{
 "what": "Externally published mathematical claims this machine has decided, one row per claim, each derived from the record that decided it. The verdicts are the instrument's, not a summary: CERTIFIED and REFUTED are theorems, PARTIAL names the fragment that was reached, NEEDS DATA measures the claimant rather than the claim, MIXED means the row is an aggregate whose record holds both, and REPAIRED means the claim as printed is refuted and an object next to it is certified. Each row names its defect kind from one closed vocabulary (kindsDefined); an aggregate row counts them. recordedOn is the first commit whose deciding record held the row.",
 "honestCounting": "Every row is DERIVED from a record; a claim with no record gets no row. ORIGIN is tracked separately: everything here is self-initiated — we chose the claim. Nothing has been submitted yet, and the submitted count stays zero until it is not.",
 "scope": "What can be decided here: claims that come down to finitely many exact arithmetic facts — exhibit a witness, verify an identity, bound a quantity, decide a constant. Everything else is REFUSED as out of scope rather than guessed at.",
 "rows": [
  {
   "id": "ai-maxwell",
   "claim": "Maxwell's point-charge bound",
   "claimant": "a manuscript produced with frontier-model help",
   "source": "published manuscript",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "at ε = 1/6 only",
   "checks": 17,
   "decidedFrom": "certs/ai-claims-summary.json",
   "page": "/reports/ai-claims-audit.html",
   "kind": "none",
   "recordedOn": "2026-08-30"
  },
  {
   "id": "ai-korenblum",
   "claim": "The Korenblum constant",
   "claimant": "a manuscript produced with frontier-model help",
   "source": "published manuscript",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the numerical criterion",
   "checks": 15,
   "decidedFrom": "certs/ai-claims-summary.json",
   "page": "/reports/ai-claims-audit.html",
   "kind": "none",
   "recordedOn": "2026-08-30"
  },
  {
   "id": "ai-lemniscate",
   "claim": "Erdős Problem #1038",
   "claimant": "a manuscript produced with frontier-model help",
   "source": "published manuscript",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the computational fragment",
   "checks": 22,
   "decidedFrom": "certs/ai-claims-summary.json",
   "page": "/reports/ai-claims-audit.html",
   "kind": "none",
   "recordedOn": "2026-08-30"
  },
  {
   "id": "ai-ranteng",
   "claim": "Ran–Teng Conjecture 20",
   "claimant": "a manuscript produced with frontier-model help",
   "source": "published manuscript",
   "origin": "self-initiated",
   "verdict": "PARTIAL",
   "scope": "machine-checkable fragment only",
   "checks": 38,
   "decidedFrom": "certs/ai-claims-summary.json",
   "page": "/reports/ai-claims-audit.html",
   "kind": "narrower-scope",
   "recordedOn": "2026-08-30"
  },
  {
   "id": "ai-mathieu",
   "claim": "The Mathieu property for Lie groups",
   "claimant": "a manuscript produced with frontier-model help",
   "source": "published manuscript",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "supporting identities only",
   "checks": null,
   "decidedFrom": "certs/ai-claims-summary.json",
   "page": "/reports/ai-claims-audit.html",
   "kind": "none",
   "recordedOn": "2026-08-30"
  },
  {
   "id": "ai-poisson",
   "claim": "The rank-two Poisson conjecture",
   "claimant": "a manuscript produced with frontier-model help",
   "source": "published manuscript",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the explicit counterexample",
   "checks": null,
   "decidedFrom": "certs/ai-claims-summary.json",
   "page": "/reports/ai-claims-audit.html",
   "kind": "none",
   "recordedOn": "2026-08-30"
  },
  {
   "id": "erdos852-cstar",
   "claim": "C* for Erdos #852, published as 0.0752403861777 with no error bound",
   "claimant": "a problem thread post produced with frontier-model help",
   "source": "erdosproblems.com problem thread",
   "origin": "self-initiated",
   "verdict": "REFUTED",
   "scope": "the constant itself, to its printed digits",
   "mechanism": "outside a certified enclosure; the corrected value is certified and public in the thread",
   "decidedFrom": "certs/erdos852-certificate.json",
   "page": "/reports/erdos852.html",
   "kind": "float-printed-as-exact",
   "recordedOn": "2026-08-25"
  },
  {
   "id": "kiss-cal-d4-24",
   "claim": "K(4) >= 24 — exact value, Musin 2003",
   "claimant": "classical (generated here)",
   "source": "D4 root directions",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the configuration as published, in exact arithmetic",
   "decidedFrom": "certs/kissing-ledger.json",
   "page": "/reports/kissing.html",
   "kind": "none",
   "recordedOn": "2026-09-03"
  },
  {
   "id": "kiss-cal-e8-240",
   "claim": "K(8) = 240 — exact value, Levenshtein / Odlyzko–Sloane 1979",
   "claimant": "classical (generated here)",
   "source": "E8 root directions",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the configuration as published, in exact arithmetic",
   "decidedFrom": "certs/kissing-ledger.json",
   "page": "/reports/kissing.html",
   "kind": "none",
   "recordedOn": "2026-09-03"
  },
  {
   "id": "kiss-alphaevolve-593",
   "claim": "K(11) >= 593 — the May 2025 record",
   "claimant": "AlphaEvolve (Novikov et al., DeepMind)",
   "source": "github.com/google-deepmind/alphaevolve_results mathematical_results.ipynb cell B.11",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the configuration as published, in exact arithmetic",
   "decidedFrom": "certs/kissing-ledger.json",
   "page": "/reports/kissing.html",
   "kind": "none",
   "recordedOn": "2026-09-03"
  },
  {
   "id": "kiss-ea-594-winner",
   "claim": "K(11) >= 594 — the solved n=594 rung, score-0 winner (solution #1492)",
   "claimant": "EinsteinArena agents (Bianchi et al. platform)",
   "source": "https://einsteinarena.com/api/solutions/best?problem_id=6",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the configuration as published, in exact arithmetic",
   "decidedFrom": "certs/kissing-ledger.json",
   "page": "/reports/kissing.html",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ea-best-kissing-number-d11",
    "pool": "einstein-arena",
    "alsoDecidedFrom": "certs/mc100-einstein-arena.json"
   },
   "kind": "none",
   "recordedOn": "2026-09-03"
  },
  {
   "id": "kiss-station-604-1",
   "claim": "K(11) >= 604 — configuration 1 of three",
   "claimant": "The Station agents (dualverse-ai)",
   "source": "github.com/dualverse-ai/station_data_v2 artifacts/kissing_number/kissing_certificates.npz",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the configuration as published, in exact arithmetic",
   "decidedFrom": "certs/kissing-ledger.json",
   "page": "/reports/kissing.html",
   "kind": "none",
   "recordedOn": "2026-09-03"
  },
  {
   "id": "kiss-station-604-2",
   "claim": "K(11) >= 604 — configuration 2 of three",
   "claimant": "The Station agents (dualverse-ai)",
   "source": "github.com/dualverse-ai/station_data_v2 artifacts/kissing_number/kissing_certificates.npz",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the configuration as published, in exact arithmetic",
   "decidedFrom": "certs/kissing-ledger.json",
   "page": "/reports/kissing.html",
   "kind": "none",
   "recordedOn": "2026-09-03"
  },
  {
   "id": "kiss-station-604-3",
   "claim": "K(11) >= 604 — configuration 3 of three",
   "claimant": "The Station agents (dualverse-ai)",
   "source": "github.com/dualverse-ai/station_data_v2 artifacts/kissing_number/kissing_certificates.npz",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the configuration as published, in exact arithmetic",
   "decidedFrom": "certs/kissing-ledger.json",
   "page": "/reports/kissing.html",
   "kind": "none",
   "recordedOn": "2026-09-03"
  },
  {
   "id": "kiss-station-shell-582",
