, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "ae-nb-5x5x5-r93/columns-permuted: 5x5 times 5x5 in 93 multiplications VERIFIED over Q — all 15625 tensor-identity equations hold exactly (layout CA); rank 93 < 125 naive", "ms": 1.7, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ae-nb-5x5x5-r93/uv-signs-flipped", "class": "uv-signs-flipped", "truth": "TRUE", "preservesOriginal": false, "transformation": "column 46 of U and of V negated (the product u·v·w unchanged)", "sha256": "eb057af48ca02face337f5d9a196789121b6cc76156be9d5bb71be5264d52360", "bytes": 14686, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": { "AC": { "ab": 0, "bc": 1, "k": 1, "sum": 0, "target": 1, "mod": null }, "CA": null } }, "decided": { "verdict": "CERTIFIED", "why": "ae-nb-5x5x5-r93/uv-signs-flipped: 5x5 times 5x5 in 93 multiplications VERIFIED over Q — all 15625 tensor-identity equations hold exactly (layout CA); rank 93 < 125 naive", "ms": 1.8, "bigInt": { "verdict": "VERIFIED", "agrees": true } }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxResidual": 0, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ae-nb-5x5x5-r93/short-row", "class": "short-row", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "U[0] shortened to 92 entries", "sha256": "eb3eab6b4658c31a1c90819e0ff76faf8306b862516af724c41a224c0bbcdc33", "bytes": 14684, "fixedFrom": "not as required (REFUTED)", "fix": 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"reason": null, "firstViolation": { "kind": "pair at less than 60 degrees", "i": 7, "j": 24, "dot": [ "2", "0" ], "normI": [ "2", "0" ], "normJ": [ "2", "0" ], "slack": [ "-12", "0" ] } }, "decided": { "verdict": "REFUTED", "why": "pair (7, 24): = 2 + 0√2, cos² ≈ 1", "ms": 0.2 }, "required": "REFUTED", "outcome": "as required", "float": { "maxCosine": 0.9999999999999998, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "kiss-cal-d4-24/row-doubled", "class": "row-doubled", "truth": "FALSE", "preservesOriginal": false, "transformation": "the last row replaced by 2 × row 3 (parallel to row 3)", "sha256": "d3bda0fa8a11f6af82f703817bb28d7d2ae2e7a7ce9fb5b839e768b90352c3f4", "bytes": 1057, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "pair at less than 60 degrees", "i": 3, "j": 23, "dot": [ "4", "0" ], "normI": [ "2", "0" ], "normJ": [ "8", "0" ], "slack": [ "-48", "0" ] } }, "decided": { "verdict": "REFUTED", "why": "pair (3, 23): = 4 + 0√2, cos² ≈ 1", "ms": 0.1 }, "required": "REFUTED", "outcome": "as required", "float": { "maxCosine": 0.9999999999999998, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "kiss-cal-d4-24/contact-sum", "class": "contact-sum", "truth": "FALSE", "preservesOriginal": false, "transformation": "row 0 + row 4 appended (an exact contact pair; the sum is at less than 60° from each)", "sha256": "ca3b77c984a07e48045acf17169d1d5654c4990f3360808a39a483e3fa44f11b", "bytes": 1099, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "pair at less than 60 degrees", "i": 0, "j": 24, "dot": [ "3", "0" ], "normI": [ "2", "0" ], "normJ": [ "6", "0" ], "slack": [ "-24", "0" ] } }, "decided": { "verdict": "REFUTED", "why": "pair (0, 24): = 3 + 0√2, cos² ≈ 0.75", "ms": 0.1 }, "required": "REFUTED", "outcome": "as required", "float": { "maxCosine": 0.8660254037844387, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "kiss-cal-d4-24/zero-vector", "class": "zero-vector", "truth": "FALSE", "preservesOriginal": false, "transformation": "the zero vector appended", "sha256": "e9f004da6a92a1293c4673e34e1e54a162d2942e6fbbc8f2dfed8c58ad45bc95", "bytes": 1099, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "zero row", "row": 24 } }, "decided": { "verdict": "REFUTED", "why": "zero vector at row 24", "ms": 0 }, "required": "REFUTED", "outcome": "as required", "float": { "maxCosine": "undefined (a zero norm)", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "kiss-cal-d4-24/negated", "class": "negated", "truth": "TRUE", "preservesOriginal": false, "transformation": "every row negated", "sha256": "f9293178f00d2b24bda589ef67dade0aabe6557b807e7daf49dcecf7e3322743", "bytes": 1057, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null }, "decided": { "verdict": "CERTIFIED", "why": "96 exact contacts, 276 pairs", "ms": 0.2 }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxCosine": 0.4999999999999999, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "kiss-cal-d4-24/coordinates-permuted", "class": "coordinates-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "coordinates rotated: k → k+1 mod 4", "sha256": "e576fd093b9d8a322f616d0af388aa7a0602212af6540f0b3067a3e59f1383ee", "bytes": 1057, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null }, "decided": { "verdict": "CERTIFIED", "why": "96 exact contacts, 276 pairs", "ms": 0.2 }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxCosine": 0.4999999999999999, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "kiss-cal-d4-24/ragged-dimensions", "class": "ragged-dimensions", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "row 3 shortened to 3 coordinates", "sha256": 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"float": { "maxCosine": 0.5, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "b64c18378b549280ff1384cebe0b8363084c46fb41375fc2fbc4f3035e163092" }, "mutants": [ { "id": "kiss-station-d12-lift/row-duplicated", "class": "row-duplicated", "truth": "FALSE", "preservesOriginal": false, "transformation": "row 7 appended again", "sha256": "6e6cf9f46efcc391838c53075affe436f788c370703e40f4af576a709f6e057b", "bytes": 75018, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "pair at less than 60 degrees", "i": 7, "j": 604, "dot": [ "4", "0" ], "normI": [ "4", "0" ], "normJ": [ "4", "0" ], "slack": [ "-48", "0" ] } }, "decided": { "verdict": "REFUTED", "why": "pair (7, 604): = 4 + 0√2, cos² ≈ 1", "ms": 2.3 }, "required": "REFUTED", "outcome": "as required", "float": { "maxCosine": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "kiss-station-d12-lift/row-doubled", "class": "row-doubled", "truth": "FALSE", 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{ "maxCosine": "undefined (a zero norm)", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "kiss-station-d12-lift/negated", "class": "negated", "truth": "TRUE", "preservesOriginal": false, "transformation": "every row negated", "sha256": "43fb9a696d2c6e3b92057ebe9e9d48494d30fafbb806b07e3a8466ff9d041571", "bytes": 74893, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null }, "decided": { "verdict": "CERTIFIED", "why": "22840 exact contacts, 182106 pairs", "ms": 63.6 }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxCosine": 0.5, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "kiss-station-d12-lift/coordinates-permuted", "class": "coordinates-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "coordinates rotated: k → k+1 mod 12", "sha256": "49def7fc3811814448c5cb6d7a3a30e44713d30bbc1b5e4f6f4b51ad18050d3b", "bytes": 74893, "witness": { "violated": false, 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"pair at less than 60 degrees", "i": 7, "j": 604, "dot": [ "36", "0" ], "normI": [ "36", "0" ], "normJ": [ "36", "0" ], "slack": [ "-3888", "0" ] } }, "decided": { "verdict": "REFUTED", "why": "pair (7, 604): = 36 + 0√2, cos² ≈ 1", "ms": 1.8 }, "required": "REFUTED", "outcome": "as required", "float": { "maxCosine": 1, "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "kiss-ea-604/row-doubled", "class": "row-doubled", "truth": "FALSE", "preservesOriginal": false, "transformation": "the last row replaced by 2 × row 3 (parallel to row 3)", "sha256": "69f582071f9a26b56c05b02413716d6905e7706b8886bc547c8a1ae22c75d3be", "bytes": 68920, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "pair at less than 60 degrees", "i": 3, "j": 603, "dot": [ "72", "0" ], "normI": [ "36", "0" ], "normJ": [ "144", "0" ], "slack": [ "-15552", "0" ] } }, "decided": { "verdict": "REFUTED", "why": "pair (3, 603): = 72 + 0√2, cos² ≈ 1", "ms": 1.2 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"zero-vector", "truth": "FALSE", "preservesOriginal": false, "transformation": "the zero vector appended", "sha256": "a9ab5d1e1ace86ecbed11c75687b71a8a5e15fa5435b0f2b402996aa50a88f8f", "bytes": 69031, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "zero row", "row": 604 } }, "decided": { "verdict": "REFUTED", "why": "zero vector at row 604", "ms": 0.5 }, "required": "REFUTED", "outcome": "as required", "float": { "maxCosine": "undefined (a zero norm)", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "kiss-ea-604/negated", "class": "negated", "truth": "TRUE", "preservesOriginal": false, "transformation": "every row negated", "sha256": "101b825ab15a2ace3d1bfb326f485d09585a27cac3222b4d9b2663e15661ff70", "bytes": 68919, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null }, "decided": { "verdict": "CERTIFIED", "why": "19704 exact contacts, 182106 pairs", "ms": 62.5 }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxCosine": 0.5000000000000001, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "kiss-ea-604/coordinates-permuted", "class": "coordinates-permuted", "truth": "TRUE", "preservesOriginal": false, "transformation": "coordinates rotated: k → k+1 mod 11", "sha256": "0fac1512a7ae2289705c2a07a5122ad716f4ad7dffc57ace51f344899487100c", "bytes": 68919, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null }, "decided": { "verdict": "CERTIFIED", "why": "19704 exact contacts, 182106 pairs", "ms": 62.2 }, "required": "CERTIFIED", "outcome": "as required", "float": { "maxCosine": 0.5000000000000001, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "kiss-ea-604/ragged-dimensions", "class": "ragged-dimensions", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "row 3 shortened to 10 coordinates", "sha256": "05e74613b1a061a269796946ec81653b1e62682a163516313679cfde09e94e8c", "bytes": 68909, "witness": { "violated": null, "malformed": true, "reason": "row 3 has 10 coordinates, row 0 has 11", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the instrument threw: ragged dimensions at row 3", "ms": 0.4 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "rows of different length", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [], "ms": 2357 }, { "rowId": "kiss-ganzhinov-592", "record": "certs/kissing-ledger.json", "entryId": "ganzhinov-592", "verdict": "QUEUED", "noObject": "the row is QUEUED: no bytes (not yet pulled)", "mutants": [], "excluded": [], "ms": 0 } ] }, "shapes": { "decider": "easota rows: instruments/easota/decide.js (hexagons.js) composed as tools/run-easota-ledger.js composes it — the decision from the bytes, printedAgrees from agree() under the row's convention, the word by instruments/easota/word.js (WITNESSED, MISPRINTED since the fix of 2026-10-21, REPAIRED, UNWITNESSED, UNDECIDED) and the register's word for it (CERTIFIED, REFUTED, REPAIRED; any other reported as the ledger says it); mc100 rows: tools/run-mc100-einstein.js easotaRow / kissingRow required as a module (the agreement rule, the platform's resolution, is theirs)", "witness": "instruments/selfaudit/witness_shapes.py", "floatcheck": "instruments/selfaudit/floatcheck_shapes.py", "redControl": null, "records": [ "certs/easota-ledger.json", "certs/mc100-einstein-arena.json" ], "classes": { "FALSE": [ "printed-plus-one-unit", "printed-minus-one-unit", "coordinate-perturbed-1e-12" ], "TRUE": [ "rigid-motion" ], "MALFORMED": [ "coordinate-missing" ] }, "rows": [ { "rowId": "ea-circles-alphaevolve_2025", "record": "certs/easota-ledger.json", "entryId": "circles/alphaevolve_2025", "verdict": "CERTIFIED", "object": "circles (easota, easota/circles-rectangle/alphaevolve_2025.json), printed 2.3658321334 (rounding)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "Σr = 2.3658321334167631, 0 overlapping pairs, box slack 0.0000000319647749; printed 2.3658321334 agrees (rounding)", "ms": 5.2 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "2.3658321334167627", "accept": { "1e-6": true, "1e-9": true, "1e-12": false } }, "sha256": "9bd193fefde7b41b5ac6d385268590e03c67bd59ddf18426fde9b67d25c4e00b" }, "mutants": [ { "id": "ea-circles-alphaevolve_2025/printed-plus-one-unit", "class": "printed-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 2.3658321334 moved + one unit in its last digit → 2.3658321335 (FALSE only when the witness finds the bar no longer agrees with the exact score under the rounding convention, else DISCARDED)", "sha256": "443aebb0c360d93b04b9924faea8861eb2512dc971bfbfe124dde3f4afd18e41", "bytes": 1134, "fixedFrom": "FALSE CERTIFICATION", "fix": "easota-word", "foundAt": "d961cda2", "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "window": [ "47316642669/20000000000", "47316642671/20000000000" ], "exact": "236583213341676313/100000000000000000" } }, "exact": "236583213341676313/100000000000000000" }, "decided": { "verdict": "REFUTED", "ledgerVerdict": "MISPRINTED", "printedAgrees": false, "why": "Σr = 2.3658321334167631, 0 overlapping pairs, box slack 0.0000000319647749; printed 2.3658321335 DOES NOT agree (rounding)", "ms": 4.5 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "2.3658321334167627", "accept": { "1e-6": true, "1e-9": true, "1e-12": false } } }, { "id": "ea-circles-alphaevolve_2025/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 2.3658321334 moved − one unit in its last digit → 2.3658321333 (FALSE only when the witness finds the bar no longer agrees with the exact score under the rounding convention, else DISCARDED)", "sha256": "93cb409931c73d99540a71075b98f9579b3be9b90ac3559a5fa974f2e9cf1471", "bytes": 1134, "fixedFrom": "FALSE CERTIFICATION", "fix": "easota-word", "foundAt": "d961cda2", "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "window": [ "9463328533/4000000000", "47316642667/20000000000" ], "exact": "236583213341676313/100000000000000000" } }, "exact": "236583213341676313/100000000000000000" }, "decided": { "verdict": "REFUTED", "ledgerVerdict": "MISPRINTED", "printedAgrees": false, "why": "Σr = 2.3658321334167631, 0 overlapping pairs, box slack 0.0000000319647749; printed 2.3658321333 DOES NOT agree (rounding)", "ms": 4.3 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "2.3658321334167627", "accept": { "1e-6": true, "1e-9": true, "1e-12": false } } }, { "id": "ea-circles-alphaevolve_2025/coordinate-perturbed-1e-12", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "preservesOriginal": false, "transformation": "circle 8 moved +10⁻¹² in x toward circle 9 (the pair with the least slack) (FALSE only with a witness: a violated constraint or an exact score past the bar, else DISCARDED)", "sha256": "106613e3711ee0b00e03ad4213018776ff933e5764f3087661b63d568004397b", "bytes": 1138, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": "236583213341676313/100000000000000000" }, "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "Σr = 2.3658321334167631, 0 overlapping pairs, box slack 0.0000000319647749; printed 2.3658321334 agrees (rounding)", "ms": 4.5 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "2.3658321334167627", "accept": { "1e-6": true, "1e-9": true, "1e-12": false } } }, { "id": "ea-circles-alphaevolve_2025/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "every circle reflected in x (x → −x): the box and Σr are invariant (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "a068461281625b18454df9db1080e63a67bf247c1e856d2130b13f0aa2c1536e", "bytes": 1155, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": "236583213341676313/100000000000000000" }, "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "Σr = 2.3658321334167631, 0 overlapping pairs, box slack 0.0000000319647749; printed 2.3658321334 agrees (rounding)", "ms": 4.4 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "2.3658321334167627", "accept": { "1e-6": true, "1e-9": true, "1e-12": false } } }, { "id": "ea-circles-alphaevolve_2025/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", 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"transformation": "the printed 0.380927 moved − one unit in its last digit → 0.380926 (FALSE only when the witness finds the bar no longer agrees with the exact score under the ceiling convention, else DISCARDED)", "sha256": "0112ba5d23be6669a95e4391f18c6372b56075e3b484a960c8db41331482a874", "bytes": 1004, "fixedFrom": "FALSE CERTIFICATION", "fix": "easota-word", "foundAt": "d961cda2", "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "window": [ "15237/40000", "190463/500000" ], "exact": "64757565083624785688821235069923/170000000000000000000000000000000" } }, "exact": "64757565083624785688821235069923/170000000000000000000000000000000" }, "decided": { "verdict": "REFUTED", "ledgerVerdict": "MISPRINTED", "printedAgrees": false, "why": "bound 0.3809268534330869, Σh − n/2 = 0.0000000000000000, in range true; printed 0.380926 DOES NOT agree (ceiling)", "ms": 0.3 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "0.38092685343308713", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-overlap-haugland_2016/coordinate-perturbed-1e-12", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "preservesOriginal": false, "transformation": "h[5] += 10⁻¹² (Σh = n/2 no longer holds) (FALSE only with a witness: a violated constraint or an exact score past the bar, else DISCARDED)", "sha256": "bda42ff6c64e46db1ab9523092fa18de1c7d2bad7eff66393c5e135d87612cc2", "bytes": 1004, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "constraint": { "kind": "Σh is not n/2", "sumMinusHalfN": "1/1000000000000" } }, "exact": "80946956354539157318380433352529/212500000000000000000000000000000" }, "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": true, "why": "bound 0.3809268534331254, Σh − n/2 = 0.0000000000010000, in range true; printed 0.380927 agrees (ceiling)", "ms": 0.6 }, "required": "REFUTED", "outcome": "not as required (REPAIRED)", "float": { "score": "0.38092685343312543", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-overlap-haugland_2016/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "the step function reversed (the correlation maximum over lags is reversal-invariant) (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "f5e49c0498398d1f1c152e3146ce723f641d8eea2beb29badb19f27013fb297a", "bytes": 1004, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": "64757565083624785688821235069923/170000000000000000000000000000000" }, "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "bound 0.3809268534330869, Σh − n/2 = 0.0000000000000000, in range true; printed 0.380927 agrees (ceiling)", "ms": 0.3 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "0.38092685343308713", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-overlap-haugland_2016/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "value 0 missing (null)", "sha256": "494f2e83aa7103479c6ccfab4e835211f062c7261f5128217326bf0cfa90ea16", "bytes": 1003, "witness": { "violated": null, "malformed": true, "reason": "a value is missing", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: a value is missing", "ms": 0 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a value is missing", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [ "control-bar-far" ], "ms": 145 }, { "rowId": "ea-overlap-alphaevolve_2025", "record": "certs/easota-ledger.json", "entryId": "overlap/alphaevolve_2025", "verdict": "REPAIRED", "object": "overlap (easota, easota/erdos-minimum-overlap/alphaevolve_2025.py), printed 0.380924 (ceiling)", "original": { "required": "REPAIRED", "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": true, "why": "bound 0.3809230351084501, Σh − n/2 = -0.0000000000000024, in range true; printed 0.380924 agrees (ceiling)", "ms": 1.7 }, "asRequired": true, "witness": { "violated": true, "malformed": false }, "float": { "score": "0.38092303510845016", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } }, "sha256": "0d0eb434e3c1fa05f0408f980ee1af784a5dd772e75ce13d42bd05a6874aa6c3" }, "mutants": [ { "id": "ea-overlap-alphaevolve_2025/printed-plus-one-unit", "class": "printed-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 0.380924 moved + one unit in its last digit → 0.380925 (FALSE only when the witness finds the bar no longer agrees with the exact score under the ceiling convention, else DISCARDED)", "sha256": "160821a5532badab11e844fa1076440b628791f3e55be5fae149f86776db5e16", "bytes": 1413, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "constraint": { "kind": "Σh is not n/2", "sumMinusHalfN": "-6013377/2500000000000000000000" }, "bar": { "window": [ "95231/250000", "15237/40000" ], "exact": "2261730520956422831156422539110690114549753/5937500000000000000000000000000000000000000" } }, "exact": "2261730520956422831156422539110690114549753/5937500000000000000000000000000000000000000" }, "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": false, "why": "bound 0.3809230351084501, Σh − n/2 = -0.0000000000000024, in range true; printed 0.380925 DOES NOT agree (ceiling)", "ms": 1.7 }, "required": "REFUTED", "outcome": "not as required (REPAIRED)", "float": { "score": "0.38092303510845016", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "ea-overlap-alphaevolve_2025/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 0.380924 moved − one unit in its last digit → 0.380923 (FALSE only when the witness finds the bar no longer agrees with the exact score under the ceiling convention, else DISCARDED)", "sha256": "c84cf9103c0bdbc37ed57633ea68422ec024efe05d125b101bf6008ceae3b2fa", "bytes": 1413, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "constraint": { "kind": "Σh is not n/2", "sumMinusHalfN": "-6013377/2500000000000000000000" }, "bar": { "window": [ "190461/500000", "380923/1000000" ], "exact": "2261730520956422831156422539110690114549753/5937500000000000000000000000000000000000000" } }, "exact": "2261730520956422831156422539110690114549753/5937500000000000000000000000000000000000000" }, "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": false, "why": "bound 0.3809230351084501, Σh − n/2 = -0.0000000000000024, in range true; printed 0.380923 DOES NOT agree (ceiling)", "ms": 1.6 }, "required": "REFUTED", "outcome": "not as required (REPAIRED)", "float": { "score": "0.38092303510845016", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-overlap-alphaevolve_2025/coordinate-perturbed-1e-12", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "preservesOriginal": false, "transformation": "h[6] += 10⁻¹² (Σh = n/2 no longer holds) (FALSE only with a witness: a violated constraint or an exact score past the bar, else DISCARDED)", "sha256": "6da801872568a104a5decf960f91e825bfe31f5c36357089c5ca8cdf8c111388", "bytes": 1413, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "constraint": { "kind": "Σh is not n/2", "sumMinusHalfN": "215731623/2500000000000000000000" } }, "exact": "2261730520956424070778992817860690114549753/5937500000000000000000000000000000000000000" }, "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": true, "why": "bound 0.3809230351084503, Σh − n/2 = 0.0000000000000862, in range true; printed 0.380924 agrees (ceiling)", "ms": 1.3 }, "required": "REFUTED", "outcome": "not as required (REPAIRED)", "float": { "score": "0.3809230351084503", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-overlap-alphaevolve_2025/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "the step function reversed (the correlation maximum over lags is reversal-invariant) (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "0d0eb434e3c1fa05f0408f980ee1af784a5dd772e75ce13d42bd05a6874aa6c3", "bytes": 1413, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "constraint": { "kind": "Σh is not n/2", "sumMinusHalfN": "-6013377/2500000000000000000000" } }, "exact": "2261730520956422831156422539110690114549753/5937500000000000000000000000000000000000000" }, "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": true, "why": "bound 0.3809230351084501, Σh − n/2 = -0.0000000000000024, in range true; printed 0.380924 agrees (ceiling)", "ms": 1.6 }, "required": "REPAIRED", "outcome": "as required", "float": { "score": "0.38092303510845016", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-overlap-alphaevolve_2025/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "value 0 missing (null)", "sha256": "7d69bb6d543d9451ed5641795dfc2069eb87dac6ce1cf012a1982834d3fb31fb", "bytes": 1412, "witness": { "violated": null, "malformed": true, "reason": "a value is missing", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: a value is missing", "ms": 0 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a value is missing", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [ "control-bar-far" ], "ms": 160 }, { "rowId": "ea-overlap-ttt_discover_2026", "record": "certs/easota-ledger.json", "entryId": "overlap/ttt_discover_2026", "verdict": "REPAIRED", "object": "overlap (easota, easota/erdos-minimum-overlap/ttt_discover_2026.py), printed 0.380876 (ceiling)", "original": { "required": "REPAIRED", "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": true, "why": "bound 0.3808753232177187, Σh − n/2 = -0.0000000000000147, in range true; printed 0.380876 agrees (ceiling)", "ms": 34.9 }, "asRequired": true, "witness": { "violated": true, "malformed": false }, "float": { "score": "0.38087532321771883", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } }, "sha256": "41701065d515312eafe569c30d1ef31f50045429505018a25fa12507501aeac4" }, "mutants": [ { "id": "ea-overlap-ttt_discover_2026/printed-plus-one-unit", "class": "printed-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 0.380876 moved + one unit in its last digit → 0.380877 (FALSE only when the witness finds the bar no longer agrees with the exact score under the ceiling convention, else DISCARDED)", "sha256": "c1847fb62299fa61bb3c148c20ea2778386e881c07cabad0e74e9c9a5dcaeb60", "bytes": 13275, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "constraint": { "kind": "Σh is not n/2", "sumMinusHalfN": "-738744548523586791/50000000000000000000000000000000" }, "bar": { "window": [ "95219/250000", "380877/1000000" ], "exact": "190437661608859374943823315779250467986684373456053/500000000000000000000000000000000000000000000000000" } }, "exact": "190437661608859374943823315779250467986684373456053/500000000000000000000000000000000000000000000000000" }, "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": false, "why": "bound 0.3808753232177187, Σh − n/2 = -0.0000000000000147, in range true; printed 0.380877 DOES NOT agree (ceiling)", "ms": 34.5 }, "required": "REFUTED", "outcome": "not as required (REPAIRED)", "float": { "score": "0.38087532321771883", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "ea-overlap-ttt_discover_2026/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 0.380876 moved − one unit in its last digit → 0.380875 (FALSE only when the witness finds the bar no longer agrees with the exact score under the ceiling convention, else DISCARDED)", "sha256": "9b2d2552890567f1f168444650b90bd2fd03f11596f9cd684f6c15f86e7adf21", "bytes": 13275, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "constraint": { "kind": "Σh is not n/2", "sumMinusHalfN": "-738744548523586791/50000000000000000000000000000000" }, "bar": { "window": [ "190437/500000", "3047/8000" ], "exact": "190437661608859374943823315779250467986684373456053/500000000000000000000000000000000000000000000000000" } }, "exact": "190437661608859374943823315779250467986684373456053/500000000000000000000000000000000000000000000000000" }, "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": false, "why": "bound 0.3808753232177187, Σh − n/2 = -0.0000000000000147, in range true; printed 0.380875 DOES NOT agree (ceiling)", "ms": 30.1 }, "required": "REFUTED", "outcome": "not as required (REPAIRED)", "float": { "score": "0.38087532321771883", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-overlap-ttt_discover_2026/coordinate-perturbed-1e-12", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "preservesOriginal": false, "transformation": "h[0] += 10⁻¹² (Σh = n/2 no longer holds) (FALSE only with a witness: a violated constraint or an exact score past the bar, else DISCARDED)", "sha256": "80a3e39eb98c5741b98d7537d7060b0f6f36e918f2ef54d8d8cd43bace81a917", "bytes": 13271, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "constraint": { "kind": "Σh is not n/2", "sumMinusHalfN": "49250353040689501409/50000000000000000000000000000000" } }, "exact": "57131298482658104098839212331308863232897677823111/150000000000000000000000000000000000000000000000000" }, "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": true, "why": "bound 0.3808753232177206, Σh − n/2 = 0.0000000000009850, in range true; printed 0.380876 agrees (ceiling)", "ms": 26.5 }, "required": "REFUTED", "outcome": "not as required (REPAIRED)", "float": { "score": "0.3808753232177207", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-overlap-ttt_discover_2026/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "the step function reversed (the correlation maximum over lags is reversal-invariant) (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "1ff5f78630ce753f1dc3179fb387154d98f015786003483d849e37d5127bc648", "bytes": 13275, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "constraint": { "kind": "Σh is not n/2", "sumMinusHalfN": "-738744548523586791/50000000000000000000000000000000" } }, "exact": "190437661608859374943823315779250467986684373456053/500000000000000000000000000000000000000000000000000" }, "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": true, "why": "bound 0.3808753232177187, Σh − n/2 = -0.0000000000000147, in range true; printed 0.380876 agrees (ceiling)", "ms": 31.9 }, "required": "REPAIRED", "outcome": "as required", "float": { "score": "0.38087532321771883", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-overlap-ttt_discover_2026/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "value 0 missing (null)", "sha256": "f7baf0440097162c870988c0e8bb17217120fc0dfad6fff04a137e3a89900872", "bytes": 13256, "witness": { "violated": null, "malformed": true, "reason": "a value is missing", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: a value is missing", "ms": 0 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a value is missing", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [ "control-bar-far" ], "ms": 845 }, { "rowId": "ea-overlap-together_ai_2026", "record": "certs/easota-ledger.json", "entryId": "overlap/together_ai_2026", "verdict": "REPAIRED", "object": "overlap (easota, easota/erdos-minimum-overlap/together_ai_2026.py), printed 0.380871 (ceiling)", "original": { "required": "REPAIRED", "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": true, "why": "bound 0.3808703105862199, Σh − n/2 = -0.0000000000000009, in range true; printed 0.380871 agrees (ceiling)", "ms": 35.2 }, "asRequired": true, "witness": { "violated": true, "malformed": false }, "float": { "score": "0.38087031058621995", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } }, "sha256": "c51f1202cdb04c228622e8a4c86a5427b30d7b2b9c13451c46aa97e5126940b9" }, "mutants": [ { "id": "ea-overlap-together_ai_2026/printed-plus-one-unit", "class": "printed-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 0.380871 moved + one unit in its last digit → 0.380872 (FALSE only when the witness finds the bar no longer agrees with the exact score under the ceiling convention, else DISCARDED)", "sha256": "107581d3fc1a017f68e9d51cc545bc96c0756ae43551b8f16c3f530952ab137a", "bytes": 15124, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "constraint": { "kind": "Σh is not n/2", "sumMinusHalfN": "-9988357469323/10000000000000000000000000000" }, "bar": { "window": [ "380871/1000000", "47609/125000" ], "exact": "380870310586219904501834982739244069809153517347567288693/1000000000000000000000000000000000000000000000000000000000" } }, "exact": "380870310586219904501834982739244069809153517347567288693/1000000000000000000000000000000000000000000000000000000000" }, "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": false, "why": "bound 0.3808703105862199, Σh − n/2 = -0.0000000000000009, in range true; printed 0.380872 DOES NOT agree (ceiling)", "ms": 29.6 }, "required": "REFUTED", "outcome": "not as required (REPAIRED)", "float": { "score": "0.38087031058621995", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "ea-overlap-together_ai_2026/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 0.380871 moved − one unit in its last digit → 0.380870 (FALSE only when the witness finds the bar no longer agrees with the exact score under the ceiling convention, else DISCARDED)", "sha256": "366018e18d50691539100df5675d6b26d4c83c607ea5cc88794558fd331db200", "bytes": 15124, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "constraint": { "kind": "Σh is not n/2", "sumMinusHalfN": "-9988357469323/10000000000000000000000000000" }, "bar": { "window": [ "380869/1000000", "38087/100000" ], "exact": "380870310586219904501834982739244069809153517347567288693/1000000000000000000000000000000000000000000000000000000000" } }, "exact": "380870310586219904501834982739244069809153517347567288693/1000000000000000000000000000000000000000000000000000000000" }, "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": false, "why": "bound 0.3808703105862199, Σh − n/2 = -0.0000000000000009, in range true; printed 0.380870 DOES NOT agree (ceiling)", "ms": 28.2 }, "required": "REFUTED", "outcome": "not as required (REPAIRED)", "float": { "score": "0.38087031058621995", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-overlap-together_ai_2026/coordinate-perturbed-1e-12", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "preservesOriginal": false, "transformation": "h[0] += 10⁻¹² (Σh = n/2 no longer holds) (FALSE only with a witness: a violated constraint or an exact score past the bar, else DISCARDED)", "sha256": "4e8daa168d5e6486e5b47b8c8fe5a1643e970f78bc9e4ca104a26ba2ef1c8dbf", "bytes": 15120, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "constraint": { "kind": "Σh is not n/2", "sumMinusHalfN": "9989719690040863/10000000000000000000000000000" } }, "exact": "76174062117244088574844417759326068554523675022938346309/200000000000000000000000000000000000000000000000000000000" }, "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": true, "why": "bound 0.3808703105862204, Σh − n/2 = 0.0000000000009989, in range true; printed 0.380871 agrees (ceiling)", "ms": 25.6 }, "required": "REFUTED", "outcome": "not as required (REPAIRED)", "float": { "score": "0.3808703105862206", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-overlap-together_ai_2026/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "the step function reversed (the correlation maximum over lags is reversal-invariant) (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "eac2e0196dc24e27710c88e39ba926bd6148600b50cb593df2c821a157eef5bd", "bytes": 15124, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "constraint": { "kind": "Σh is not n/2", "sumMinusHalfN": "-9988357469323/10000000000000000000000000000" } }, "exact": "380870310586219904501834982739244069809153517347567288693/1000000000000000000000000000000000000000000000000000000000" }, "decided": { "verdict": "REPAIRED", "ledgerVerdict": "REPAIRED", "printedAgrees": true, "why": "bound 0.3808703105862199, Σh − n/2 = -0.0000000000000009, in range true; printed 0.380871 agrees (ceiling)", "ms": 33.6 }, "required": "REPAIRED", "outcome": "as required", "float": { "score": "0.3808703105862201", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-overlap-together_ai_2026/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "value 0 missing (null)", "sha256": "88ca18cf8029005204cf835c4963139a072294586818f3fdbe8a8f854d065f0f", "bytes": 