   "claim": "K(11) >= 582 — the pre-2022 record shell, integer norm-4 maximum (Lean-proved maximal by the Station)",
   "claimant": "classical (Best 1977 class; bytes from the Station bundle)",
   "source": "github.com/dualverse-ai/station_data_v2 artifacts/kissing_number/kissing_certificates.npz",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the configuration as published, in exact arithmetic",
   "decidedFrom": "certs/kissing-ledger.json",
   "page": "/reports/kissing.html",
   "kind": "none",
   "recordedOn": "2026-09-03"
  },
  {
   "id": "kiss-station-d12-lift",
   "claim": "construction device: 604 integer D12 vectors whose oblique shadow is configuration 3 (also a valid 604-point direction set in R^12)",
   "claimant": "The Station agents (dualverse-ai)",
   "source": "github.com/dualverse-ai/station_data_v2 artifacts/kissing_number/kissing_certificates.npz",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the configuration as published, in exact arithmetic",
   "decidedFrom": "certs/kissing-ledger.json",
   "page": "/reports/kissing.html",
   "kind": "none",
   "recordedOn": "2026-09-03"
  },
  {
   "id": "kiss-ea-604",
   "claim": "K(11) >= 604 — the paper's headline result, credited by Cohn's reference table (2026-06-22)",
   "claimant": "EinsteinArena (Bianchi, Kwon, Pappu, Zou — arXiv:2606.10402)",
   "source": "github.com/togethercomputer/EinsteinArena-new-SOTA kissing-number/solutions/solution_n=604_d=11.json",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the configuration as published, in exact arithmetic",
   "decidedFrom": "certs/kissing-ledger.json",
   "page": "/reports/kissing.html",
   "kind": "none",
   "recordedOn": "2026-09-03"
  },
  {
   "id": "kiss-ganzhinov-592",
   "claim": "K(11) >= 592 — the 2022 record the AI ladder started from",
   "claimant": "M. Ganzhinov (arXiv:2207.08266, Highly symmetric lines)",
   "source": "not yet pulled",
   "origin": "self-initiated",
   "verdict": "QUEUED",
   "scope": "the configuration as published, in exact arithmetic",
   "decidedFrom": "certs/kissing-ledger.json",
   "page": "/reports/kissing.html",
   "kind": "none",
   "recordedOn": "2026-09-03"
  },
  {
   "id": "rm-registry",
   "claim": "the published Ramanujan Machine result sheets, 52 printed rows",
   "claimant": "the Ramanujan Machine project",
   "source": "published result sheets",
   "origin": "self-initiated",
   "verdict": "MIXED",
   "scope": "51 rows survive their certified enclosure, 1 refuted exactly",
   "decidedFrom": "ledger.json (family ramanujan-audit)",
   "page": "/reports/rm-audit.html",
   "kind": "sign-slip",
   "kinds": {
    "none": 51,
    "sign-slip": 1
   },
   "recordedOn": "2026-08-25"
  },
  {
   "id": "mm-strassen-1969",
   "claim": "2×2×2 matrix multiplication in 7 multiplications over Q",
   "claimant": "Strassen",
   "source": "Strassen, Numer. Math. 13 (1969) — the textbook transcription; the audit is the check",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every tensor-identity equation, exactly, over Q",
   "kind": "none",
   "decidedFrom": "certs/strassen-certificate.json",
   "page": "/reports/alphaevolve.html",
   "recordedOn": "2026-08-25"
  },
  {
   "id": "mm-strassen-squared-4x4x4",
   "claim": "4×4×4 matrix multiplication in 49 multiplications over Q",
   "claimant": "generated here: Strassen ⊗ Strassen by exact Kronecker composition",
   "source": "generated here: Strassen ⊗ Strassen by exact Kronecker composition, re-decided from scratch",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every tensor-identity equation, exactly, over Q",
   "kind": "none",
   "decidedFrom": "certs/strassen-certificate.json",
   "page": "/reports/alphaevolve.html",
   "recordedOn": "2026-08-25"
  },
  {
   "id": "mm-alphatensor-q-2x2x2",
   "claim": "2×2×2 matrix multiplication in 7 multiplications over Q",
   "claimant": "AlphaTensor",
   "source": "AlphaTensor (DeepMind, Nature 610, 2022), key 2,2,2 of alphatensor_r.npz",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every tensor-identity equation, exactly, over Q",
   "kind": "none",
   "decidedFrom": "certs/strassen-certificate.json",
   "page": "/reports/alphaevolve.html",
   "recordedOn": "2026-08-25"
  },
  {
   "id": "mm-alphatensor-q-3x3x3",
   "claim": "3×3×3 matrix multiplication in 23 multiplications over Q",
   "claimant": "AlphaTensor",
   "source": "AlphaTensor (DeepMind, Nature 610, 2022), key 3,3,3 of alphatensor_r.npz",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every tensor-identity equation, exactly, over Q",
   "kind": "none",
   "decidedFrom": "certs/strassen-certificate.json",
   "page": "/reports/alphaevolve.html",
   "recordedOn": "2026-08-25"
  },
  {
   "id": "mm-alphatensor-q-4x4x4",
   "claim": "4×4×4 matrix multiplication in 49 multiplications over Q",
   "claimant": "AlphaTensor",
   "source": "AlphaTensor (DeepMind, Nature 610, 2022), key 4,4,4 of alphatensor_r.npz",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every tensor-identity equation, exactly, over Q",
   "kind": "none",
   "decidedFrom": "certs/strassen-certificate.json",
   "page": "/reports/alphaevolve.html",
   "recordedOn": "2026-08-25"
  },
  {
   "id": "mm-alphatensor-q-3x4x5",
   "claim": "3×4×5 matrix multiplication in 47 multiplications over Q",
   "claimant": "AlphaTensor",
   "source": "AlphaTensor (DeepMind, Nature 610, 2022), key 3,4,5 of alphatensor_r.npz",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every tensor-identity equation, exactly, over Q",
   "kind": "none",
   "decidedFrom": "certs/strassen-certificate.json",
   "page": "/reports/alphaevolve.html",
   "recordedOn": "2026-08-25"
  },
  {
   "id": "mm-alphatensor-q-4x5x5",
   "claim": "4×5×5 matrix multiplication in 76 multiplications over Q",
   "claimant": "AlphaTensor",
   "source": "AlphaTensor (DeepMind, Nature 610, 2022), key 4,5,5 of alphatensor_r.npz",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every tensor-identity equation, exactly, over Q",
   "kind": "none",
   "decidedFrom": "certs/strassen-certificate.json",
   "page": "/reports/alphaevolve.html",
   "recordedOn": "2026-08-25"
  },
  {
   "id": "mm-alphatensor-f2-4x4x4",
   "claim": "4×4×4 matrix multiplication in 47 multiplications over F2",
   "claimant": "AlphaTensor",
   "source": "AlphaTensor (DeepMind, Nature 610, 2022), key 4,4,4 of alphatensor_f2.npz",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every tensor-identity equation, exactly, over F2; the same scheme is refuted over Q — the claim is a characteristic-2 claim",
   "kind": "none",
   "decidedFrom": "certs/strassen-certificate.json",
   "page": "/reports/alphaevolve.html",
   "recordedOn": "2026-08-25"
  },
  {
   "id": "mm-alphatensor-f2-5x5x5",
   "claim": "5×5×5 matrix multiplication in 96 multiplications over F2",
   "claimant": "AlphaTensor",
   "source": "AlphaTensor (DeepMind, Nature 610, 2022), key 5,5,5 of alphatensor_f2.npz",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every tensor-identity equation, exactly, over F2; the same scheme is refuted over Q — the claim is a characteristic-2 claim",
   "kind": "none",
   "decidedFrom": "certs/strassen-certificate.json",
   "page": "/reports/alphaevolve.html",
   "recordedOn": "2026-08-25"
  },
  {
   "id": "mm-alphaevolve-48-4x4x4",
   "claim": "4×4×4 matrix multiplication in 48 multiplications over Z[i]",
   "claimant": "AlphaEvolve",
   "source": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131), mathematical_results.ipynb of google-deepmind/alphaevolve_results @ commit 4226acb - the first-party byte source",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every tensor-identity equation, exactly, over Z[i]",
   "kind": "none",
   "decidedFrom": "certs/strassen-certificate.json",
   "page": "/reports/alphaevolve.html",
   "recordedOn": "2026-08-26"
  },
  {
   "id": "ea-circles-alphaevolve_2025",
   "claim": "n = 21 circles in a rectangle of perimeter 4 (bounding box w + h ≤ 2), no overlaps: Σ r = 2.3658321334",
   "claimant": "AlphaEvolve V2 (Georgiev, Gómez-Serrano, Tao, Wagner — arXiv:2511.02864)",
   "source": "corpus/easota/circles-rectangle/alphaevolve_2025.json (sha256 ede505bcbca6…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-circles-ours_2026",
   "claim": "n = 21 circles in a rectangle of perimeter 4 (bounding box w + h ≤ 2), no overlaps: Σ r = 2.3658323759",
   "claimant": "Together AI agents (the EinsteinArena repository)",
   "source": "corpus/easota/circles-rectangle/ours_2026.json (sha256 6060cc9f78f9…)",
   "origin": "self-initiated",
   "verdict": "REPAIRED",
   "scope": "as published, a witness only within a verifier's tolerance (whose, and when — the platform's or the repository notebook's — in the easota ledger's platformRule); a repaired construction next to it is certified",
   "kind": "tolerance-witness",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-heilbronn-alphaevolve_2025",
   "claim": "n = 14 points, min triangle area / convex-hull area = 0.0278355715",
   "claimant": "AlphaEvolve V2 (arXiv:2511.02864)",
   "source": "corpus/easota/heilbronn-convex/alphaevolve_2025.json (sha256 0006a49a12e1…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-heilbronn-ours_2026",
   "claim": "n = 14 points, min triangle area / convex-hull area = 0.0278355805",
   "claimant": "Together AI agents (the EinsteinArena repository)",
   "source": "corpus/easota/heilbronn-convex/ours_2026.json (sha256 2b16263e2994…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-mindist-alphaevolve_2025",
   "claim": "n = 16 points, (max distance / min distance)² = 12.889266",
   "claimant": "AlphaEvolve (Novikov et al. — arXiv:2506.13131)",
   "source": "corpus/easota/min-distance-ratio-2d/alphaevolve_2025.json (sha256 07c7449a55b9…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-mindist-ours_2026",
   "claim": "n = 16 points, (max distance / min distance)² = 12.889230",
   "claimant": "Together AI agents (the EinsteinArena repository)",
   "source": "corpus/easota/min-distance-ratio-2d/ours_2026.json (sha256 9236e69edf32…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ea-best-min-distance-ratio-2d",
    "pool": "einstein-arena",
    "alsoDecidedFrom": "certs/mc100-einstein-arena.json"
   },
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-overlap-haugland_2016",
   "claim": "a step function h with 51 steps, 0 ≤ h ≤ 1, Σh = n/2: upper bound 0.380927",
   "claimant": "J. K. Haugland (arXiv:1609.08000)",
   "source": "corpus/easota/erdos-minimum-overlap/haugland_2016.py (sha256 93bce13461a1…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-overlap-alphaevolve_2025",
   "claim": "a step function h with 95 steps, 0 ≤ h ≤ 1, Σh = n/2: upper bound 0.380924",
   "claimant": "AlphaEvolve (arXiv:2506.13131)",
   "source": "corpus/easota/erdos-minimum-overlap/alphaevolve_2025.py (sha256 11f33879398e…)",
   "origin": "self-initiated",
   "verdict": "REPAIRED",
   "scope": "as published, a witness only within a verifier's tolerance (whose, and when — the platform's or the repository notebook's — in the easota ledger's platformRule); a repaired construction next to it is certified",
   "kind": "tolerance-witness",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-overlap-ttt_discover_2026",
   "claim": "a step function h with 600 steps, 0 ≤ h ≤ 1, Σh = n/2: upper bound 0.380876",
   "claimant": "TTT-Discover (Yuksekgonul et al. — arXiv:2601.16175)",
   "source": "corpus/easota/erdos-minimum-overlap/ttt_discover_2026.py (sha256 586e77b49e07…)",
   "origin": "self-initiated",
   "verdict": "REPAIRED",
   "scope": "as published, a witness only within a verifier's tolerance (whose, and when — the platform's or the repository notebook's — in the easota ledger's platformRule); a repaired construction next to it is certified",
   "kind": "tolerance-witness",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-overlap-together_ai_2026",
   "claim": "a step function h with 600 steps, 0 ≤ h ≤ 1, Σh = n/2: upper bound 0.380871",
   "claimant": "Together AI agents (the EinsteinArena repository)",
   "source": "corpus/easota/erdos-minimum-overlap/together_ai_2026.py (sha256 3a2d93e27438…)",
   "origin": "self-initiated",
   "verdict": "REPAIRED",
   "scope": "as published, a witness only within a verifier's tolerance (whose, and when — the platform's or the repository notebook's — in the easota ledger's platformRule); a repaired construction next to it is certified",
   "kind": "tolerance-witness",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-edges-alphaevolve_2025",
   "claim": "100 rows of 20 weights → (edge density, triangle density) points; the platform's envelope score = -0.712494",
   "claimant": "AlphaEvolve V2 (arXiv:2511.02864)",
   "source": "corpus/easota/edges-vs-triangles/alphaevolve_2025.py (sha256 7be8fc911181…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-edges-ours_2026",
   "claim": "100 rows of 20 weights → (edge density, triangle density) points; the platform's envelope score = -0.712256",
   "claimant": "Together AI agents (the EinsteinArena repository)",
   "source": "corpus/easota/edges-vs-triangles/ours_2026.py (sha256 350cbf63494f…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-autocorr-alphaevolve_2025",
   "claim": "f ≥ 0 as 600 values on [−1/4, 1/4]: C₁ ≤ 1.50529397",
   "claimant": "AlphaEvolve (arXiv:2506.13131)",
   "source": "corpus/easota/first-autocorrelation/alphaevolve_2025.py (sha256 dea4517da376…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-autocorr-alphaevolve_v2_2025",
   "claim": "f ≥ 0 as 1319 values on [−1/4, 1/4]: C₁ ≤ (no value printed for this file)",
   "claimant": "AlphaEvolve V2 (arXiv:2511.02864)",
   "source": "corpus/easota/first-autocorrelation/alphaevolve_v2_2025.json (sha256 92a023d37ea8…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-autocorr-ttt_discover_2026",
   "claim": "f ≥ 0 as 30000 values on [−1/4, 1/4]: C₁ ≤ 1.50286290",
   "claimant": "TTT-Discover (arXiv:2601.16175)",
   "source": "corpus/easota/first-autocorrelation/ttt_discover_2026.json (sha256 4f24a0ef2515…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-autocorr-ours_2026",
   "claim": "f ≥ 0 as 30000 values on [−1/4, 1/4]: C₁ ≤ 1.50286286",
   "claimant": "Together AI agents (the EinsteinArena repository)",
   "source": "corpus/easota/first-autocorrelation/ours_2026.json (sha256 6cc34889cb40…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-flat-alphaevolve_2025",
   "claim": "70 coefficients ±1: C⁺ = max_{|z|=1} |g(z)| / √71 = 1.340925",
   "claimant": "AlphaEvolve V2 (arXiv:2511.02864)",
   "source": "corpus/easota/flat-polynomials/alphaevolve_2025.py (sha256 c403c792b179…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-flat-ours_2026",
   "claim": "70 coefficients ±1: C⁺ = max_{|z|=1} |g(z)| / √71 = 1.280932",
   "claimant": "Together AI agents (the EinsteinArena repository)",
   "source": "corpus/easota/flat-polynomials/ours_2026.py (sha256 d2a51b1c92cf…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-hexagons-alphaevolve_2025",
   "claim": "12 unit hexagons inside a hexagon of side 3.9419123, no overlaps, all inside: score = the outer side",
   "claimant": "AlphaEvolve V2 (arXiv:2511.02864)",
   "source": "corpus/easota/hexagon-packing/alphaevolve_2025.json (sha256 daa887e9ba08…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ea-hexagons-ours_2026",
   "claim": "12 unit hexagons inside a hexagon of side 3.9416523, no overlaps, all inside: score = the outer side",
   "claimant": "Together AI agents (the EinsteinArena repository)",
   "source": "corpus/easota/hexagon-packing/ours_2026.json (sha256 1d83e40b7786…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the construction as published, in exact arithmetic",