15104, "witness": { "violated": null, "malformed": true, "reason": "a value is missing", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: a value is missing", "ms": 0 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a value is missing", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [ "control-bar-far" ], "ms": 808 }, { "rowId": "ea-edges-alphaevolve_2025", "record": "certs/easota-ledger.json", "entryId": "edges/alphaevolve_2025", "verdict": "CERTIFIED", "object": "edges (easota, easota/edges-vs-triangles/alphaevolve_2025.py), printed -0.712494 (rounding)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "score -0.7124938782214395; printed -0.712494 agrees (rounding)", "ms": 457.7 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "-0.7124938782214396", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } }, "sha256": "2d123a9d9151623f72bd80e6f93f696d3c7f1ba982407928d6a716fbcb229de4" }, "mutants": [ { "id": "ea-edges-alphaevolve_2025/printed-plus-one-unit", "class": "printed-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed -0.712494 moved + one unit in its last digit → -0.712493 (FALSE only when the witness finds the bar no longer agrees with the exact score under the rounding convention, else DISCARDED)", "sha256": "727af2eac0165f6e8be5cc543860b75ecbe3d3d4a7aacb90cc1707b680cc3803", "bytes": 20689, "fixedFrom": "FALSE CERTIFICATION", "fix": "easota-word", "foundAt": "d961cda2", "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "window": [ "-1424987/2000000", "-284997/400000" ], "exact": 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}, "decided": { "verdict": "REFUTED", "ledgerVerdict": "MISPRINTED", "printedAgrees": false, "why": "score -0.7124938782214395; printed -0.712493 DOES NOT agree (rounding)", "ms": 454.8 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "-0.7124938782214396", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-edges-alphaevolve_2025/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed -0.712494 moved − one unit in its last digit → -0.712495 (FALSE only when the witness finds the bar no longer agrees with the exact score under the rounding convention, else DISCARDED)", "sha256": "3d0fdc1e90e54e06d62128f2f889e730b76f456911aa36ba3d395357dbeadf8f", "bytes": 20689, "fixedFrom": "FALSE CERTIFICATION", "fix": "easota-word", "foundAt": "d961cda2", "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "window": [ "-1424991/2000000", "-1424989/2000000" ], "exact": 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}, "decided": { "verdict": "REFUTED", "ledgerVerdict": "MISPRINTED", "printedAgrees": false, "why": "score -0.7124938782214395; printed -0.712495 DOES NOT agree (rounding)", "ms": 470.8 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "-0.7124938782214396", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "ea-edges-alphaevolve_2025/coordinate-perturbed-1e-12", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "preservesOriginal": false, "transformation": "weights[0][0] += 10⁻¹² (FALSE only with a witness: a violated constraint or an exact score past the bar, else DISCARDED)", "sha256": "887c7985b91e1d53f22c0b6e4c923179efa3d02077bbcc6b98680d5c25cf57b4", "bytes": 20689, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": 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}, "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "score -0.7124938782214395; printed -0.712494 agrees (rounding)", "ms": 458.6 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "-0.7124938782214396", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-edges-alphaevolve_2025/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "the weight rows reversed (the curve is sorted by ρ) (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "9f6d6c3c702839bfb34b71caa9108d49881e7c9aefc5dc11ced311a2f5ae77b9", "bytes": 20689, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": 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}, "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "score -0.7124938782214395; printed -0.712494 agrees (rounding)", "ms": 442.2 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "-0.7124938782214396", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-edges-alphaevolve_2025/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "row 0 with 19 weights", "sha256": "16195eda6c2af5a2a3bf3aad2ee6042ef11af27bfa63954a33d3becb78216376", "bytes": 20667, "witness": { "violated": null, "malformed": true, "reason": "row 0 has 19 weights", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: a row without 20 weights", "ms": 0 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a row without 20 weights", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [ "control-bar-far" ], "ms": 2651 }, { "rowId": "ea-edges-ours_2026", "record": "certs/easota-ledger.json", "entryId": "edges/ours_2026", "verdict": "CERTIFIED", "object": "edges (easota, easota/edges-vs-triangles/ours_2026.py), printed -0.712256 (rounding)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "score -0.7122563326979318; printed -0.712256 agrees (rounding)", "ms": 65.8 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "-0.7122563326979321", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } }, "sha256": "495738350a4d6e2372c91b91a2454e66463a49360cd2623474b52dd358d5ad84" }, "mutants": [ { "id": "ea-edges-ours_2026/printed-plus-one-unit", "class": "printed-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed -0.712256 moved + one unit in its last digit → -0.712255 (FALSE only when the witness finds the bar no longer agrees with the exact score under the rounding convention, else DISCARDED)", "sha256": "1f61ec4959e59c0be4854aa9cbdefbda2c2a6c1075a8385616066a4461723a07", "bytes": 18569, "fixedFrom": "FALSE CERTIFICATION", "fix": "easota-word", "foundAt": "d961cda2", "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "window": [ "-1424511/2000000", "-1424509/2000000" ], "exact": 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}, "decided": { "verdict": "REFUTED", "ledgerVerdict": "MISPRINTED", "printedAgrees": false, "why": "score -0.7122563326979318; printed -0.712255 DOES NOT agree (rounding)", "ms": 65.4 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "-0.7122563326979321", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "ea-edges-ours_2026/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed -0.712256 moved − one unit in its last digit → -0.712257 (FALSE only when the witness finds the bar no longer agrees with the exact score under the rounding convention, else DISCARDED)", "sha256": "351ca554ee7714b32daa04d748b720e8939ba88915a50aeaebec30a0744c0a46", "bytes": 18569, "fixedFrom": "FALSE CERTIFICATION", "fix": "easota-word", "foundAt": "d961cda2", "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "window": [ "-284903/400000", 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"reason": null, "firstViolation": { "bar": { "window": [ "15028629/10000000", "150286291/100000000" ], "exact": "9017177389534960453073255343945818186531611658165103644880000/6000000000000000717612319644499700914825151864452703446981849" } }, "exact": "9017177389534960453073255343945818186531611658165103644880000/6000000000000000717612319644499700914825151864452703446981849" }, "decided": { "verdict": "REFUTED", "ledgerVerdict": "MISPRINTED", "printedAgrees": false, "why": "C1 = 1.5028628982558265; printed 1.50286291 DOES NOT agree (ceiling)", "ms": 858.5 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "1.5028628982563323", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-autocorr-ttt_discover_2026/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 1.50286290 moved − one unit in its last digit → 1.50286289 (FALSE only when the witness finds the bar no 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false, "1e-12": false } } }, { "id": "ea-autocorr-ttt_discover_2026/coordinate-perturbed-1e-12", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "preservesOriginal": false, "transformation": "f[0] += 10⁻¹² (FALSE only with a witness: a violated constraint or an exact score past the bar, else DISCARDED)", "sha256": "de5527a857eeccc876bbc9a34e55162201b1e0a94c9745ef8a7b42d8b87d1d5f", "bytes": 702871, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": "9017177389534960453073255343945818186531611658165103644880000/6000000000000049707407175308164594500533752724452703446981849" }, "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "C1 = 1.5028628982558142; printed 1.50286290 agrees (ceiling)", "ms": 1216.6 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "1.5028628982563204", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-autocorr-ttt_discover_2026/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "f reversed (the autoconvolution's maximum is reversal-invariant) (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "6acdb3021a2a3e5bf8faf0de55414e11b84f01540e8843e84f8092cc36c27fb2", "bytes": 702871, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": "9017177389534960453073255343945818186531611658165103644880000/6000000000000000717612319644499700914825151864452703446981849" }, "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "C1 = 1.5028628982558265; printed 1.50286290 agrees (ceiling)", "ms": 1156.5 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "1.502862898256741", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-autocorr-ttt_discover_2026/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "value 0 missing (null)", "sha256": "f8505901c1d6bc33e8f1fc82dc1cdb201ed9a1a5242750a5f1883ddf1d647088", "bytes": 702854, "witness": { "violated": null, "malformed": true, "reason": "a value is missing", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: a value is missing", "ms": 0.1 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a value is missing", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [ "control-bar-far" ], "ms": 22800 }, { "rowId": "ea-autocorr-ours_2026", "record": "certs/easota-ledger.json", "entryId": "autocorr/ours_2026", "verdict": "CERTIFIED", "object": "autocorr (easota, easota/first-autocorrelation/ours_2026.json), printed 1.50286286 (ceiling)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "C1 = 1.5028628587049711; printed 1.50286286 agrees (ceiling)", "ms": 868.5 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "1.5028628587063821", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } }, "sha256": "f53957b176c8089eb044e6f7eedf4c5f91447c4704d740fc66003d8a0c49c41e" }, "mutants": [ { "id": "ea-autocorr-ours_2026/printed-plus-one-unit", "class": "printed-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 1.50286286 moved + one unit in its last digit → 1.50286287 (FALSE only when the witness finds the bar no longer agrees with the exact score under the ceiling convention, else DISCARDED)", "sha256": "ffd5c7af24b077348064777247be4fbf4ad6cac03146371721776fb5e8fca6dd", "bytes": 728164, "fixedFrom": "FALSE CERTIFICATION", "fix": "easota-word", "foundAt": "d961cda2", "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "window": [ "75143143/50000000", "150286287/100000000" ], "exact": "4174619051959196322579972723494195237298696688053499906630000/2777777777777777503436379545578895662577139448703456269758049" } }, "exact": "4174619051959196322579972723494195237298696688053499906630000/2777777777777777503436379545578895662577139448703456269758049" }, "decided": { "verdict": "REFUTED", "ledgerVerdict": "MISPRINTED", "printedAgrees": false, "why": "C1 = 1.5028628587049711; printed 1.50286287 DOES NOT agree (ceiling)", "ms": 675.3 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "1.5028628587063821", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-autocorr-ours_2026/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 1.50286286 moved − one unit in its last digit → 1.50286285 (FALSE only when the witness finds the bar no longer agrees with the exact score under the ceiling convention, else DISCARDED)", "sha256": "7915c3a60f4dbac96ab58f7089a260376e5d0550db2c99944b0b58fc774a0111", "bytes": 728164, "fixedFrom": "FALSE CERTIFICATION", "fix": "easota-word", "foundAt": "d961cda2", "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "window": [ "37571571/25000000", "30057257/20000000" ], "exact": "4174619051959196322579972723494195237298696688053499906630000/2777777777777777503436379545578895662577139448703456269758049" } }, "exact": "4174619051959196322579972723494195237298696688053499906630000/2777777777777777503436379545578895662577139448703456269758049" }, "decided": { "verdict": "REFUTED", "ledgerVerdict": "MISPRINTED", "printedAgrees": false, "why": "C1 = 1.5028628587049711; printed 1.50286285 DOES NOT agree (ceiling)", "ms": 665.3 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "1.5028628587063821", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-autocorr-ours_2026/coordinate-perturbed-1e-12", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "preservesOriginal": false, "transformation": "f[0] += 10⁻¹² (FALSE only with a witness: a violated constraint or an exact score past the bar, else DISCARDED)", "sha256": "b285d652983b075aa0e5bbf5d00347b01af1053d45ec9216befb3da2f1e71ba6", "bytes": 728164, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": "37571571467632766921576275261689638135688270192481499159670000/25000000000049997530927440907740988379104465038331106427822441" }, "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "C1 = 1.5028628587019653; printed 1.50286286 agrees (ceiling)", "ms": 653 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "1.502862858703377", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-autocorr-ours_2026/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "f reversed (the autoconvolution's maximum is reversal-invariant) (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "48bc08040b06377d5aeb06889eca48306f52613d8ba3cf712944e320d6d9aaa4", "bytes": 728164, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": "4174619051959196322579972723494195237298696688053499906630000/2777777777777777503436379545578895662577139448703456269758049" }, "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "C1 = 1.5028628587049711; printed 1.50286286 agrees (ceiling)", "ms": 651.8 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "1.5028628587063155", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-autocorr-ours_2026/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "value 0 missing (null)", "sha256": "c1d5b840136bf30acbdec6e5756bc1b552ee5ebbce3ee7cebb94542755734d9c", "bytes": 728144, "witness": { "violated": null, "malformed": true, "reason": "a value is missing", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: a value is missing", "ms": 0.1 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a value is missing", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [ "control-bar-far" ], "ms": 22054 }, { "rowId": "ea-flat-alphaevolve_2025", "record": "certs/easota-ledger.json", "entryId": "flat/alphaevolve_2025", "verdict": "CERTIFIED", "object": "flat (easota, easota/flat-polynomials/alphaevolve_2025.py), printed 1.340925 (rounding)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "C⁺ ∈ [1.3409252804007615, 1.3409252804007616]; printed 1.340925 agrees (rounding)", "ms": 431.7 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "1.3409252796863158", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } }, "sha256": "ffa2357ba0356fe245bfb9cc4e42d93b6289af02c69ee513dab274f02c890165" }, "mutants": [ { "id": "ea-flat-alphaevolve_2025/printed-plus-one-unit", "class": "printed-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 1.340925 moved + one unit in its last digit → 1.340926 (FALSE only when the witness finds the bar no longer agrees with the exact score under the rounding convention, else DISCARDED)", "sha256": "ea8a92ac221f4bdfabb9427366e8ad72a64d67f2b84458529cf254ffc3fbeaaf", "bytes": 430, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": null }, "decided": { "verdict": "REFUTED", "ledgerVerdict": "MISPRINTED", "printedAgrees": false, "why": "C⁺ ∈ [1.3409252804007615, 1.3409252804007616]; printed 1.340926 DOES NOT agree (rounding)", "ms": 400.4 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "1.3409252796863158", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-flat-alphaevolve_2025/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 1.340925 moved − one unit in its last digit → 1.340924 (FALSE only when the witness finds the bar no longer agrees with the exact score under the rounding convention, else DISCARDED)", "sha256": "ee61972da2a1ea210e48cff5817bad3e729f0e8a0aa52544a192debc3bb9c130", "bytes": 430, "fixedFrom": "FALSE CERTIFICATION", "fix": "easota-word", "foundAt": "d961cda2", "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "windowTop": "2681849/2000000", "lowerBoundOfCplusSquared": 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"note": "a lower bound only: a bar above the supremum cannot be witnessed here" } }, "exact": null }, "decided": { "verdict": "REFUTED", "ledgerVerdict": "MISPRINTED", "printedAgrees": false, "why": "C⁺ ∈ [1.3409252804007615, 1.3409252804007616]; printed 1.340924 DOES NOT agree (rounding)", "ms": 393.5 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "1.3409252796863158", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "ea-flat-alphaevolve_2025/coordinate-perturbed-1e-12", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "preservesOriginal": false, "transformation": "coefficient 0 moved by +10⁻¹²: no longer ±1 (FALSE only with a witness: a violated constraint or an exact score past the bar, else DISCARDED)", "sha256": "379b8c68d2781501cd391ff3c1ace58a6e0d0b5c1ae5aa19bf52f76927c6c474", "bytes": 443, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "constraint": { "kind": "a coefficient that is not ±1", "index": 0 } }, "exact": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: a coefficient that is not an integer literal", "ms": 0 }, "required": "REFUTED", "outcome": "refused", "float": { "score": "nan", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-flat-alphaevolve_2025/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "the coefficients reversed: the reciprocal polynomial has the same modulus on the circle (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "9161f0d207e3ac39f18e215ab7241e6f46108b6b68dadd8b2bfe5a221875387a", "bytes": 430, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": null }, "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "C⁺ ∈ [1.3409252804007615, 1.3409252804007616]; printed 1.340925 agrees (rounding)", "ms": 393.5 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "1.340925279686317", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-flat-alphaevolve_2025/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "coefficient 0 missing (null)", "sha256": "21d6482b0e712570ee5d93c93363e9dd6cd557a5b1e23d3ca949f316714b73c9", "bytes": 431, "witness": { "violated": null, "malformed": true, "reason": "a coefficient is missing", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: a coefficient that is not an integer literal", "ms": 0 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a value is missing", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [ "control-bar-far" ], "ms": 53443 }, { "rowId": "ea-flat-ours_2026", "record": "certs/easota-ledger.json", "entryId": "flat/ours_2026", "verdict": "CERTIFIED", "object": "flat (easota, easota/flat-polynomials/ours_2026.py), printed 1.280932 (rounding)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "C⁺ ∈ [1.2809320528750416, 1.2809320528750417]; printed 1.280932 agrees (rounding)", "ms": 472.3 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "1.2809320520720795", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } }, "sha256": "dbaf8e2bd3b415dc114131b258fc7acd8ed20eaa82932b1c57f7d16df3ed6ebc" }, "mutants": [ { "id": "ea-flat-ours_2026/printed-plus-one-unit", "class": "printed-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 1.280932 moved + one unit in its last digit → 1.280933 (FALSE only when the witness finds the bar no longer agrees with the exact score under the rounding convention, else DISCARDED)", "sha256": "f506841748d6b418c64bcc21e4130e046b2090dbcdcb8cfb1e277e720b312478", "bytes": 425, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": null }, "decided": { "verdict": "REFUTED", "ledgerVerdict": "MISPRINTED", "printedAgrees": false, "why": "C⁺ ∈ [1.2809320528750416, 1.2809320528750417]; printed 1.280933 DOES NOT agree (rounding)", "ms": 485.9 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "1.2809320520720795", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-flat-ours_2026/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 1.280932 moved − one unit in its last digit → 1.280931 (FALSE only when the witness finds the bar no longer agrees with the exact score under the rounding convention, else DISCARDED)", "sha256": "41ad697f093e73ea5d4ad019a3cbabefb8dfc3f56d3ab695b8bc1bc5215e6989", "bytes": 425, "fixedFrom": "FALSE CERTIFICATION", "fix": "easota-word", "foundAt": "d961cda2", "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "windowTop": "2561863/2000000", "lowerBoundOfCplusSquared": 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"index": 0 } }, "exact": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: a coefficient that is not an integer literal", "ms": 0 }, "required": "REFUTED", "outcome": "refused", "float": { "score": "1.280932052072078", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-flat-ours_2026/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "the coefficients reversed: the reciprocal polynomial has the same modulus on the circle (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "8265e397ecde5aeb88183f8fbb63edc8641ede9634af672c4f5f4026e3d636cb", "bytes": 425, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": null }, "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "C⁺ ∈ [1.2809320528750416, 1.2809320528750417]; printed 1.280932 agrees (rounding)", "ms": 441.3 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "1.280932052072079", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-flat-ours_2026/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "coefficient 0 missing (null)", "sha256": "9af26157d2e14239e19f36b218b35d649e779262c02d2fd73014127f1806f84e", "bytes": 425, "witness": { "violated": null, "malformed": true, "reason": "a coefficient is missing", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: a coefficient that is not an integer literal", "ms": 0 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a value is missing", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [ "control-bar-far" ], "ms": 60284 }, { "rowId": "ea-hexagons-alphaevolve_2025", "record": "certs/easota-ledger.json", "entryId": "hexagons/alphaevolve_2025", "verdict": "CERTIFIED", "object": "hexagons (easota, easota/hexagon-packing/alphaevolve_2025.json), printed 3.9419123 (exact)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "pairs {\"SEPARATED\":66}, vertices {\"INSIDE\":72}; printed 3.9419123 agrees (exact)", "ms": 12.9 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "3.9419123", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "8e325a70033e87d01c18687ba3c6ef77d6a04426b8edf43a0f86d8c8c9dba9f9" }, "mutants": [ { "id": "ea-hexagons-alphaevolve_2025/printed-plus-one-unit", "class": "printed-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 3.9419123 moved + one unit in its last digit → 3.9419124 (FALSE only when the witness finds the bar no longer agrees with the exact score under the exact convention, else DISCARDED)", "sha256": 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"preservesOriginal": true, "transformation": "every hexagon and the outer hexagon translated by (0.125, -0.375) (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "4c52edf386d177d41f964eb569d01c9a092417ee15ff8e390e9bf7efb1d43f5b", "bytes": 996, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": "39419123/10000000", "constraintsWitnessed": false }, "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "pairs {\"SEPARATED\":66}, vertices {\"INSIDE\":72}; printed 3.9419123 agrees (exact)", "ms": 2.5 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "3.9419123", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "ea-hexagons-alphaevolve_2025/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "hexagon 0 without its angle", "sha256": "79dd19e39624b05123b10a8857f4446b4c45837010b11a202b2d990bda2611da", "bytes": 975, "witness": { "violated": null, "malformed": true, "reason": "hexagon 0 has 2 numbers", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: a hexagon without three numbers", "ms": 0 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a hexagon without three numbers", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [ { "class": "coordinate-perturbed-1e-12", "reason": "the hexagons' constraints (separation, containment) are cosines and sines of printed angles; a standard-library witness of a violated constraint would need certified trigonometry, which it does not have" } ], "controlsFired": [ "control-bar-far" ], "ms": 220 }, { "rowId": "ea-hexagons-ours_2026", "record": "certs/easota-ledger.json", "entryId": "hexagons/ours_2026", "verdict": "CERTIFIED", "object": "hexagons (easota, easota/hexagon-packing/ours_2026.json), 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CERTIFICATION", "fix": "easota-word", "foundAt": "d961cda2", "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "window": [ "9854131/2500000", "9854131/2500000" ], "exact": "39416523/10000000" } }, "exact": "39416523/10000000", "constraintsWitnessed": false }, "decided": { "verdict": "REFUTED", "ledgerVerdict": "MISPRINTED", "printedAgrees": false, "why": "pairs {\"SEPARATED\":66}, vertices {\"INSIDE\":72}; printed 3.9416524 DOES NOT agree (exact)", "ms": 2.1 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "3.9416523", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-hexagons-ours_2026/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 3.9416523 moved − one unit in its last digit → 3.9416522 (FALSE only when the witness finds the bar no longer agrees with the exact score under the exact convention, else DISCARDED)", "sha256": "5b8758f2f4c0dc378daa8fe21de7ac928f2d9811ae2fde358f031aa0329a6a7a", "bytes": 995, "fixedFrom": "FALSE CERTIFICATION", "fix": "easota-word", "foundAt": "d961cda2", "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "window": [ "19708261/5000000", "19708261/5000000" ], "exact": "39416523/10000000" } }, "exact": "39416523/10000000", "constraintsWitnessed": false }, "decided": { "verdict": "REFUTED", "ledgerVerdict": "MISPRINTED", "printedAgrees": false, "why": "pairs {\"SEPARATED\":66}, vertices {\"INSIDE\":72}; printed 3.9416522 DOES NOT agree (exact)", "ms": 2.1 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "3.9416523", "accept": { "1e-6": true, "1e-9": false, "1e-12": false } } }, { "id": "ea-hexagons-ours_2026/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "every hexagon and the outer hexagon translated by (0.125, -0.375) (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "9449a74ec93db8d1678fc7d75709c093124b83f1152ef372358af5dcba589a68", "bytes": 995, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": "39416523/10000000", "constraintsWitnessed": false }, "decided": { "verdict": "CERTIFIED", "ledgerVerdict": "WITNESSED", "printedAgrees": true, "why": "pairs {\"SEPARATED\":66}, vertices {\"INSIDE\":72}; printed 3.9416523 agrees (exact)", "ms": 2 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "3.9416523", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "ea-hexagons-ours_2026/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "hexagon 0 without its angle", "sha256": "53d4eb60693ae48bf2e575a5a1053181e5f73385caea138f80071dce23e5438c", "bytes": 974, "witness": { "violated": null, "malformed": true, "reason": "hexagon 0 has 2 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expected a number literal", "ms": 0.1 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a value is missing", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [ "control-bar-far" ], "ms": 58322 }, { "rowId": "mc100-ea-best-edges-vs-triangles", "record": "certs/mc100-einstein-arena.json", "entryId": "ea-best-edges-vs-triangles", "verdict": "CERTIFIED", "object": "edges (mc100, einstein-arena/best-13.json), printed -0.7117091757692579 (platform, minImprovement 0.000001)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "500 rows of 20 weights: the platform's envelope score −(area + 10·max gap) = -0.71170917576925610657… exactly (the printed -0.7117091757692579 agrees, below)", "ms": 31600.4 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "-0.711709175769258", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "2ec4be4fd665504bed0c9222d710e9360f685c25f28b9efe2abf343b36287399" }, "mutants": [ { "id": "mc100-ea-best-edges-vs-triangles/printed-plus-one-unit", "class": "printed-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed -0.7117091757692579 moved + one unit in its last digit → -0.7117091757692578 (FALSE only when the witness finds the bar no longer agrees with the exact score under the platform convention, else DISCARDED)", "sha256": "aac9d0b802129f8b9a61d366c903eed0c8d02160b6bc5e649fd4eebc15d9c73b", "bytes": 86107, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": 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0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" }, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "500 rows of 20 weights: the platform's envelope score −(area + 10·max gap) = -0.71170917576925610657… exactly (the printed -0.7117091757692578 agrees, below)", "ms": 31612.4 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "-0.711709175769258", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ea-best-edges-vs-triangles/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed -0.7117091757692579 moved − one unit in its last digit → -0.7117091757692580 (FALSE only when the witness finds the bar no longer agrees with the exact score under the platform convention, else DISCARDED)", "sha256": "35a8223895a50b1d79b172450945ac160ca2bdb3afb42b2d37027896df5a63e0", "bytes": 86107, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": 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}, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "500 rows of 20 weights: the platform's envelope score −(area + 10·max gap) = -0.71170917576925610657… exactly (the printed -0.7117091757692580 agrees, below)", "ms": 31533.7 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "-0.711709175769258", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ea-best-edges-vs-triangles/coordinate-perturbed-1e-12", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "preservesOriginal": false, "transformation": "weights[0][0] += 10⁻¹² (FALSE only with a witness: a violated constraint or an exact score past the bar, else DISCARDED)", "sha256": "a0429364f43736663c772e984d2f75644c254fea0f07b270aefe6554e135e718", "bytes": 86107, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": 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}, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "500 rows of 20 weights: the platform's envelope score −(area + 10·max gap) = -0.71170917578774239352… exactly (the printed -0.7117091757692579 agrees, above)", "ms": 31189.4 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "-0.7117091757877454", "accept": { "1e-6": true, "1e-9": true, "1e-12": false } } }, { "id": "mc100-ea-best-edges-vs-triangles/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "the weight rows reversed (the curve is sorted by ρ) (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "aa7f3f235692d11a953e114d0411a516743502cb682265d250c387c924e7538f", "bytes": 86107, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": 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0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" }, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "500 rows of 20 weights: the platform's envelope score −(area + 10·max gap) = -0.71170917576925610657… exactly (the printed -0.7117091757692579 agrees, below)", "ms": 31264.9 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "-0.711709175769258", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ea-best-edges-vs-triangles/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "row 0 with 19 weights", "sha256": "38a6f6897ecb6e8b69442389ed0a1eda30819c572c15bc9fd42b92c0c031587c", "bytes": 86103, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "row 0 has 19 weights", "firstViolation": null }, "decided": { "verdict": "REFUSED", "kind": "none", "why": "a row without 20 weights: malformed, not decided", "ms": 3.3 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a row without 20 weights", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [ "control-bar-far" ], "ms": 159935 }, { "rowId": "mc100-ea-best-circles-rectangle", "record": "certs/mc100-einstein-arena.json", "entryId": "ea-best-circles-rectangle", "verdict": "CERTIFIED", "object": "circles (mc100, einstein-arena/best-18.json), printed 2.3658323759098576 (platform, minImprovement 1e-10)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "21 circles, no two overlapping and the bounding box at w + h ≤ 2, exactly: Σr = 2.36583237590985849000… (the printed 2.3658323759098576 agrees, below)", "ms": 9.2 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "2.365832375909858", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "8630efa37b193231137fca6d3ede3b64c0457007c5384b0db84f6eeb183640a0" }, "mutants": [ { "id": "mc100-ea-best-circles-rectangle/printed-plus-one-unit", "class": "printed-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 2.3658323759098576 moved + one unit in its last digit → 2.3658323759098577 (FALSE only when the witness finds the bar no longer agrees with the exact score under the platform convention, else DISCARDED)", "sha256": "14920cf03a10482ba7a9f62c804f61acc3fd7e743f597dc2ec6572e61bfc8426", "bytes": 1556, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": "236583237590985849/100000000000000000" }, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "21 circles, no two overlapping and the bounding box at w + h ≤ 2, exactly: Σr = 2.36583237590985849000… (the printed 2.3658323759098577 agrees, below)", "ms": 9 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "2.365832375909858", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ea-best-circles-rectangle/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 2.3658323759098576 moved − one unit in its last digit → 2.3658323759098575 (FALSE only when the witness finds the bar no longer agrees with the exact score under the platform convention, else DISCARDED)", "sha256": "79fb5f908e0618ec71ea81497b597198b4f55da08d3e6de6c5df0941d57a0955", "bytes": 1556, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": "236583237590985849/100000000000000000" }, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "21 circles, no two overlapping and the bounding box at w + h ≤ 2, exactly: Σr = 2.36583237590985849000… (the printed 2.3658323759098575 agrees, below)", "ms": 8.9 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "2.365832375909858", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ea-best-circles-rectangle/coordinate-perturbed-1e-12", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "preservesOriginal": false, "transformation": "circle 10 moved +10⁻¹² in x toward circle 20 (the pair with the least slack) (FALSE only with a witness: a violated constraint or an exact score past the bar, else