   "kind": "none",
   "decidedFrom": "certs/easota-ledger.json",
   "page": "/reports/easota.html",
   "recordedOn": "2026-09-08"
  },
  {
   "id": "ecbench-counts",
   "claim": "the exceedance counts printed for the environmental-contour benchmark's 150 contours",
   "claimant": "the benchmark's contributing teams (Haselsteiner et al., Ocean Eng. 2021)",
   "source": "the benchmark repository, pinned by commit",
   "origin": "self-initiated",
   "verdict": "MIXED",
   "scope": "174 of 176 printed counts agree with the exact count (173 exactly), 2 do not; 30 contours are not simple curves",
   "kind": "not-from-the-published-data",
   "kinds": {
    "none": 174,
    "not-from-the-published-data": 2
   },
   "decidedFrom": "certs/ecbench-ledger.json",
   "page": "/reports/ec-benchmark.html",
   "recordedOn": "2026-09-15"
  },
  {
   "id": "gsm8k-keys",
   "claim": "the worked solutions of GSM8K's 8,792 test and train keys",
   "claimant": "GSM8K (Cobbe et al., 2021)",
   "source": "the dataset, pinned by commit",
   "origin": "self-initiated",
   "verdict": "MIXED",
   "scope": "every calculator annotation exact (27,998, two train ones refused); 26 printed prose steps do not hold (2 test, 24 train); equations that are not arithmetic are counted UNREAD, not decided",
   "kind": "arithmetic-slip",
   "kinds": {
    "arithmetic-slip": 26
   },
   "decidedFrom": "certs/gsm8k-ledger.json",
   "page": "/reports/gsm8k-audit.html",
   "recordedOn": "2026-09-21"
  },
  {
   "id": "metr-horizon",
   "claim": "the time-horizon coefficients and 50% horizons METR prints for 23 models",
   "claimant": "METR (Time Horizon 1.1)",
   "source": "METR's runs and site files, pinned by commit",
   "origin": "self-initiated",
   "verdict": "MIXED",
   "scope": "44 of 44 fits certified; the printed coefficients are the rounding of the certified optimum for 22 of 23; the printed 50% horizons lie inside the enclosure for 0 of 23 (an optimiser's tolerance, all inside METR's own bootstrap interval)",
   "kind": "not-the-optimum",
   "kinds": {
    "none": 22,
    "not-the-optimum": 1
   },
   "decidedFrom": "certs/horizon-ledger.json",
   "page": "/reports/time-horizon.html",
   "recordedOn": "2026-09-22"
  },
  {
   "id": "ecbench-marginals",
   "claim": "the 15 Hs marginal fits the benchmark teams printed for buoys A, B and C",
   "claimant": "the environmental-contour benchmark's contributing teams",
   "source": "Appendix A of the benchmark paper, pinned by sha256",
   "origin": "self-initiated",
   "verdict": "MIXED",
   "scope": "5 reproduce a certified maximum-likelihood fit; 1 printed as Hs reproduce the certified fit of Tz; 0 stated as maximum likelihood are off its maximum; 3 use another estimator (least squares) and are not decided here; 6 are not decidable at the printed precision",
   "kind": "wrong-quantity",
   "kinds": {
    "none": 5,
    "wrong-quantity": 1
   },
   "decidedFrom": "certs/hseva-ledger.json",
   "page": "/reports/return-levels.html",
   "recordedOn": "2026-09-27"
  },
  {
   "id": "design-table-bhaskaran-2023",
   "claim": "the annual-maximum Hs fits of 20 printed rows for five South Atlantic lease areas",
   "claimant": "Bhaskaran et al. (Energies 16, 6935, 2023)",
   "source": "corpus/design-tables/bhaskaran-2023.json (the PDF pinned by sha256 828c27607aee…)",
   "origin": "self-initiated",
   "verdict": "NEEDS DATA",
   "scope": "the fits are to a commercial hindcast nobody outside can re-run; against the nearest cells of the public one they are 19 OFF THE MAXIMUM, 1 OUTSIDE ITS SUPPORT — the distance between two records, not an error",
   "kind": "data-not-public",
   "decidedFrom": "certs/design-table-audit.json",
   "page": "/instruments/return-level-atlas/",
   "recordedOn": "2026-09-28"
  },
  {
   "id": "navier-stokes-openai-2026",
   "claim": "finite-time blowup for the 3D Navier–Stokes equations with finite energy (Clay alternatives C and D)",
   "claimant": "OpenAI (2026-09-08; the Lean amended 2026-09-10)",
   "source": "github.com/openai/NavierStokesAndEuler @ f9e8bc5b (announced at 8937a8f4) and the paper, pinned by sha256",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "at f9e8bc5b (2026-09-10) the Lean proves the paper's Theorem 1.1 as stated, finite energy included (theorem_1_1, its statement read here clause by clause), and derives Clay's (C) and (D) from it — 486 changed or dependent modules rebuilt here over the pin's build, only the standard axioms for all 7 declarations asked; at the announced commit 8937a8f4 the finite-energy clause was not formal (PARTIAL, kept as history). Comparator judged (C) and (D) at 8937a8f4 and was not re-run at f9e8bc5b; Theorem 1.1's statement is OpenAI's own, not Comparator-judged",
   "kind": "none",
   "decidedFrom": "corpus/navier-stokes/audit.json",
   "alsoDecidedFrom": "corpus/navier-stokes/upstream-f9e8bc5b.json",
   "history": [
    {
     "at": "8937a8f4",
     "verdict": "PARTIAL",
     "kind": "clause-missing-from-formal-statement",
     "scope": "the Lean certificate holds for Clay's (C) and (D) — 2,486 modules built here, only the standard axioms, Comparator on both — and the finite-energy clause the paper's Theorem 1.1 states is not in the formal statement",
     "decidedFrom": "corpus/navier-stokes/audit.json",
     "recordedOn": "2026-09-09"
    }
   ],
   "page": "/reports/navier-stokes.html",
   "recordedOn": "2026-10-05"
  },
  {
   "id": "optconst-3b",
   "claim": "C3b >= 1.77898884 (the registry's asterisked lower bound)",
   "claimant": "Mosaic Intelligence (2026)",
   "source": "doi:10.5281/zenodo.20794135 (teorth/optimizationproblems PR #92)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the entropy ratio of the cited 13-point certificate, enclosed to 40 digits: 1.77898884142069354980…",
   "kind": "none",
   "decidedFrom": "certs/sumdiff-ledger.json",
   "page": "/reports/optimization-constants.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "optconst-3c",
   "claim": "C3c >= 1.6747338950414058 (the registry's asterisked lower bound)",
   "claimant": "Y. Lin (2026)",
   "source": "gist CoolRmal/5368357c @ 62621d2d (teorth/optimizationproblems PR #185)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the entropy ratio of the cited 147-point certificate, enclosed to 40 digits: 1.67473389504140587006…",
   "kind": "none",
   "decidedFrom": "certs/sumdiff-ledger.json",
   "page": "/reports/optimization-constants.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "optconst-3c-95",
   "claim": "C3c >= 1.6747338950208249 (superseded in the registry)",
   "claimant": "Mosaic Intelligence (2026)",
   "source": "doi:10.5281/zenodo.20794135 (teorth/optimizationproblems PR #93), superseded by the 147-point certificate",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the entropy ratio of the cited 95-point certificate, enclosed to 40 digits: 1.67473389502082499337…",
   "kind": "none",
   "decidedFrom": "certs/sumdiff-ledger.json",
   "page": "/reports/optimization-constants.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "optconst-71",
   "claim": "C71 > 6.521845710923046575 (the registry's asterisked lower bound)",
   "claimant": "Numaro (numaro.tech, \"AI Autoresearch\"), Zenodo 10.5281/zenodo.21497769",
   "source": "https://doi.org/10.5281/zenodo.21497769 (CC BY 4.0), the n = 18 truth table",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "H/(I-1) for the balanced n = 18 function, I = 261/128 exact and H in outward-rounded intervals: 6.52184571092304657565…; the amplification rule (O'Donnell–Tan, Hod) is cited, not re-proved",
   "kind": "none",
   "decidedFrom": "certs/fei-ledger.json",
   "page": "/reports/optimization-constants.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "optconst-84b",
   "claim": "C84b <= 1.999281 (c >= 0.000719) (the registry's asterisked upper bound)",
   "claimant": "I. Althoefer with ChatGPT 5.5 (the note, 28 May 2026), as the registry quotes it",
   "source": "the note (https://althofer.de/improved_constant_052.tex, sha256 2f6bbdcbf38c…), as registry/84b.md cites it",
   "origin": "self-initiated",
   "verdict": "REPAIRED",
   "scope": "holds as C84b <= 1.9993 (c >= 0.0007, the note's own theorem); for every choice of the chain's parameters c <= 0.0007150507 < 0.000719, so the quoted constant is out of reach of the calculation cited",
   "kind": "arithmetic-slip",
   "decidedFrom": "certs/sumproduct-ledger.json",
   "page": "/reports/optimization-constants.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "optconst-42a",
   "claim": "C42 <= 0.6906538 (the registry's asterisked upper bound)",
   "claimant": "S. Griego (github.com/sebastian-griego/turan-c42-certificate v1.0.0)",
   "source": "github.com/sebastian-griego/turan-c42-certificate v1.0.0 (the certificate pinned by sha256 a76e91323002…)",
   "origin": "self-initiated",
   "verdict": "PARTIAL",
   "scope": "the limiting certificate decided (|Y|/D <= 0.690653695151… < 0.6906538, |1-alpha| < C, |eta| < C, tau > 1/3); the asymptotic reduction to it, with no finite threshold, is the note's prose",
   "kind": "narrower-scope",
   "decidedFrom": "certs/turan-ledger.json",
   "page": "/reports/optimization-constants.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "optconst-42a-pr184",
   "claim": "C42 <= 0.688983 (an open pull request to the registry)",
   "claimant": "A. Röhrig with Codex (teorth/optimizationproblems PR #184, 9 Sep 2026)",
   "source": "github.com/teorth/optimizationproblems/pull/184 (open on 2026-09-29) (its certificate transcribed; note and checker pinned by sha256)",
   "origin": "self-initiated",
   "verdict": "PARTIAL",
   "scope": "the eight-block limiting certificate decided (|Y|/D <= 0.688982098504… < 0.688983, every block inside C, gap 9.7997e-07); the asymptotic reduction is the note's prose",
   "kind": "narrower-scope",
   "decidedFrom": "certs/turan-ledger.json",
   "page": "/reports/optimization-constants.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "countex-aim-problems",
   "claim": "Borcea-Branden AIM problems",
   "claimant": "GPT-5 (Pro), GPT-5.6 (Pro), Opus 5 (S. Sra's counterexample library)",
   "source": "github.com/suvrit/count-ex-machina @ dbf67374",
   "origin": "self-initiated",
   "verdict": "PARTIAL",
   "scope": "Problems 36, 37 and 38 certified; Problem 35's nonexistence over all positive semidefinite A rests on universal theorems the case cites (Marcus 1963, Lieb 1966, via Wanless 2022) — the witness's own violations of both are certified, the universal step is not re-derived",
   "kind": "narrower-scope",
   "decidedFrom": "certs/countex-ledger.json",
   "page": "/reports/counterexample-machine.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "countex-courtade-volume-conjecture",
   "claim": "Courtade's volume conjecture for Minkowski sums is false",
   "claimant": "Suvrit Sra, by hand (S. Sra's counterexample library)",
   "source": "github.com/suvrit/count-ex-machina @ dbf67374",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the counterexample needs, re-derived from the published artifact",
   "kind": "none",
   "decidedFrom": "certs/countex-ledger.json",
   "page": "/reports/counterexample-machine.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "countex-dpp-feasible-step",
   "claim": "Feasible Picard steps for DPP likelihood",
   "claimant": "GPT-5.6 (S. Sra's counterexample library)",
   "source": "github.com/suvrit/count-ex-machina @ dbf67374",
   "origin": "self-initiated",
   "verdict": "PARTIAL",
   "scope": "CERTIFIED when \"feasible\" means the step keeps the iterate positive definite (the case's context paragraph): a = 5 does, and the likelihood falls. The case's statement block reads \"feasibility is the bound a ≤ 1/(1 − γ) of Prop. A.1\", and for this L0 that bound is about 1.90, which a = 5 exceeds; under that reading the witness refutes nothing, and the steps tried inside the bound (a = 1, 3/2, 9/5, 1899/1000) all ascend",
   "kind": "depends-on-reading",
   "decidedFrom": "certs/countex-ledger.json",
   "page": "/reports/counterexample-machine.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "countex-hamiltonian-nepv-identity",
   "claim": "Failure of the proposed Hamiltonian NEPv Rayleigh identity",
   "claimant": "OpenAI Codex (S. Sra's counterexample library)",
   "source": "github.com/suvrit/count-ex-machina @ dbf67374",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the counterexample needs, re-derived from the published artifact",
   "kind": "none",
   "decidedFrom": "certs/countex-ledger.json",
   "page": "/reports/counterexample-machine.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "countex-lorentzian-jensen",
   "claim": "Log-volume midpoint gap and its Lorentzian generalization",
   "claimant": "GPT-5.6 Pro (S. Sra's counterexample library)",
   "source": "github.com/suvrit/count-ex-machina @ dbf67374",
   "origin": "self-initiated",
   "verdict": "PARTIAL",
   "scope": "the Lorentzian generalization certified (G strictly Lorentzian, the triangle violation enclosed to 60 digits); the log-volume-distance result needs convex bodies that exist only through a cited realization theorem (Shephard), none exhibited",
   "kind": "narrower-scope",
   "decidedFrom": "certs/countex-ledger.json",
   "page": "/reports/counterexample-machine.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "countex-macdonald-schur-convexity",
   "claim": "Macdonald lattice Schur-convexity",
   "claimant": "GPT-5.6 (Pro) (S. Sra's counterexample library)",
   "source": "github.com/suvrit/count-ex-machina @ dbf67374",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the counterexample needs, re-derived from the published artifact",
   "kind": "none",
   "decidedFrom": "certs/countex-ledger.json",
   "page": "/reports/counterexample-machine.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "countex-odonnell-matrix-conjecture",
   "claim": "No dimension-free constant in O'Donnell's matrix conjecture",
   "claimant": "GPT-5.6 Pro (S. Sra's counterexample library)",
   "source": "github.com/suvrit/count-ex-machina @ dbf67374",
   "origin": "self-initiated",
   "verdict": "PARTIAL",
   "scope": "every family member to m = 11 certified (unit trace, PSD, ratio above m/32; built exactly, densely at n = 512); unboundedness over all m, which refuting a universal constant needs, is argued in prose (a trace-norm duality bound and dyadic sums past m = 14)",
   "kind": "narrower-scope",
   "decidedFrom": "certs/countex-ledger.json",
   "page": "/reports/counterexample-machine.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "countex-osi-sketch-and-solve",
   "claim": "An oblivious subspace injection need not give relative-error sketch-and-solve",
   "claimant": "OpenAI Codex (S. Sra's counterexample library)",
   "source": "github.com/suvrit/count-ex-machina @ dbf67374",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the counterexample needs, re-derived from the published artifact",
   "kind": "none",
   "decidedFrom": "certs/countex-ledger.json",
   "page": "/reports/counterexample-machine.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "countex-qrcp-orthonormal-greedy",
   "claim": "Exact QRCP can miss the orthonormal-row conditioning bound",
   "claimant": "OpenAI Codex (S. Sra's counterexample library)",
   "source": "github.com/suvrit/count-ex-machina @ dbf67374",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the counterexample needs, re-derived from the published artifact",
   "kind": "none",
   "decidedFrom": "certs/countex-ledger.json",
   "page": "/reports/counterexample-machine.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "countex-quantum-coupon-collector",