DISCARDED)", "sha256": "85e1370c1100c7bd423310874d6186ac24848f11f151ba81508fd646b987a23f", "bytes": 1556, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "constraint": { "kind": "overlapping circles", "pairs": 2, "worst": [ 10, 20 ], "slackSquared": "-248819702497100077679/500000000000000000000000000000000" } }, "exact": "236583237590985849/100000000000000000" }, "decided": { "verdict": "REPAIRED", "kind": "tolerance-witness", "why": "as published, 2 pairs overlap, exactly (the platform's verifier has had no slack since 2026-08-24 (corpus/sources/easota-platform/einstein-arena-changelog_9cd6fbfb.md; circles-rectangle_9cd6fbfb.ts)); the printed 2.3658323759098576 is the a", "ms": 86.1 }, "required": "REFUTED", "outcome": "not as required (REPAIRED)", "float": { "score": "2.365832375909858", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ea-best-circles-rectangle/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "every circle reflected in x (x → −x): the box and Σr are invariant (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "072f2b9d1bcb7dc43aa5153c0f533cbd636b4652158dc0c2f4319a991c822b67", "bytes": 1577, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": "236583237590985849/100000000000000000" }, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "21 circles, no two overlapping and the bounding box at w + h ≤ 2, exactly: Σr = 2.36583237590985849000… (the printed 2.3658323759098576 agrees, below)", "ms": 8.9 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "2.365832375909858", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ea-best-circles-rectangle/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "circle 0 without its radius", "sha256": "6ea791c5578714ca19a8741b5256e1ce3c3b8e55da80ed7fb7161c54633cd5ea", "bytes": 1534, "witness": { "violated": null, "malformed": true, "reason": "circle 0 has 2 numbers", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: Cannot read properties of undefined (reading 'd')", "ms": 0.2 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a circle without three numbers", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [ "control-bar-far" ], "ms": 307 }, { "rowId": "mc100-ea-best-kissing-number-d12", "record": "certs/mc100-einstein-arena.json", "entryId": "ea-best-kissing-number-d12", "verdict": "CERTIFIED", "object": "kissing (mc100, einstein-arena/best-22.json), printed 2 (platform, minImprovement 0)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "NOT a kissing configuration of 841: 1 pair (0 & 840) point in the same direction (cos = 1 exactly) and every other pair is at 60° or more, exactly — 840 distinct directions form a kissing configuration (40,992 exact contacts); the platform'", "ms": 178.4 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "2.0", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "bf496ef8bc19166c85ed20298b0201b4f07972857b29c9ed63d4671463585aca" }, "mutants": [ { "id": "mc100-ea-best-kissing-number-d12/printed-plus-one-unit", "class": "printed-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 2 moved + one unit in its last digit → 3 (FALSE only when the witness finds the bar no longer agrees with the exact score under the platform convention, else DISCARDED)", "sha256": "f285f84b0a00074142a0533dbf56443b96c95b2db732b82596d6b50dec40f068", "bytes": 50371, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "window": [ "2999999999997/1000000000000", "3000000000003/1000000000000" ], "exact": "2" } }, "exact": [ "2", "2" ] }, "decided": { "verdict": "REFUTED", "kind": "not-from-the-published-data", "why": "the platform's score 3 is not the exact penalty of the object, enclosed in [2.000000000000000000000000000000, 2.000000000000000000000000000000]", "ms": 168.1 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "2.0", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-ea-best-kissing-number-d12/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 2 moved − one unit in its last digit → 1 (FALSE only when the witness finds the bar no longer agrees with the exact score under the platform convention, else DISCARDED)", "sha256": "34dee2bf957a8ed288b65042ee4dc04b6cf41bc66d5235c58bce852ea4630164", "bytes": 50371, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "window": [ "999999999999/1000000000000", "1000000000001/1000000000000" ], "exact": "2" } }, "exact": [ "2", "2" ] }, "decided": { "verdict": "REFUTED", "kind": "not-from-the-published-data", "why": "the platform's score 1 is not the exact penalty of the object, enclosed in [2.000000000000000000000000000000, 2.000000000000000000000000000000]", "ms": 153.9 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "2.0", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-ea-best-kissing-number-d12/coordinate-perturbed-1e-12", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "preservesOriginal": false, "transformation": "vectors[0][0] += 10⁻¹² (FALSE only with a witness: a violated constraint or an exact score past the bar, else DISCARDED)", "sha256": "586c29daf9161fcebff32f078545e4572d69add5cbc8d1ade981a5a7185e3def", "bytes": 50384, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": [ "2", "2" ] }, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "NOT a kissing configuration of 841: 1 pair (0 & 840) point in the same direction (cos = 1 exactly) and every other pair is at 60° or more, exactly — 840 distinct directions form a kissing configuration (40,992 exact contacts); the platform'", "ms": 159 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "2.0", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ea-best-kissing-number-d12/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "the coordinates rotated by one (the penalty is invariant) (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "d0f01e2432d19d8feef644f10795e567327b718365ccf03c30ebc5655625af1b", "bytes": 50371, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": [ "2", "2" ] }, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "NOT a kissing configuration of 841: 1 pair (0 & 840) point in the same direction (cos = 1 exactly) and every other pair is at 60° or more, exactly — 840 distinct directions form a kissing configuration (40,992 exact contacts); the platform'", "ms": 154.9 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "2.0", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ea-best-kissing-number-d12/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "vector 0 short by one coordinate", "sha256": "4ff06f0c131352c82a59e2745b0a6793eb4cb62b726ad516c59b09bc388c2aa1", "bytes": 50367, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "vector 1 has 12 coordinates, vector 0 has 11", "firstViolation": null }, "decided": { "verdict": "REFUSED", "kind": "none", "why": "the object is not 841 vectors in R^12 (841 rows): malformed, not decided", "ms": 0.7 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "vectors of different dimension", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [ "control-bar-far" ], "ms": 7105 }, { "rowId": "mc100-ea-best-kissing-number-d11-605", "record": "certs/mc100-einstein-arena.json", "entryId": "ea-best-kissing-number-d11-605", "verdict": "CERTIFIED", "object": "kissing (mc100, einstein-arena/best-24.json), printed 1.7102381876301676 (platform, minImprovement 0)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "NOT a kissing configuration of 605 (as the platform's score itself says): 9,510 of 182,710 pairs are closer than 60°, decided exactly; the worst, vectors 601 and 604, has cos²θ = 1/4 + δ with δ = an exact rational (in the ledger), cos θ − 1", "ms": 111.9 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "1.710238187632024", "accept": { "1e-6": true, "1e-9": true, "1e-12": false } }, "sha256": "ccbfedf50ec805af5c94bae74e5cbbd4be28948004f1ad93fed81cc6b8f329ae" }, "mutants": [ { "id": "mc100-ea-best-kissing-number-d11-605/printed-plus-one-unit", "class": "printed-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 1.7102381876301676 moved + one unit in its last digit → 1.7102381876301677 (FALSE only when the witness finds the bar no longer agrees with the exact score under the platform convention, else DISCARDED)", "sha256": "b77627e9b7ab02b0caad840abf4f3ae2185f7e97554c83e16e4d467a3fdff994", "bytes": 153176, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": [ "1.71023818763016759486325585270663368141378202037737668293745", "1.71023818763016759486325585270663368141378202037737668297546" ] }, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "NOT a kissing configuration of 605 (as the platform's score itself says): 9,510 of 182,710 pairs are closer than 60°, decided exactly; the worst, vectors 601 and 604, has cos²θ = 1/4 + δ with δ = an exact rational (in the ledger), cos θ − 1", "ms": 107.4 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "1.710238187632024", "accept": { "1e-6": true, "1e-9": true, "1e-12": false } } }, { "id": "mc100-ea-best-kissing-number-d11-605/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 1.7102381876301676 moved − one unit in its last digit → 1.7102381876301675 (FALSE only when the witness finds the bar no longer agrees with the exact score under the platform convention, else DISCARDED)", "sha256": "f67883eec298474c38686aae16e24f35632541bf9b7d2f62143bea745f567b21", "bytes": 153176, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": [ "1.71023818763016759486325585270663368141378202037737668293745", "1.71023818763016759486325585270663368141378202037737668297546" ] }, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "NOT a kissing configuration of 605 (as the platform's score itself says): 9,510 of 182,710 pairs are closer than 60°, decided exactly; the worst, vectors 601 and 604, has cos²θ = 1/4 + δ with δ = an exact rational (in the ledger), cos θ − 1", "ms": 107.8 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "1.710238187632024", "accept": { "1e-6": true, "1e-9": true, "1e-12": false } } }, { "id": "mc100-ea-best-kissing-number-d11-605/coordinate-perturbed-1e-12", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "preservesOriginal": false, "transformation": "vectors[0][0] += 10⁻¹² (FALSE only with a witness: a violated constraint or an exact score past the bar, else DISCARDED)", "sha256": "7c3f390276d9764eebd6ee9e36eebf55c8ded1973fc9954d81254019a452f751", "bytes": 153176, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": [ "1.71023818763150041153375346872419672225304170246956007475806", "1.71023818763150041153375346872419672225304170246956007479611" ] }, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "NOT a kissing configuration of 605 (as the platform's score itself says): 9,512 of 182,710 pairs are closer than 60°, decided exactly; the worst, vectors 601 and 604, has cos²θ = 1/4 + δ with δ = an exact rational (in the ledger), cos θ − 1", "ms": 107.7 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "1.7102381876333634", "accept": { "1e-6": true, "1e-9": true, "1e-12": false } } }, { "id": "mc100-ea-best-kissing-number-d11-605/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "the coordinates rotated by one (the penalty is invariant) (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "8c11ff0ebf34702ed0a50867e374829f476459b19fd7b85432e5633b006f8b92", "bytes": 153176, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": [ "1.71023818763016759486325585270663368141378202037737668293745", "1.71023818763016759486325585270663368141378202037737668297546" ] }, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "NOT a kissing configuration of 605 (as the platform's score itself says): 9,510 of 182,710 pairs are closer than 60°, decided exactly; the worst, vectors 601 and 604, has cos²θ = 1/4 + δ with δ = an exact rational (in the ledger), cos θ − 1", "ms": 107.4 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "1.7102381876320214", "accept": { "1e-6": true, "1e-9": true, "1e-12": false } } }, { "id": "mc100-ea-best-kissing-number-d11-605/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "vector 0 short by one coordinate", "sha256": "7885f39b9c3284d6680f73086dd4e636250d639351aada92afce4bf55cdede7f", "bytes": 153153, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "vector 1 has 11 coordinates, vector 0 has 10", "firstViolation": null }, "decided": { "verdict": "REFUSED", "kind": "none", "why": "the object is not 605 vectors in R^11 (605 rows): malformed, not decided", "ms": 1 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "vectors of different dimension", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [ "control-bar-far" ], "ms": 5987 }, { "rowId": "mc100-ea-best-kissing-number-d12-842", "record": "certs/mc100-einstein-arena.json", "entryId": "ea-best-kissing-number-d12-842", "verdict": "CERTIFIED", "object": "kissing (mc100, einstein-arena/best-25.json), printed 0.5469062458557645 (platform, minImprovement 0)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "NOT a kissing configuration of 842 (as the platform's score itself says): 237 of 354,061 pairs are closer than 60°, decided exactly; the worst, vectors 510 and 547, has cos²θ = 1/4 + δ with δ = an exact rational (in the ledger), cos θ − 1/2", "ms": 126.4 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "0.5469062458558096", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "e0c1c0777340b952b961940b733761d4f5939cd2be4ffff13c591f30bbfddc75" }, "mutants": [ { "id": "mc100-ea-best-kissing-number-d12-842/printed-plus-one-unit", "class": "printed-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 0.5469062458557645 moved + one unit in its last digit → 0.5469062458557646 (FALSE only when the witness finds the bar no longer agrees with the exact score under the platform convention, else DISCARDED)", "sha256": "8f6e87d07c5622d0f744097eb18bd835280cfb97fb7cd6ed40fa9e1b3de8fb63", "bytes": 226539, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": [ "0.54690624585576453779831542286181732346512324608522431109155", "0.54690624585576453779831542286181732346512324608522431109254" ] }, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "NOT a kissing configuration of 842 (as the platform's score itself says): 237 of 354,061 pairs are closer than 60°, decided exactly; the worst, vectors 510 and 547, has cos²θ = 1/4 + δ with δ = an exact rational (in the ledger), cos θ − 1/2", "ms": 122 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "0.5469062458558096", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ea-best-kissing-number-d12-842/printed-minus-one-unit", "class": "printed-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the printed 0.5469062458557645 moved − one unit in its last digit → 0.5469062458557644 (FALSE only when the witness finds the bar no longer agrees with the exact score under the platform convention, else DISCARDED)", "sha256": "08fc6dcf21eea05149cf9ed0bbd7c83008e39f43da349412bd406674c94d142e", "bytes": 226539, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": [ "0.54690624585576453779831542286181732346512324608522431109155", "0.54690624585576453779831542286181732346512324608522431109254" ] }, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "NOT a kissing configuration of 842 (as the platform's score itself says): 237 of 354,061 pairs are closer than 60°, decided exactly; the worst, vectors 510 and 547, has cos²θ = 1/4 + δ with δ = an exact rational (in the ledger), cos θ − 1/2", "ms": 119 }, "required": "REFUTED", "outcome": "DISCARDED", "float": { "score": "0.5469062458558096", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ea-best-kissing-number-d12-842/coordinate-perturbed-1e-12", "class": "coordinate-perturbed-1e-12", "truth": "FALSE", "preservesOriginal": false, "transformation": "vectors[0][0] += 10⁻¹² (FALSE only with a witness: a violated constraint or an exact score past the bar, else DISCARDED)", "sha256": "383f37ba0699c821c976faca99783a042c5858248db06b3d998cec94fc28abfd", "bytes": 226539, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "bar": { "window": [ "1093812491709529/2000000000000000", "1093812491713529/2000000000000000" ], "exact": [ "1709082018312323836393278993181908508594040988084264848439/3125000000000000000000000000000000000000000000000000000000", "1093812491719887255291698555636421445500186232373929503003/2000000000000000000000000000000000000000000000000000000000" ] } }, "exact": [ "0.54690624585994362764584927781821072275009311618696475150048", "0.54690624585994362764584927781821072275009311618696475150150" ] }, "decided": { "verdict": "REFUTED", "kind": "not-from-the-published-data", "why": "the platform's score 0.5469062458557645 is not the exact penalty of the object, enclosed in [0.546906245859943627645849277818, 0.546906245859943627645849277818]", "ms": 115.3 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "0.5469062458599889", "accept": { "1e-6": true, "1e-9": true, "1e-12": false } } }, { "id": "mc100-ea-best-kissing-number-d12-842/rigid-motion", "class": "rigid-motion", "truth": "TRUE", "preservesOriginal": true, "transformation": "the coordinates rotated by one (the penalty is invariant) (preserves the original's status: a REPAIRED row is REPAIRED again)", "sha256": "adcdbb0b5f46ac373367beb9d0e51f736d35529d44f07a8f6f3bc3d4894aa5e6", "bytes": 226539, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": [ "0.54690624585576453779831542286181732346512324608522431109155", "0.54690624585576453779831542286181732346512324608522431109254" ] }, "decided": { "verdict": "CERTIFIED", "kind": "none", "why": "NOT a kissing configuration of 842 (as the platform's score itself says): 237 of 354,061 pairs are closer than 60°, decided exactly; the worst, vectors 510 and 547, has cos²θ = 1/4 + δ with δ = an exact rational (in the ledger), cos θ − 1/2", "ms": 118.3 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "0.5469062458558334", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "mc100-ea-best-kissing-number-d12-842/coordinate-missing", "class": "coordinate-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "vector 