   "claim": "Quantum coupon collection: positivity of an alternating sum of inverses",
   "claimant": "GPT Pro (S. Sra's counterexample library)",
   "source": "github.com/suvrit/count-ex-machina @ dbf67374",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the counterexample needs, re-derived from the published artifact",
   "kind": "none",
   "decidedFrom": "certs/countex-ledger.json",
   "page": "/reports/counterexample-machine.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "countex-rank-two-mixed-norm",
   "claim": "A mixed-norm Cauchy-Schwarz question of Sah, Sawhney, Stoner and Zhao",
   "claimant": "GPT-5.6 Sol (Pro), Opus 5 (S. Sra's counterexample library)",
   "source": "github.com/suvrit/count-ex-machina @ dbf67374",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the counterexample needs, re-derived from the published artifact",
   "kind": "none",
   "decidedFrom": "certs/countex-ledger.json",
   "page": "/reports/counterexample-machine.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "countex-sdd-nystrom-diminishing-returns",
   "claim": "Strict diagonal dominance does not ensure diminishing Nyström error reductions",
   "claimant": "OpenAI Codex (S. Sra's counterexample library)",
   "source": "github.com/suvrit/count-ex-machina @ dbf67374",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the counterexample needs, re-derived from the published artifact",
   "kind": "none",
   "decidedFrom": "certs/countex-ledger.json",
   "page": "/reports/counterexample-machine.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "countex-theta-derivative-log-concavity",
   "claim": "Derivatives of the Jacobi-theta kernel",
   "claimant": "GPT-5.5 (Pro) (S. Sra's counterexample library)",
   "source": "github.com/suvrit/count-ex-machina @ dbf67374",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the counterexample needs, re-derived from the published artifact",
   "kind": "none",
   "decidedFrom": "certs/countex-ledger.json",
   "page": "/reports/counterexample-machine.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "countex-variance-only-matrix-discrepancy",
   "claim": "Variance-sensitive Matrix Spencer",
   "claimant": "GPT-5.5 (Pro) (S. Sra's counterexample library)",
   "source": "github.com/suvrit/count-ex-machina @ dbf67374",
   "origin": "self-initiated",
   "verdict": "PARTIAL",
   "scope": "m = 2..10 certified exactly (discrepancy by exhaustion, ratio squared up to 81/11 at m = 10); unboundedness over all m, which refuting a universal constant needs, is a three-line argument in the case's prose, checked by hand and not by code",
   "kind": "narrower-scope",
   "decidedFrom": "certs/countex-ledger.json",
   "page": "/reports/counterexample-machine.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "horizonmath-ramsey-asymptotic",
   "claim": "R(k,k) <= 3.6960839126^(k+o(k)), improving 3.7992 (Gupta–Ndiaye–Norin–Wei), by a certificate that satisfies their Theorem 14",
   "claimant": "GPT-5.4 Pro, reproduced by GPT-5.6 Sol Max (HorizonMath, arXiv 2603.15617v2, Appendix A.3)",
   "source": "arXiv:2603.15617v2, Appendix A; github.com/ewang26/HorizonMath @ 4ef0b61a",
   "origin": "self-initiated",
   "verdict": "REFUTED",
   "scope": "the certificate is refuted, not the inequality: its pair (X(1), Y(1)) = (0.22745, 0.9988), at the point that sets c, lies outside R — Erdos's 1947 bound at e = 13/2000, p = 11981/500000 exceeds the pair's rate by 0.00130 — and 56 of its 201 decided points are outside R, 128 more not placed in R by the bound the problem names. The problem's own rule accepts every pair with x <= e^-U(1) = 0.26292, whatever y is: it asks one of the two inequalities membership needs",
   "kind": "checker-wider-than-definition",
   "decidedFrom": "certs/horizonmath-ledger.json",
   "page": "/reports/horizonmath.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "horizonmath-keich-thin-triangles-128",
   "claim": "Area(E) = 0.1091479892... < 0.1148103258186177 (the AlphaEvolve baseline)",
   "claimant": "GPT-5.4 Pro, reproduced by GPT-5.6 Sol Max (HorizonMath, arXiv 2603.15617v2, Appendix A.2)",
   "source": "arXiv:2603.15617v2, Appendix A; github.com/ewang26/HorizonMath @ 4ef0b61a",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "the union of the 128 printed triangles has area exactly 6008623/55050240 = 0.10914798918224…, 0.00566233 below the printed AlphaEvolve baseline; the printed 0.1091479892 is its rounding",
   "kind": "none",
   "decidedFrom": "certs/horizonmath-ledger.json",
   "page": "/reports/horizonmath.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "horizonmath-gpt56-closed-forms",
   "claim": "three closed forms that \"pass the compliance check and match the high-precision reference\"",
   "claimant": "GPT-5.6 Sol Max (HorizonMath, arXiv 2603.15617v2)",
   "source": "arXiv:2603.15617v2, Appendix A; github.com/ewang26/HorizonMath @ 4ef0b61a",
   "origin": "self-initiated",
   "verdict": "NEEDS DATA",
   "scope": "the expressions are not published: the paper says all six discoveries \"are detailed in Appendix A\", which details three (A.1–A.3), none of these; agreement with a reference to 20 digits would not decide equality in any case",
   "kind": "data-not-public",
   "decidedFrom": "certs/horizonmath-ledger.json",
   "page": "/reports/horizonmath.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "gnnw-gai-3782",
   "claim": "R(k,k) <= 3.78233^(k+o(k)): Theorem 1 of Gupta–Ndiaye–Norin–Wei holds with G_AI (one more iteration of Theorem 14)",
   "claimant": "ChatGPT 5.6 Sol, printed by Gupta, Ndiaye, Norin and Wei as preliminary and unverified (arXiv 2407.19026v2)",
   "source": "arXiv:2407.19026v2, the remark after Remark 17 (the PDF pinned by sha256)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "Theorem 14's inequality decided on all of (0, 1] in interval arithmetic for F = h + G_AI, with a continuous M chosen here and Y from Lemma 15 for the proved F_0.03, by two independent programs; the theorem, the lemma and Theorem 1 are the paper's. Base e^F(1) = 3.78232877553731…; the printed 3.78233 is its rounding",
   "kind": "none",
   "decidedFrom": "certs/gnnw-certificate.json",
   "page": "/reports/diagonal-ramsey.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "polymaps-gao-g",
   "claim": "G: a polynomial map of C^3 with det J = 2 that is not injective (a counterexample to the Jacobian conjecture), printed in full",
   "claimant": "S. Gao, with Claude Fable 5 assisting (arXiv 2608.00222)",
   "source": "arXiv 2608.00222, Thm 3.5 (the TeX mirrored in corpus/polymaps, CC BY 4.0)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the claim needs, as an exact identity or evaluation",
   "kind": "none",
   "decidedFrom": "certs/polymaps-ledger.json",
   "page": "/reports/polymaps.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "polymaps-gao-f4",
   "claim": "F4: a polynomial map of C^4 with det J = -44/9 that is not injective (a counterexample to the Jacobian conjecture), printed in full",
   "claimant": "S. Gao, with Claude Fable 5 assisting (arXiv 2608.00222)",
   "source": "arXiv 2608.00222, Thm 4.3 (the TeX mirrored in corpus/polymaps, CC BY 4.0)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the claim needs, as an exact identity or evaluation",
   "kind": "none",
   "decidedFrom": "certs/polymaps-ledger.json",
   "page": "/reports/polymaps.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "polymaps-gao-f5",
   "claim": "F5: a polynomial map of C^4 with det J = 160/29 that is not injective (a counterexample to the Jacobian conjecture), printed in full",
   "claimant": "S. Gao, with Claude Fable 5 assisting (arXiv 2608.00222)",
   "source": "arXiv 2608.00222, Thm 4.4 (the TeX mirrored in corpus/polymaps, CC BY 4.0)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the claim needs, as an exact identity or evaluation",
   "kind": "none",