0 short by one coordinate", "sha256": "c88a71a0b6fab67c25777042d7c4dbee8cb425f64f8d6be505547169eed28714", "bytes": 226517, "fixedFrom": "not as required (REFUTED)", "fix": "malformed-word", "foundAt": "d961cda2", "witness": { "violated": null, "malformed": true, "reason": "vector 1 has 12 coordinates, vector 0 has 11", "firstViolation": null }, "decided": { "verdict": "REFUSED", "kind": "none", "why": "the object is not 842 vectors in R^12 (842 rows): malformed, not decided", "ms": 1.5 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "vectors of different dimension", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [ "control-bar-far" ], "ms": 8235 } ] }, "erdos852": { "decider": "instruments/erdos852/constants.js decideClaimedDigits on the enclosure cstar({limit: 30000000, P: 192}) computes (VERIFIED, VERIFIED_ROUNDED → CERTIFIED; REFUTED; UNDECIDED or a throw → REFUSED), the path of tools/export-erdos852-certificate.js", "witness": "instruments/selfaudit/witness_erdos852.py", "floatcheck": "instruments/selfaudit/floatcheck_erdos852.py", "redControl": "truncation-plus-one-unit", "records": [ "certs/erdos852-certificate.json" ], "classes": { "FALSE": [ "the original (the published digits)", "truncation-plus-one-unit", "truncation-minus-one-unit" ], "TRUE": [ "digits-coarsened-13", "digits-coarsened-11" ], "MALFORMED": [ "non-numeric-digit" ] }, "rows": [ { "rowId": "erdos852-cstar", "record": "certs/erdos852-certificate.json", "entryId": "cstar", "verdict": "REFUTED", "object": "C* = (1/2)(prod over primes p>=3 of (1 + 1/(p-1)^3) - 1), published as 0.0752403861777; certified enclosure [0.0752403861783092455893, 0.0752403861783095651674]", "original": { "required": "REFUTED", "decided": { "verdict": "REFUTED", "why": "REFUTED (13 decimals) against the instrument's enclosure of C* (cstar at 30,000,000, 192 bits)", "ms": 4239.2 }, "asRequired": true, "witness": { "violated": true, "malformed": false }, "float": { "floatValue": "0.07524038617774187", "difference": 4.1869285816176216e-14, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "71d3516d59b2b615296f79e1c91a035f23c79ea5640e893c4bdb0a78e8d5d2b6" }, "mutants": [ { "id": "erdos852-cstar/truncation-plus-one-unit", "class": "truncation-plus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the corrected 13-decimal truncation 0.0752403861783 raised by one unit in its last place → 0.0752403861784", "sha256": "63cbae84714661fcdf97e1fddd7bd7c3c156a2f6af54922046051466a36b4380", "bytes": 47, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "claim": "0.0752403861784", "window": [ "1504807723567/20000000000000", "150480772357/2000000000000" ], "enclosure": [ "0.07524038617830811764660687855", "0.07524038617832609391766308564" ], "side": "the enclosure lies entirely below the window" } }, "decided": { "verdict": "REFUTED", "why": "REFUTED (13 decimals) against the instrument's enclosure of C* (cstar at 30,000,000, 192 bits)", "ms": 0 }, "required": "REFUTED", "outcome": "as required", "float": { "floatValue": "0.07524038617774187", "difference": 6.58126331209985e-13, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "erdos852-cstar/truncation-minus-one-unit", "class": "truncation-minus-one-unit", "truth": "FALSE", "preservesOriginal": false, "transformation": "the corrected 13-decimal truncation 0.0752403861783 lowered by one unit in its last place → 0.0752403861782", "sha256": "b6e178e06b5ca74203988dc9a0900f1cac34478f2d9be88b8c2a3bb8adcae154", "bytes": 47, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "claim": "0.0752403861782", "window": [ "1504807723563/20000000000000", "752403861783/10000000000000" ], "enclosure": [ "0.07524038617830811764660687855", "0.07524038617832609391766308564" ], "side": "the enclosure lies entirely above the window" } }, "decided": { "verdict": "REFUTED", "why": "REFUTED (13 decimals) against the instrument's enclosure of C* (cstar at 30,000,000, 192 bits)", "ms": 0 }, "required": "REFUTED", "outcome": "as required", "float": { "floatValue": "0.07524038617774187", "difference": 4.581335311115708e-13, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "erdos852-cstar/digits-coarsened-13", "class": "digits-coarsened-13", "truth": "TRUE", "preservesOriginal": false, "transformation": "the enclosure widened outward to a 13-decimal window: the digits 0.0752403861783 (whose truncation window contains the enclosure)", "sha256": "c7cc842dc45fc26558cd72d7f330da34f80c8916347dcb5aa5223cf56869b616", "bytes": 47, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null }, "decided": { "verdict": "CERTIFIED", "why": "VERIFIED (13 decimals) against the instrument's enclosure of C* (cstar at 30,000,000, 192 bits)", "ms": 0 }, "required": "CERTIFIED", "outcome": "as required", "float": { "floatValue": "0.07524038617774187", "difference": 5.581368700546818e-13, "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "erdos852-cstar/digits-coarsened-11", "class": "digits-coarsened-11", "truth": "TRUE", "preservesOriginal": false, "transformation": "the enclosure widened outward to an 11-decimal window: the digits 0.07524038617", "sha256": "e3b94665c7cdca7c767ef69b14ce28acae91e441f41ed5a2864264d84e83e896", "bytes": 45, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null }, "decided": { "verdict": "CERTIFIED", "why": "VERIFIED (11 decimals) against the instrument's enclosure of C* (cstar at 30,000,000, 192 bits)", "ms": 0 }, "required": "CERTIFIED", "outcome": "as required", "float": { "floatValue": "0.07524038617774187", "difference": 7.741862706467373e-12, "accept": { "1e-6": true, "1e-9": true, "1e-12": false } } }, { "id": "erdos852-cstar/non-numeric-digit", "class": "non-numeric-digit", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "the published digits with the letter O in place of a zero", "sha256": "c1e2b3a36b32de38fc97eeaac16274cc12f61bbe8a2d11b9c536f552f70196b7", "bytes": 47, "witness": { "violated": null, "malformed": true, "reason": "not a decimal string \"int.frac\": '0.O752403861777'", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the instrument threw: erdos852.decideClaimedDigits: claim must be \"int.frac\", got 0.O752403861777", "ms": 0 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "could not convert string to float: '0.O752403861777'", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [], "ms": 5257 } ] }, "polymaps": { "decider": "instruments/polymaps/decide.py — keller (det JF expanded symbolically over Q, the degrees, the collision evaluated) and my_field (the nilpotency identity, the zeros evaluated), composed as decide() composes them, run as tools/run-polymaps-ledger.py and tools/run-mc100-station.py run it (python3 -I); F7 as the ledger decides it, the determinant resting on the lemma", "witness": "instruments/selfaudit/witness_polymaps.py", "floatcheck": "instruments/selfaudit/floatcheck_polymaps.py", "redControl": "witness-point-moved", "records": [ "certs/polymaps-ledger.json", "certs/mc100-station-v2.json" ], "classes": { "FALSE": [ "coefficient-plus-one", "witness-point-moved" ], "TRUE": [ "translated", "witness-order-swapped" ], "MALFORMED": [ "exponent-missing" ] }, "rows": [ { "rowId": "polymaps-gao-g", "record": "certs/polymaps-ledger.json", "entryId": "gao-g", "verdict": "CERTIFIED", "object": "G: a polynomial map of Q^3 with det J = 2, 33 terms, 2 witness points (corpus/polymaps/maps.json G)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "det JF is identically the printed constant 2: ok · component degrees are the printed [4, 11, 12]: ok · 2 distinct rational points with one image: F is not injectiv: ok", "ms": 73.9 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "2.000000000000003", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "4d18bcbbc8e9d8aab0c130e3ed645176da1954d550c9137adfd47e8868ff48bd" }, "mutants": [ { "id": "polymaps-gao-g/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first term of component 0 (2 x^(1,0,0)) + 1: det JF is no longer the constant 2", "sha256": "e7073dca2307bc6a679ef13a6173ae49a184b84740b349d8e25c21e2ec086247", "bytes": 619, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "det JF at p0 is not the printed constant", "p0": [ "1/2", "1/3", "1/5" ], "detAtP0": "41884181477/13436928000", "printed": "2" } }, "decided": { "verdict": "REFUTED", "why": "det JF is identically the printed constant 2: FAILED · component degrees are the printed [4, 11, 12]: ok · 2 distinct rational points with one image: F is not injectiv: FAILED", "ms": 74.5 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "3.1170950292358537", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-gao-g/witness-point-moved", "class": "witness-point-moved", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first coordinate of witness point 0 + 1: the printed points no longer have one image", "sha256": "963aaf9d07d65a9617315b8c2322338c89b0bb9397550a3d4667eb85b24e29ae", "bytes": 620, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "the printed witness points do not share one image", "images": [ [ "-7579/512", "189977635/134217728", "-1225285125/8589934592" ], [ "1", "5/4", "0" ] ] } }, "decided": { "verdict": "REFUTED", "why": "det JF is identically the printed constant 2: ok · component degrees are the printed [4, 11, 12]: ok · 2 distinct rational points with one image: F is not injectiv: FAILED", "ms": 72.9 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "2.000000000000003", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-gao-g/translated", "class": "translated", "truth": "TRUE", "preservesOriginal": true, "transformation": "F'(x) = F(x + e₁) − F(e₁): det JF, the degrees and the collision kept, the points moved to p − e₁", "sha256": "277e7e87f5a717d31df602db83a37d68018aa083cd3cbbe0eb24a7d103365d2c", "bytes": 2024, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null }, "decided": { "verdict": "CERTIFIED", "why": "det JF is identically the printed constant 2: ok · component degrees are the printed [4, 11, 12]: ok · 2 distinct rational points with one image: F is not injectiv: ok", "ms": 105.7 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "1.9999999999999372", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "polymaps-gao-g/exponent-missing", "class": "exponent-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "the first term's exponent tuple short by one entry", "sha256": "dd2ebbd147d5755bf82f474e8ca2b1d6696985bc9166fcbe3906f2821b0c1aa2", "bytes": 617, "witness": { "violated": null, "malformed": true, "reason": "a term whose exponent tuple does not have 3 non-negative entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: 25, in \n return [[f.diff(j) for j in range(n)] for f in F]\n File \"/Users/carlostoledo/Projects/cert-machine/instruments/polymaps/poly.py\", line 47, in diff\n if e[i]:\nIndexError: tuple index out of range\n", "ms": 71.8 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a term whose exponent tuple does not have n entries", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [], "ms": 556 }, { "rowId": "polymaps-gao-f4", "record": "certs/polymaps-ledger.json", "entryId": "gao-f4", "verdict": "CERTIFIED", "object": "F4: a polynomial map of Q^4 with det J = -44/9, 188 terms, 3 witness points (corpus/polymaps/maps.json F4)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "det JF is identically the printed constant -44/9: ok · component degrees are the printed [4, 11, 12, 21]: ok · 3 distinct rational points with one image: F is not injectiv: ok", "ms": 227.8 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "-4.888888888888618", "accept": { "1e-6": true, "1e-9": true, "1e-12": false } }, "sha256": "ca41c0293ea82bdadb1a9db877f7e6a97490e756c3fd48fc9f216548bd86d203" }, "mutants": [ { "id": "polymaps-gao-f4/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first term of component 0 (1 x^(1,0,0,0)) + 1: det JF is no longer the constant -44/9", "sha256": "501c099e98c758df8cfcdabd0091ad7645965d359c2d4327aedbb275c30a68ed", "bytes": 3858, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "det JF at p0 is not the printed constant", "p0": [ "1/2", "1/3", "1/5", "1/7" ], "detAtP0": "5593572886148155335127921/617374924669440000000000", "printed": "-44/9" } }, "decided": { "verdict": "REFUTED", "why": "det JF is identically the printed constant -44/9: FAILED · component degrees are the printed [4, 11, 12, 21]: ok · 3 distinct rational points with one image: F is not injectiv: FAILED", "ms": 231.4 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "9.06025279394592", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-gao-f4/witness-point-moved", "class": "witness-point-moved", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first coordinate of witness point 0 + 1: the printed points no longer have one image", "sha256": "7d592a09bcc31e516b0f88a8db4fca58a3ab75383cd2f3147083c8b7d9d07d1b", "bytes": 3857, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "the printed witness points do not share one image", "images": [ [ "-923532650495/7801396416", "-5703200091216385741459560055706159/1725037249848489774197637120", "-26054282691409399018270534642084772237/931520114918184478066724044800", "-4058425209482070397725346047545677397139264814594135309643575487/1224589923195407791560897587032149377203572918190080" ], [ "1", "-1289/270", "-113/90", "1453/90" ], [ "1", "-1289/270", "-113/90", "1453/90" ] ] } }, "decided": { "verdict": "REFUTED", "why": "det JF is identically the printed constant -44/9: ok · component degrees are the printed [4, 11, 12, 21]: ok · 3 distinct rational points with one image: F is not injectiv: FAILED", "ms": 228.5 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "-4.888888888888618", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-gao-f4/translated", "class": "translated", "truth": "TRUE", "preservesOriginal": true, "transformation": "F'(x) = F(x + e₁) − F(e₁): det JF, the degrees and the collision kept, the points moved to p − e₁", "sha256": "15844eb1eab0665894e7ccc3ddf28947df61a61937a11f98f30a1205e71dd2c5", "bytes": 21493, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null }, "decided": { "verdict": "CERTIFIED", "why": "det JF is identically the printed constant -44/9: ok · component degrees are the printed [4, 11, 12, 21]: ok · 3 distinct rational points with one image: F is not injectiv: ok", "ms": 8179.8 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "-4.888888888892849", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-gao-f4/exponent-missing", "class": "exponent-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "the first term's exponent tuple short by one entry", "sha256": "2b2a83fd4fea8eccd1282081bcca5380b0ac0fb395d73f8b302ef1f343b52628", "bytes": 3856, "witness": { "violated": null, "malformed": true, "reason": "a term whose exponent tuple does not have 4 non-negative entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: 25, in \n return [[f.diff(j) for j in range(n)] for f in F]\n File \"/Users/carlostoledo/Projects/cert-machine/instruments/polymaps/poly.py\", line 47, in diff\n if e[i]:\nIndexError: tuple index out of range\n", "ms": 74.6 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a term whose exponent tuple does not have n entries", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [], "ms": 9203 }, { "rowId": "polymaps-gao-f5", "record": "certs/polymaps-ledger.json", "entryId": "gao-f5", "verdict": "CERTIFIED", "object": "F5: a polynomial map of Q^4 with det J = 160/29, 114 terms, 2 witness points (corpus/polymaps/maps.json F5)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "det JF is identically the printed constant 160/29: ok · component degrees are the printed [3, 12, 14, 16]: ok · 2 distinct rational points with one image: F is not injectiv: ok", "ms": 124.1 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "5.51724137931092", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } }, "sha256": "400fafa42c105d656a485188a7ccb0171ab6c8ab5368fc4c65fc0e7d71485217" }, "mutants": [ { "id": "polymaps-gao-f5/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first term of component 0 (1 x^(1,0,0,0)) + 1: det JF is no longer the constant 160/29", "sha256": "d9e2bcff57e0dc58f2b3788ec872278bbacea07306f4e08c8360c598f3d645f0", "bytes": 3484, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "det JF at p0 is not the printed constant", "p0": [ "1/2", "1/3", "1/5", "1/7" ], "detAtP0": "85578270070453384251300119469289547053154/4195958700225121246217171091654209390625", "printed": "160/29" } }, "decided": { "verdict": "REFUTED", "why": "det JF is identically the printed constant 160/29: FAILED · component degrees are the printed [3, 12, 14, 16]: ok · 2 distinct rational points with one image: F is not injectiv: FAILED", "ms": 125.1 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "20.395403335563476", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-gao-f5/witness-point-moved", "class": "witness-point-moved", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first coordinate of witness point 0 + 1: the printed points no longer have one image", "sha256": "4447664f8aeadfa84e5de8a9f8ded1229d0070005746d0df251b102ebcd7918d", "bytes": 3484, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "the printed witness points do not share one image", "images": [ [ "644661/13456", "1047483341597103425664997746585474392586069/499219874218014557150484889600", "78295374188370372516392348924344260442795809334319379/249353697531968656063348243915866112000", "-2458285482404570418073374150653927050288143423195961211702421143/9730379726571493684366400513382493768908800000" ], [ "1", "-89/116", "-605/116", "-109/58" ] ] } }, "decided": { "verdict": "REFUTED", "why": "det JF is identically the printed constant 160/29: ok · component degrees are