   "decidedFrom": "certs/polymaps-ledger.json",
   "page": "/reports/polymaps.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "polymaps-gao-f6",
   "claim": "F6: the map the printed construction defines (n = 5), det J = -290, not injective",
   "claimant": "S. Gao, with Claude Fable 5 assisting (arXiv 2608.00222)",
   "source": "arXiv 2608.00222, Thm 4.5 (the full map is not printed; the promised ancillary files are not on arXiv) (the TeX mirrored in corpus/polymaps, CC BY 4.0)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the claim needs, as an exact identity or evaluation (the full map is not printed; rebuilt from the printed construction)",
   "kind": "none",
   "decidedFrom": "certs/polymaps-ledger.json",
   "page": "/reports/polymaps.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "polymaps-gao-f7",
   "claim": "F7: the map the printed construction defines (n = 5), det J = 119377, not injective",
   "claimant": "S. Gao, with Claude Fable 5 assisting (arXiv 2608.00222)",
   "source": "arXiv 2608.00222, Thm 4.13 (the TeX mirrored in corpus/polymaps, CC BY 4.0)",
   "origin": "self-initiated",
   "verdict": "PARTIAL",
   "scope": "non-injective and the factors' determinants decided; the constant determinant of the whole rests on the paper's factorisation lemma (the full map is not printed; rebuilt from the printed construction)",
   "kind": "narrower-scope",
   "decidedFrom": "certs/polymaps-ledger.json",
   "page": "/reports/polymaps.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "polymaps-chv-x14",
   "claim": "X on R^14 (degree 7): JX has spectrum {-1} at every point and X has three zeros, so the weak Markus–Yamabe conjecture fails in dimension 14",
   "claimant": "Castañeda, Honorato, Valenzuela-Henríquez (arXiv 2608.05392)",
   "source": "arXiv 2608.05392, Thm 5.1 (the TeX mirrored in corpus/polymaps, CC BY 4.0)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the claim needs, as an exact identity or evaluation",
   "kind": "none",
   "decidedFrom": "certs/polymaps-ledger.json",
   "page": "/reports/polymaps.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "polymaps-chv-phi",
   "claim": "Phi, a cubic map of C^11 with det J = -2 that is not injective (the gist that first published it says ChatGPT generated it)",
   "claimant": "Castañeda, Honorato, Valenzuela-Henríquez (arXiv 2608.05392); the map first published in a gist that says ChatGPT generated it",
   "source": "arXiv 2608.05392, Prop 6.2 (the TeX mirrored in corpus/polymaps, CC BY 4.0)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the claim needs, as an exact identity or evaluation",
   "kind": "none",
   "decidedFrom": "certs/polymaps-ledger.json",
   "page": "/reports/polymaps.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "polymaps-chv-xhat18",
   "claim": "X-hat on R^18 (degree 3): spectrum {-1} everywhere, three zeros — decided as a symbolic identity where the paper's appendix checks one sample point",
   "claimant": "Castañeda, Honorato, Valenzuela-Henríquez (arXiv 2608.05392)",
   "source": "arXiv 2608.05392, Thm 8.1 (the TeX mirrored in corpus/polymaps, CC BY 4.0)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the claim needs, as an exact identity or evaluation",
   "kind": "none",
   "decidedFrom": "certs/polymaps-ledger.json",
   "page": "/reports/polymaps.html",
   "recordedOn": "2026-09-29"
  },
  {
   "id": "mc100-ae-nb-2x4x5-r32",
   "claim": "the notebook's \"Rank-32 decomposition of <2,4,5> over 0.5*Z\" is a decomposition of that tensor of rank 32 over that ring",
   "claimant": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131)",
   "source": "corpus/sources/alphaevolve_mathematical_results.ipynb (google-deepmind/alphaevolve_results @ 4226acb), section \"Rank-32 decomposition of <2,4,5>\" (sha256 2cce2543e48c…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 1,600 tensor-identity equations, exactly, over (1/2)Z, decided as the integer identity 8·T after the factors were scaled by 2·2·2 (so the scheme holds over every commutative ring in which 2 is invertible) — C-layout CA; rank 32 < 40 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ae-nb-2x4x5-r32",
    "pool": "alphaevolve-nb-matmul"
   },
   "decidedFrom": "certs/mc100-alphaevolve-nb-matmul.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphaevolve-nb-matmul.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-ae-nb-2x4x7-r45",
   "claim": "the notebook's \"Rank-45 decomposition of <2,4,7> over Z\" is a decomposition of that tensor of rank 45 over that ring",
   "claimant": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131)",
   "source": "corpus/sources/alphaevolve_mathematical_results.ipynb (google-deepmind/alphaevolve_results @ 4226acb), section \"Rank-45 decomposition of <2,4,7>\" (sha256 2cce2543e48c…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 3,136 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 45 < 56 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ae-nb-2x4x7-r45",
    "pool": "alphaevolve-nb-matmul"
   },
   "decidedFrom": "certs/mc100-alphaevolve-nb-matmul.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphaevolve-nb-matmul.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-ae-nb-2x4x8-r51",
   "claim": "the notebook's \"Rank-51 decomposition of <2,4,8> over Z\" is a decomposition of that tensor of rank 51 over that ring",
   "claimant": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131)",
   "source": "corpus/sources/alphaevolve_mathematical_results.ipynb (google-deepmind/alphaevolve_results @ 4226acb), section \"Rank-51 decomposition of <2,4,8>\" (sha256 2cce2543e48c…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 4,096 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 51 < 64 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ae-nb-2x4x8-r51",
    "pool": "alphaevolve-nb-matmul"
   },
   "decidedFrom": "certs/mc100-alphaevolve-nb-matmul.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphaevolve-nb-matmul.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-ae-nb-2x5x6-r47",
   "claim": "the notebook's \"Rank-47 decomposition of <2,5,6> over Z\" is a decomposition of that tensor of rank 47 over that ring",
   "claimant": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131)",
   "source": "corpus/sources/alphaevolve_mathematical_results.ipynb (google-deepmind/alphaevolve_results @ 4226acb), section \"Rank-47 decomposition of <2,5,6>\" (sha256 2cce2543e48c…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 3,600 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 47 < 60 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ae-nb-2x5x6-r47",
    "pool": "alphaevolve-nb-matmul"
   },
   "decidedFrom": "certs/mc100-alphaevolve-nb-matmul.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphaevolve-nb-matmul.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-ae-nb-3x3x3-r23",
   "claim": "the notebook's \"Rank-23 decomposition of <3,3,3> over Z\" is a decomposition of that tensor of rank 23 over that ring",
   "claimant": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131)",
   "source": "corpus/sources/alphaevolve_mathematical_results.ipynb (google-deepmind/alphaevolve_results @ 4226acb), section \"Rank-23 decomposition of <3,3,3>\" (sha256 2cce2543e48c…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 729 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 23 < 27 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ae-nb-3x3x3-r23",
    "pool": "alphaevolve-nb-matmul"
   },
   "decidedFrom": "certs/mc100-alphaevolve-nb-matmul.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphaevolve-nb-matmul.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-ae-nb-3x4x6-r54",
   "claim": "the notebook's \"Rank-54 decomposition of <3,4,6> over 0.5*Z\" is a decomposition of that tensor of rank 54 over that ring",