the printed [3, 12, 14, 16]: ok · 2 distinct rational points with one image: F is not injectiv: FAILED", "ms": 124.9 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "5.51724137931092", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-gao-f5/translated", "class": "translated", "truth": "TRUE", "preservesOriginal": true, "transformation": "F'(x) = F(x + e₁) − F(e₁): det JF, the degrees and the collision kept, the points moved to p − e₁", "sha256": "686cbb479e2a5a621add7741a9dca996452c258282d9515841abd3e3437867b3", "bytes": 17175, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null }, "decided": { "verdict": "CERTIFIED", "why": "det JF is identically the printed constant 160/29: ok · component degrees are the printed [3, 12, 14, 16]: ok · 2 distinct rational points with one image: F is not injectiv: ok", "ms": 2757.4 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "5.51724211722307", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-gao-f5/exponent-missing", "class": "exponent-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "the first term's exponent tuple short by one entry", "sha256": "693528ba2db3fff3cef4520b06e04e3915c207c0c524d40e84971c959575f6e3", "bytes": 3482, "witness": { "violated": null, "malformed": true, "reason": "a term whose exponent tuple does not have 4 non-negative entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: 25, in \n return [[f.diff(j) for j in range(n)] for f in F]\n File \"/Users/carlostoledo/Projects/cert-machine/instruments/polymaps/poly.py\", line 47, in diff\n if e[i]:\nIndexError: tuple index out of range\n", "ms": 73 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a term whose exponent tuple does not have n entries", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [], "ms": 3394 }, { "rowId": "polymaps-gao-f6", "record": "certs/polymaps-ledger.json", "entryId": "gao-f6", "verdict": "CERTIFIED", "object": "F6: a polynomial map of Q^5 with det J = -290, 2180 terms, 2 witness points (rebuilt by instruments/polymaps from the printed recipe (6/342/421/507/904 terms))", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "det JF is identically the printed constant -290: ok · component degrees are the printed [7, 38, 40, 42, 44]: ok · 2 distinct rational points with one image: F is not injectiv: ok", "ms": 46984.2 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "-4.682385563813812e+40", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } }, "sha256": "b477d1be223f58c6a745872d5323cc38224b2a6889d0c02ac916ffe459232381" }, "mutants": [ { "id": "polymaps-gao-f6/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first term of component 0 (-29 x^(2,1,0,0,0)) + 1: det JF is no longer the constant -290", "sha256": "8d9fbc5bf8efd69dba01ce51df957738c34c8484a2ae8947b91eb4b2aa2ee5cd", "bytes": 70820, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "det JF at p0 is not the printed constant", "p0": [ "1/2", "1/3", "1/5", "1/7", "1/11" ], "detAtP0": "42783438063557859640284296627171963768699721537844773655/182458062976484577550270464", "printed": "-290" } }, "decided": { "verdict": "REFUTED", "why": "det JF is identically the printed constant -290: FAILED · component degrees are the printed [7, 38, 40, 42, 44]: ok · 2 distinct rational points with one image: F is not injectiv: FAILED", "ms": 57428.6 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "-1.2707119804527554e+41", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-gao-f6/witness-point-moved", "class": "witness-point-moved", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first coordinate of witness point 0 + 1: the printed points no longer have one image", "sha256": "edd57b0e0da4bccd74941cf3817f70e8192b754d6db814dce258e169bd313eed", "bytes": 70823, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "the printed witness points do not share one image", "images": [ [ "3720633771860209195948101621306091688249986075282410423477/135376970738541899113566039592000000000000", "109901394375352991092054628857462041311751967744937674744644357486806520963685416487046736544812048951647443181161467718100289615028562375503590561719106918946848854350750351511010612899297279639922141270309574242602279491280976332780818581136973309715645168543292623552655808703235666978505113/15875832982256661187263138501377709307400623230416442113357591636544432443208247439767828019470531345448539382627547717263125768741163574464128000000000000000000000000000000000000000000000000000000000", "-391480652988967241206522370721426180176755357152747248510863886405053920363220501131560541880631520813836854162908944460978124016188940645386336358985203357257250882999626470669885551635066739928189102620110103424175060866631904250987546836971616933669258241309740094523171450894436570823694158875411203489/216594783168576741410890361731221156966332072763733040574643290576957519044312280233124466061037432672521695224156764884006688019224131704592821510400000000000000000000000000000000000000000000000000000000000", "1394496425961983532387105760966288168578878922686610425807109196752187293605831519670809862096954796335255421501865617184479758525849390495813847995598922750677141191415165797121655612132302479841875901658386225807199472694373989943815120610227612331294153557490542419784712995400645125500860903894144530778328672957417/2955013456508050911905847749617136805549516785319248059211887145505960280197504654834528746694036745822847114027931951150747444980675790052345093507462720000000000000000000000000000000000000000000000000000000000000", "-29615265577883566953013045660887725210994694389181476162967028480354188287820291282307918921187002101683005725064737645540128158168663578599880407587498046297450556742106422437956017417777859326031793592107259468309949272437614151866752739103507352414315948526253085801257948081563040683256098437200861658152727401832498494017762937022225903791827951179921439608890647533071532079161/3763983607128770045138622568417511926336238000450827349236776822620132645412472835101958863983953125125252309617835964012918359295959439401043417723810822627481148011754880626312552348160000000000000000000000000000000000000000000000000000000000000000000000000000" ], [ "1", "1", "2", "-508", "-660" ] ] } }, "decided": { "verdict": "REFUTED", "why": "det JF is identically the printed constant -290: ok · component degrees are the printed [7, 38, 40, 42, 44]: ok · 2 distinct rational points with one image: F is not injectiv: FAILED", "ms": 46084.1 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "-4.682385563813812e+40", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-gao-f6/witness-order-swapped", "class": "witness-order-swapped", "truth": "TRUE", "preservesOriginal": true, "transformation": "the witness points listed in the other order (the map is too large to translate and expand here)", "sha256": "b1fb3ab3242d68735fc041c3698e92bdf9a3335c5715f181a3f27772938dc3bf", "bytes": 70820, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null }, "decided": { "verdict": "CERTIFIED", "why": "det JF is identically the printed constant -290: ok · component degrees are the printed [7, 38, 40, 42, 44]: ok · 2 distinct rational points with one image: F is not injectiv: ok", "ms": 45281.6 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "-4.682385563813812e+40", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-gao-f6/exponent-missing", "class": "exponent-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "the first term's exponent tuple short by one entry", "sha256": "a144df1aade71467e0cdd735ca3f05efe8aa1ef1a9ccae58c5ef2c3d807b6fbe", "bytes": 70818, "witness": { "violated": null, "malformed": true, "reason": "a term whose exponent tuple does not have 5 non-negative entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: 25, in \n return [[f.diff(j) for j in range(n)] for f in F]\n File \"/Users/carlostoledo/Projects/cert-machine/instruments/polymaps/poly.py\", line 47, in diff\n if e[i]:\nIndexError: tuple index out of range\n", "ms": 83.8 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a term whose exponent tuple does not have n entries", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [], "ms": 196814 }, { "rowId": "polymaps-gao-f7", "record": "certs/polymaps-ledger.json", "entryId": "gao-f7", "verdict": "PARTIAL", "object": "F7: a polynomial map of Q^5 with det J = 119377, 79107 terms, 2 witness points (rebuilt by instruments/polymaps from the printed recipe (7/14445/17727/21410/25518 terms); its determinant rests on the paper's lemma)", "original": { "required": "PARTIAL", "decided": { "verdict": "PARTIAL", "why": "2 distinct rational points with one image: ok · det J constant: rests on the paper's lemma: rests on the lemma", "ms": 19100.4 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "None", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } }, "sha256": "80a34bddbaefbab5538e9b2e3359a45bb369eafbe64f324343d309d96bf94a5b" }, "mutants": [ { "id": "polymaps-gao-f7/witness-point-moved", "class": "witness-point-moved", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first coordinate of witness point 0 + 1: the printed points no longer have one image", "sha256": "edef451aeda307dddcb0ef5c355c9b1dcb12709d1a6d17ccbf2b429fe6ff25c5", "bytes": 5076806, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "the printed witness points do not share one image", "images": [ [ "98723127465681523896797065381969948063030031569731411295430127379742344128723097/49452153931022964153795360122732871950032183683464664250492657846272", 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], [ "1", "27/11", "142/33", "-53/11", "761/33" ] ] } }, "decided": { "verdict": "REFUTED", "why": "2 distinct rational points with one image: FAILED · det J constant: rests on the paper's lemma: rests on the lemma", "ms": 22025.4 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "None", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-gao-f7/witness-order-swapped", "class": "witness-order-swapped", "truth": "TRUE", "preservesOriginal": true, "transformation": "the witness points listed in the other order (the map is too large to translate and expand here)", "sha256": "06cd76c2bbd8f68941bcefbf8acf932eb47975f7065343762eecdc6dfdd4f821", "bytes": 5076804, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null }, "decided": { "verdict": "PARTIAL", "why": "2 distinct rational points with one image: ok · det J constant: rests on the paper's lemma: rests on the lemma", "ms": 20148.8 }, "required": "PARTIAL", "outcome": "as required", "float": { "score": "None", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-gao-f7/exponent-missing", "class": "exponent-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "the first term's exponent tuple short by one entry", "sha256": "2485b4f527e6d7903e960ed083a5fa7aa71780c43b94a4b33bd6cdd812cd66cb", "bytes": 5076802, "witness": { "violated": null, "malformed": true, "reason": "a term whose exponent tuple does not have 5 non-negative entries", "firstViolation": null }, "decided": { "verdict": "PARTIAL", "why": "2 distinct rational points with one image: ok · det J constant: rests on the paper's lemma: rests on the lemma", "ms": 19559.3 }, "required": "REFUSED", "outcome": "not as required (PARTIAL)", "float": { "error": "a term whose exponent tuple does not have n entries", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [ { "class": "coefficient-plus-one", "reason": "F7's determinant rests on the paper's lemma (the row is PARTIAL): a coefficient moved changes nothing the decider decides but the collision, which the witness-point class covers" } ], "controlsFired": [], "ms": 141705 }, { "rowId": "polymaps-chv-x14", "record": "certs/polymaps-ledger.json", "entryId": "chv-x14", "verdict": "CERTIFIED", "object": "X14: a polynomial field on R^14, 39 terms, 3 witness points (corpus/polymaps/maps.json X14)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "(JX + I)^k = 0 identically (k = 14 <= 14): every eigenvalue : ok · 3 distinct zeros of X: ok", "ms": 119.7 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "1.938553484404082e-16", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "b055aefbff5c18f5b77ed6f50bd318cd995c60c86fd055cff01bbab68c712ad6" }, "mutants": [ { "id": "polymaps-chv-x14/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first term of component 0 (1 x^(0,0,0,1,0,0,0,0,0,0,0,0,0,0)) + 1: (JX + I) is no longer nilpotent", "sha256": "57fc7e178d833c69d2d33e41c4f0fede39e58674e19b4a55eda75ced450e4210", "bytes": 1791, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "(JX + I)^n is not zero at p0", "p0": [ "1/2", "1/3", "1/5", "1/7", "1/11", "1/13", "1/17", "1/19", "1/23", "1/29", "1/31", "1/37", "1/41", "1/43" ] } }, "decided": { "verdict": "REFUTED", "why": "(JX + I)^k = 0 identically (k = None <= 14): every eigenvalu: FAILED · 3 distinct zeros of X: FAILED", "ms": 146 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "1.7433261111111058", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-chv-x14/witness-point-moved", "class": "witness-point-moved", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first coordinate of witness point 0 + 1: the point is no longer a zero of X", "sha256": "3e27280e32cbdb46dcc7c2472b50a1f0a8796f17469d2bcd5e926156327ff48f", "bytes": 1791, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "a printed zero is not a zero of X", "point": [ "1", "0", "-1/4", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], "X": [ "-1", "3/4", "0", "0", "0", "0", "-1/8", "0", "0", "0", "0", "0", "0", "0" ] } }, "decided": { "verdict": "REFUTED", "why": "(JX + I)^k = 0 identically (k = 14 <= 14): every eigenvalue : ok · 3 distinct zeros of X: FAILED", "ms": 115.2 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "1.938553484404082e-16", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-chv-x14/translated", "class": "translated", "truth": "TRUE", "preservesOriginal": true, "transformation": "X'(x) = X(x + e₁): nilpotency kept, the zeros moved to z − e₁", "sha256": "c0faed6a676a81d8f429d8c51a687ad8043c5bffec086548d0f0d8d66a65ab74", "bytes": 2686, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null }, "decided": { "verdict": "CERTIFIED", "why": "(JX + I)^k = 0 identically (k = 14 <= 14): every eigenvalue : ok · 3 distinct zeros of X: ok", "ms": 407.8 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "2.4252821972936545e-13", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "polymaps-chv-x14/exponent-missing", "class": "exponent-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "the first term's exponent tuple short by one entry", "sha256": "ebc050ef7aa4cfcfec1f2cb628c20b8b8565e407aeb318da48f8ef4f9d8287b9", "bytes": 1789, "witness": { "violated": null, "malformed": true, "reason": "a term whose exponent tuple does not have 14 non-negative entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: i].diff(j) + (1 if i == j else 0) for j in range(n)] for i in range(n)]\n File \"/Users/carlostoledo/Projects/cert-machine/instruments/polymaps/poly.py\", line 47, in diff\n if e[i]:\nIndexError: tuple index out of range\n", "ms": 79.8 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a term whose exponent tuple does not have n entries", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [], "ms": 1427 }, { "rowId": "polymaps-chv-phi", "record": "certs/polymaps-ledger.json", "entryId": "chv-phi", "verdict": "CERTIFIED", "object": "Phi: a polynomial map of Q^11 with det J = -2, 52 terms, 3 witness points (corpus/polymaps/maps.json Phi)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "det J is identically -2: ok · three distinct points with one image: ok", "ms": 470.5 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "-1.9999999999999998", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "99bf2d813c6f9b6e18807e051943efec123c278e01b4ebe0d208e42e89cebfc0" }, "mutants": [ { "id": "polymaps-chv-phi/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first term of component 0 (-1 x^(0,0,0,0,0,0,1,0,1,0,0)) + 1: det JF is no longer the constant -2", "sha256": "f0dd3bc1b1117a2f99cf95ae24d94f02a2324d8eb5b49bb89bcbe41f1948e01e", "bytes": 1866, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "det JF at p0 is not the printed constant", "p0": [ "1/2", "1/3", "1/5", "1/7", "1/11", "1/13", "1/17", "1/19", "1/23", "1/29", "1/31" ], "detAtP0": "-32285311/21039200", "printed": "-2" } }, "decided": { "verdict": "REFUTED", "why": "det J is identically -2: FAILED · three distinct points with one image: FAILED", "ms": 476.5 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "-1.5345313034716133", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-chv-phi/witness-point-moved", "class": "witness-point-moved", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first coordinate of witness point 0 + 1: the printed points no longer have one image", "sha256": "b6b47b4c5395a7f378676ea7f68abb9d8147ce478475dc153a3c572ed07cd24b", "bytes": 1867, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "the printed witness points do not share one image", "images": [ [ "-1/4", "-3/4", "2", "0", "0", "0", "0", "3/2", "0", "-1", "-1/4" ], [ "-1/4", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-1/4", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ] ] } }, "decided": { "verdict": "REFUTED", "why": "det J is identically -2: ok · three distinct points with one image: FAILED", "ms": 471.8 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "-1.9999999999999998", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-chv-phi/translated", "class": "translated", "truth": "TRUE", "preservesOriginal": true, "transformation": "F'(x) = F(x + e₁) − F(e₁): det JF, the degrees and the collision kept, the points moved to p − e₁", "sha256": "805058ebf84e16b8c9dcdb1e6b6247e3cc46ce68735d63220c7030f5b838f945", "bytes": 2506, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null }, "decided": { "verdict": "CERTIFIED", "why": "det J is identically -2: ok · three distinct points with one image: ok", "ms": 1755.2 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "-1.9999999999999707", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "polymaps-chv-phi/exponent-missing", "class": "exponent-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "the first term's exponent tuple short by one entry", "sha256": "2360689fa4de1b16f2c2b76ce9a8720740c55c2245788e91b1cc39d8a4175a27", "bytes": 1865, "witness": { "violated": null, "malformed": true, "reason": "a term whose exponent tuple does not have 11 non-negative entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: 25, in \n return [[f.diff(j) for j in range(n)] for f in F]\n File \"/Users/carlostoledo/Projects/cert-machine/instruments/polymaps/poly.py\", line 47, in diff\n if e[i]:\nIndexError: tuple index out of range\n", "ms": 77.8 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a term whose exponent tuple does not have n entries", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [], "ms": 3439 }, { "rowId": "polymaps-chv-xhat18", "record": "certs/polymaps-ledger.json", "entryId": "chv-xhat18", "verdict": "CERTIFIED", "object": "Xhat18: a polynomial field on R^18, 76 terms, 3 witness points (corpus/polymaps/maps.json Xhat18)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "(JX + I)^k = 0 identically (k = 17 <= 18): every eigenvalue : ok · 3 distinct zeros of X: ok", "ms": 682 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "3.352826089145386e-17", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "43a93da4fb87bdb8ac1b4de3e8e1097a5aa95dfa62fcecf55174caf54cdd47c7" }, "mutants": [ { "id": "polymaps-chv-xhat18/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first term of component 0 (1 x^(0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0)) + 1: (JX + I) is no longer nilpotent", "sha256": "e3a0f89f7048245c6843cac878adc70db47e979c4cd725469e9a762be2b9b4d1", "bytes": 3836, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "(JX + I)^n is not zero at p0", "p0": [ "1/2", "1/3", "1/5", "1/7", "1/11", "1/13", "1/17", "1/19", "1/23", "1/29", "1/31", "1/37", "1/41", "1/43", "1/47", "1/53", "1/59", "1/61" ] } }, "decided": { "verdict": "REFUTED", "why": "(JX + I)^k = 0 identically (k = None <= 18): every eigenvalu: FAILED · 3 distinct zeros of X: FAILED", "ms": 18183.8 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "2.330216545825407", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-chv-xhat18/witness-point-moved", "class": "witness-point-moved", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first coordinate of witness point 0 + 1: the point is no longer a zero of X", "sha256": "4d9bbb6ea7e522791ea6fa062a19a4a8f7ba9308c00374ec356aa4d43bca82b2", "bytes": 3836, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "a printed zero is not a zero of X", "point": [ "1", "0", "-1/4", "0", "0", "1/2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], "X": [ "-1", "3/4", "0", "0", "0", "0", "0", "-3/2", "0", "1", "1/4", "0", "0", "0", "0", "0", "0", "0" ] } }, "decided": { "verdict": "REFUTED", "why": "(JX + I)^k = 0 identically (k = 17 <= 18): every eigenvalue : ok · 3 distinct zeros of X: FAILED", "ms": 651 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "3.352826089145386e-17", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "polymaps-chv-xhat18/translated", "class": "translated", "truth": "TRUE", "preservesOriginal": true, "transformation": "X'(x) = X(x + e₁): nilpotency kept, the zeros moved to z − e₁", "sha256": "c0dc16f77df966ac642caf8608b134dc602dff35eea26f3909a8123b2af51155", "bytes": 4914, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null }, "decided": { "verdict": "CERTIFIED", "why": "(JX + I)^k = 0 identically (k = 17 <= 18): every eigenvalue : ok · 3 distinct zeros of X: ok", "ms": 3903 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "5.412715420328169e-13", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "polymaps-chv-xhat18/exponent-missing", "class": "exponent-missing", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "the first term's exponent tuple short by one entry", "sha256": "99ad41cc75a18d921b47b93f7137ac8c08aed9b56102fc7e0af3e9dd3fbcf124", "bytes": 3834, "witness": { "violated": null, "malformed": true, "reason": "a term whose exponent tuple does not have 18 non-negative entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: i].diff(j) + (1 if i == j else 0) for j in range(n)] for i in range(n)]\n File \"/Users/carlostoledo/Projects/cert-machine/instruments/polymaps/poly.py\", line 47, in diff\n if e[i]:\nIndexError: tuple index out of range\n", "ms": 73.7 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a term whose exponent tuple does not have n entries", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [], "ms": 24630 }, { "rowId": "mc100-st-jacobian", "record": "certs/mc100-station-v2.json", "entryId": "st-jacobian", "verdict": "CERTIFIED", "object": "station: a polynomial map of Q^3 with det J = -6, 16 terms, 3 witness points (corpus/station-v2/jacobian/construction.json reconstructed_map)", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": "det JF is identically the printed constant -6: ok · component degrees are the printed [4, 6, 7]: ok · 3 distinct rational points with one image: F is not injectiv: ok", "ms": 73.6 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "-6.000000000000001", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "f957cb0facf60175b6aa322ad596eb1e37f10b22cca9c0432ba34de5068da542" }, "mutants": [ { "id": "mc100-st-jacobian/coefficient-plus-one", "class": "coefficient-plus-one", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first term of component 0 (6 x^(1,0,0)) + 1: det JF is no longer the constant -6", "sha256": "73d2b817a0f7320d54412f5895f2b52d9b59312cb4cfa0b56faa0daec0f7f52b", "bytes": 385, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "det JF at p0 is not the printed constant", "p0": [ "1/2", "1/3", "1/5" ], "detAtP0": "-33179/5184", "printed": "-6" } }, "decided": { "verdict": "REFUTED", "why": "det JF is identically the printed constant -6: FAILED · component degrees are the printed [4, 6, 7]: ok · 3 distinct rational points with one image: F is not injectiv: FAILED", "ms": 74.1 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "-6.4002700617283965", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-st-jacobian/witness-point-moved", "class": "witness-point-moved", "truth": "FALSE", "preservesOriginal": false, "transformation": "the first coordinate of witness point 0 + 1: the printed points no longer have one image", "sha256": "fdbaab4ea255de079faca5a07e20c8981cdb3931622f3f3b00ca27a5f17b1498", "bytes": 384, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "the printed witness points do not share one image", "images": [ [ "125/216", "-62755/7776", "2630467/46656" ], [ "1", "7/3", "0" ], [ "1", "7/3", "0" ] ] } }, "decided": { "verdict": "REFUTED", "why": "det JF is identically the printed constant -6: ok · component degrees are the printed [4, 6, 7]: ok · 3 distinct rational points with one image: F is not injectiv: FAILED", "ms": 73.5 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "-6.000000000000001", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } }, { "id": "mc100-st-jacobian/translated", "class": "translated", "truth": "TRUE", "preservesOriginal": true, "transformation": "F'(x) = F(x + e₁) − F(e₁): det JF, the degrees and the 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have 3 non-negative entries", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the decider threw: 25, in \n return [[f.diff(j) for j in range(n)] for f in F]\n File \"/Users/carlostoledo/Projects/cert-machine/instruments/polymaps/poly.py\", line 47, in diff\n if e[i]:\nIndexError: tuple index out of range\n", "ms": 72.6 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a term whose exponent tuple does not have n entries", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [], "ms": 517 } ] }, "countex": { "decider": "instruments/countex/cases/.py, one decider per case (standard library, written from each case's statement, reading the published artifact), composed by tools/run-countex-ledger.py", "witness": null, "floatcheck": null, "redControl": null, "records": [ "certs/countex-ledger.json" ], "classes": { "FALSE": [], "TRUE": [], "MALFORMED": [] }, "rows": [ { "rowId": "countex-aim-problems", 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null }, "decided": { "verdict": "REFUSED", "why": "the instrument threw: REFUSED: the weights sum to 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001/100000000000000000000000000000000000000000000000", "ms": 0.4 }, "required": "REFUSED", "outcome": "as required", "float": { "score": "1.6747338950208246", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } } ], "excluded": [], "controlsFired": [], "ms": 501 }, { "rowId": "optconst-71", "record": "certs/fei-ledger.json", "entryId": "71", "verdict": "CERTIFIED", "object": "the n = 18 truth table (2770 nonzero Fourier weights), the bar 6.521845710923046575", "original": { "required": "CERTIFIED", "decided": { "verdict": "CERTIFIED", "why": " ratio ∈ [6.5218457109230465756581439729, 6.5218457109230465756581439729]", "ms": 1790.9 }, "asRequired": true, "witness": { "violated": false, "malformed": false }, "float": { "score": "6.52184571092304", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } }, "sha256": "498e0f2e8c72370a1a55861bf4143721fa0d8812a7c8c95379b1f9fddf693280" }, "mutants": [ { "id": "optconst-71/bar-above-ratio", "class": "bar-above-ratio", "truth": "FALSE", "preservesOriginal": false, "transformation": "the bar raised to the certificate's own printed upper end 6.5218457109230465756581439729485784683667 plus one unit in its last digit → 6.5218457109230465756581439729485784683668", "sha256": "afbe49cf2958687bd1873558d4a41fd62bc150f23e1f4d7553124df20abb771c", "bytes": 66266, "witness": { "violated": true, "malformed": false, "reason": null, "firstViolation": { "kind": "the ratio lies at or below the bar", "ratioHi": "6.521845710923046575658143972948578468366662292229", "bar": "6.5218457109230465756581439729485784683668" }, "exact": [ "6.521845710923046575658143972948578468366662292229", "6.521845710923046575658143972948578468366662292229" ] }, "decided": { "verdict": "REFUTED", "why": "H/(I-1) > 6.5218457109230465756581439729485784683668, the registry's bound: the ratio is at most the bar: r_hi <= 6.5218457109230465756581439729485784683668 ratio ∈ [6.5218457109230465756581439729, 6.5218457109230465756581439729]", "ms": 1878.2 }, "required": "REFUTED", "outcome": "as required", "float": { "score": "6.52184571092304", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "optconst-71/inputs-rotated", "class": "inputs-rotated", "truth": "TRUE", "preservesOriginal": true, "transformation": "the n input coordinates rotated by one (f'(x) = f(π(x))) and the artifact re-bound to the new table's sha256: every Fourier weight, I, balance and monotonicity unchanged", "sha256": "dffdf654e763edfdcfad4ef9eec2655b2b12037e078549c57ca15230d191a488", "bytes": 66244, "witness": { "violated": false, "malformed": false, "reason": null, "firstViolation": null, "exact": [ "6.521845710923046575658143972948578468366662292229", "6.521845710923046575658143972948578468366662292229" ] }, "decided": { "verdict": "CERTIFIED", "why": " ratio ∈ [6.5218457109230465756581439729, 6.5218457109230465756581439729]", "ms": 1853 }, "required": "CERTIFIED", "outcome": "as required", "float": { "score": "6.52184571092304", "accept": { "1e-6": true, "1e-9": true, "1e-12": true } } }, { "id": "optconst-71/hex-beyond-2n", "class": "hex-beyond-2n", "truth": "MALFORMED", "preservesOriginal": false, "transformation": "a hex digit prepended: a bit at or beyond 2^n", "sha256": "d4d63bfe1d3e8ff94149f45711f12798cef29cb9d0a505eb560851c8776b7043", "bytes": 66245, "witness": { "violated": null, "malformed": true, "reason": "a bit at or beyond 2^18", "firstViolation": null }, "decided": { "verdict": "REFUSED", "why": "the truth table reads: hexadecimal, no input at or beyond 2^n: the mask has bits beyond 2^n inputs", "ms": 80.5 }, "required": "REFUSED", "outcome": "as required", "float": { "error": "a bit beyond 2^n", "accept": { "1e-6": false, "1e-9": false, "1e-12": false } } } ], "excluded": [], "controlsFired": [], "ms": 22102 } ] }, "turan": { "decider": "instruments/turan/c42.py decide / decide_profile (Decimal intervals at 60 digits on the note's four exact facts and the limiting inequality), the path of tools/run-turan-ledger.py", "witness": null, "floatcheck": null, "redControl": null, "records": [ "certs/turan-ledger.json" ], "classes": { "FALSE": [], "TRUE": [], "MALFORMED": [] }, "rows": [ { "rowId": "optconst-42a", "record": "certs/turan-ledger.json", "entryId": "optconst-42a", "verdict": "PARTIAL", "noObject": "a handful of real parameters whose decided conditions are the note's series inequalities; a FALSE witness would re-sum the series with tail bounds (a second implementation, not a witness); no admissible class", "mutants": [], "excluded": [], "ms": 0 }, { "rowId": "optconst-42a-pr184", "record": "certs/turan-ledger.json", "entryId": "optconst-42a-pr184", "verdict": "PARTIAL", "noObject": "the same, for the open pull request's profile", "mutants": [], "excluded": [], "ms": 0 } ] }, "horizonmath": { "decider": "instruments/horizonmath/ramsey_region.py and kakeya_area.py (standard library, written from the problem statements), the path of tools/run-horizonmath-ledger.py", "witness": null, "floatcheck": null, "redControl": null, "records": [ "certs/horizonmath-ledger.json" ], "classes": { "FALSE": [], "TRUE": [], "MALFORMED": [] }, "rows": [ { "rowId": "horizonmath-ramsey-asymptotic", "record": "certs/horizonmath-ledger.json", "entryId": "horizonmath-ramsey-asymptotic", "verdict": "REFUTED", "noObject": "the decided fact is a gap between two definitions (the checker's and the theorem's); a mutation of the certificate's numbers does not touch it", "mutants": [], "excluded": [], "ms": 0 }, { "rowId": "horizonmath-keich-thin-triangles-128", "record": "certs/horizonmath-ledger.json", "entryId": "horizonmath-keich-thin-triangles-128", "verdict": "CERTIFIED", "noObject": "a FALSE witness would compute the exact area of the thin-triangle construction — the decider's own geometry, a second implementation, not a witness", "mutants": [], "excluded": [], "ms": 0 }, { "rowId": "horizonmath-gpt56-closed-forms", "record": "certs/horizonmath-ledger.json", "entryId": "horizonmath-gpt56-closed-forms", "verdict": "NEEDS DATA", "noObject": "NEEDS DATA: the closed forms are not published; no object", "mutants": [], "excluded": [], "ms": 0 } ] }, "gnnw": { "decider": "tools/verify_gnnw_gai.py (Decimal intervals on GNNW Theorem 14 over (0, 1], the certificate's q and m), the path of tools/run-gnnw-ledger.py --check; instruments/gnnw/second.js is its second implementation", "witness": null, "floatcheck": null, "redControl": null, "records": [ "certs/gnnw-certificate.json" ], "classes": { "FALSE": [], "TRUE": [], "MALFORMED": [] }, "rows": [ { "rowId": "gnnw-gai-3782", "record": "certs/gnnw-certificate.json", "entryId": "gnnw-gai-3782", "verdict": "CERTIFIED", "noObject": "a FALSE witness would enclose Theorem 14's slack — the verifier's own computation; the second implementation is Phase 4's concordance partner, not a mutation witness", "mutants": [], "excluded": [], "ms": 0 } ] }, "sumproduct": { "decider": "instruments/sumproduct/c84b.py decide (Decimal intervals on the note's chain: f(s), the factors at Y = 1415, the sweep over s and Y), the path of tools/run-sumproduct-ledger.py", "witness": null, "floatcheck": null, "redControl": null, "records": [ "certs/sumproduct-ledger.json" ], "classes": { "FALSE": [], "TRUE": [], "MALFORMED": [] }, "rows": [ { "rowId": "optconst-84b", "record": "certs/sumproduct-ledger.json", "entryId": "optconst-84b", "verdict": "REPAIRED", "noObject": "a chain of cited constants and two sweeps, already REPAIRED as printed; a FALSE witness would be the sweep again; no admissible class", "mutants": [], "excluded": [], "ms": 0 } ] } }, "repinned": [ { "at": "2026-10-21T18:36:26.072Z", "git": "6d80fdef", "why": "Amendment 2026-10-22 (Phase 5, the freeze): the note amended with the fixes, the open finding, the exclusions and this re-pin; the easota ledger record's grammar string gained MISPRINTED; the inventory regenerated; no mutant or decision touched", "before": { "preregistration": "a6ca4457a022a33ce75e8ba294dd4e8ae1b0408771f5244e4fc207152ec22cd3", "inventory": "170766e6eedb97b980d2e1deca2cef197ff7ca8361fab68f5f725ef0ee61d367", "recordsMoved": [ { "record": "certs/easota-ledger.json", "from": "e577361347e77561617610d9be19cbf72ac0a8846219bf03c86e20fb5121c503", "to": "57f46876a7c79b0c6f7f236f0cb133e0ce896f9773cc85b36cf9d8e7fa3f627b" } ] }, "after": { "preregistration": "b799715c0f840d2a201b7a7907025137e70653095319ad8c97a3b7f8be7b23c2", "inventory": "752389f8c27e251ac8ef1bc556171f1c867de315a17544d606b2ac4ccaca5e74" } }, { "at": "2026-10-22T01:17:25.150Z", "git": "16849460", "why": "lane A of Pedro's 2026-10-21 review: interval kernel tightened (π enclosure, erf tail, Spouge margin, transcendental tails, lnΓ minimum, Sum2 hypotheses); the wave records re-derived identical but for stamps and timings", "before": { "preregistration": "b799715c0f840d2a201b7a7907025137e70653095319ad8c97a3b7f8be7b23c2", "inventory": "752389f8c27e251ac8ef1bc556171f1c867de315a17544d606b2ac4ccaca5e74", "recordsMoved": [] }, "after": { "preregistration": "b799715c0f840d2a201b7a7907025137e70653095319ad8c97a3b7f8be7b23c2", "inventory": "b5f226e1eff7d9810a0a95b59039de184316f589ee8f0de0d6b9b2734a015b8e" } } ] }