   "claimant": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131)",
   "source": "corpus/sources/alphaevolve_mathematical_results.ipynb (google-deepmind/alphaevolve_results @ 4226acb), section \"Rank-54 decomposition of <3,4,6>\" (sha256 2cce2543e48c…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 5,184 tensor-identity equations, exactly, over (1/2)Z, decided as the integer identity 8·T after the factors were scaled by 2·2·2 (so the scheme holds over every commutative ring in which 2 is invertible) — C-layout CA; rank 54 < 72 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ae-nb-3x4x6-r54",
    "pool": "alphaevolve-nb-matmul"
   },
   "decidedFrom": "certs/mc100-alphaevolve-nb-matmul.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphaevolve-nb-matmul.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-ae-nb-3x4x7-r63",
   "claim": "the notebook's \"Rank-63 decomposition of <3,4,7> over 0.5*C\" is a decomposition of that tensor of rank 63 over that ring",
   "claimant": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131)",
   "source": "corpus/sources/alphaevolve_mathematical_results.ipynb (google-deepmind/alphaevolve_results @ 4226acb), section \"Rank-63 decomposition of <3,4,7>\" (sha256 2cce2543e48c…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 7,056 tensor-identity equations, exactly, over (1/2)Z[i], decided as the Gaussian-integer identity 8·T after the factors were scaled by 2·2·2, imaginary part exactly 0 — C-layout CA; rank 63 < 84 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ae-nb-3x4x7-r63",
    "pool": "alphaevolve-nb-matmul"
   },
   "decidedFrom": "certs/mc100-alphaevolve-nb-matmul.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphaevolve-nb-matmul.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-ae-nb-3x4x8-r74",
   "claim": "the notebook's \"Rank-74 decomposition of <3,4,8> over Z\" is a decomposition of that tensor of rank 74 over that ring",
   "claimant": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131)",
   "source": "corpus/sources/alphaevolve_mathematical_results.ipynb (google-deepmind/alphaevolve_results @ 4226acb), section \"Rank-74 decomposition of <3,4,8>\" (sha256 2cce2543e48c…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 9,216 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 74 < 96 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ae-nb-3x4x8-r74",
    "pool": "alphaevolve-nb-matmul"
   },
   "decidedFrom": "certs/mc100-alphaevolve-nb-matmul.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphaevolve-nb-matmul.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-ae-nb-3x5x6-r68",
   "claim": "the notebook's \"Rank-68 decomposition of <3,5,6> over Z\" is a decomposition of that tensor of rank 68 over that ring",
   "claimant": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131)",
   "source": "corpus/sources/alphaevolve_mathematical_results.ipynb (google-deepmind/alphaevolve_results @ 4226acb), section \"Rank-68 decomposition of <3,5,6>\" (sha256 2cce2543e48c…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 8,100 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 68 < 90 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ae-nb-3x5x6-r68",
    "pool": "alphaevolve-nb-matmul"
   },
   "decidedFrom": "certs/mc100-alphaevolve-nb-matmul.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphaevolve-nb-matmul.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-ae-nb-3x5x7-r80",
   "claim": "the notebook's \"Rank-80 decomposition of <3,5,7> over Z\" is a decomposition of that tensor of rank 80 over that ring",
   "claimant": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131)",
   "source": "corpus/sources/alphaevolve_mathematical_results.ipynb (google-deepmind/alphaevolve_results @ 4226acb), section \"Rank-80 decomposition of <3,5,7>\" (sha256 2cce2543e48c…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 11,025 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 80 < 105 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ae-nb-3x5x7-r80",
    "pool": "alphaevolve-nb-matmul"
   },
   "decidedFrom": "certs/mc100-alphaevolve-nb-matmul.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphaevolve-nb-matmul.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-ae-nb-4x4x8-r96",
   "claim": "the notebook's \"Rank-96 decomposition of <4,4,8> over 0.5*C\" is a decomposition of that tensor of rank 96 over that ring",
   "claimant": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131)",
   "source": "corpus/sources/alphaevolve_mathematical_results.ipynb (google-deepmind/alphaevolve_results @ 4226acb), section \"Rank-96 decomposition of <4,4,8>\" (sha256 2cce2543e48c…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 16,384 tensor-identity equations, exactly, over (1/2)Z[i], decided as the Gaussian-integer identity 8·T after the factors were scaled by 2·2·2, imaginary part exactly 0 — C-layout CA; rank 96 < 128 naive; the object is not printed; rebuilt here from the printed recipe and the printed <4,4,4>",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ae-nb-4x4x8-r96",
    "pool": "alphaevolve-nb-matmul"
   },
   "decidedFrom": "certs/mc100-alphaevolve-nb-matmul.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphaevolve-nb-matmul.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-ae-nb-4x4x5-r61",
   "claim": "the notebook's \"Rank-61 decomposition of <4,4,5> over Z\" is a decomposition of that tensor of rank 61 over that ring",
   "claimant": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131)",
   "source": "corpus/sources/alphaevolve_mathematical_results.ipynb (google-deepmind/alphaevolve_results @ 4226acb), section \"Rank-61 decomposition of <4,4,5>\" (sha256 2cce2543e48c…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 6,400 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 61 < 80 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ae-nb-4x4x5-r61",
    "pool": "alphaevolve-nb-matmul"
   },
   "decidedFrom": "certs/mc100-alphaevolve-nb-matmul.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphaevolve-nb-matmul.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-ae-nb-4x4x7-r85",
   "claim": "the notebook's \"Rank-85 decomposition of <4,4,7> over Z\" is a decomposition of that tensor of rank 85 over that ring",
   "claimant": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131)",
   "source": "corpus/sources/alphaevolve_mathematical_results.ipynb (google-deepmind/alphaevolve_results @ 4226acb), section \"Rank-85 decomposition of <4,4,7>\" (sha256 2cce2543e48c…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 12,544 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 85 < 112 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ae-nb-4x4x7-r85",
    "pool": "alphaevolve-nb-matmul"
   },
   "decidedFrom": "certs/mc100-alphaevolve-nb-matmul.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphaevolve-nb-matmul.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-ae-nb-4x5x6-r90",
   "claim": "the notebook's \"Rank-90 decomposition of <4,5,6> over Z\" is a decomposition of that tensor of rank 90 over that ring",
   "claimant": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131)",
   "source": "corpus/sources/alphaevolve_mathematical_results.ipynb (google-deepmind/alphaevolve_results @ 4226acb), section \"Rank-90 decomposition of <4,5,6>\" (sha256 2cce2543e48c…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 14,400 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 90 < 120 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ae-nb-4x5x6-r90",
    "pool": "alphaevolve-nb-matmul"
   },
   "decidedFrom": "certs/mc100-alphaevolve-nb-matmul.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphaevolve-nb-matmul.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-ae-nb-5x5x5-r93",
   "claim": "the notebook's \"Rank-93 decomposition of <5,5,5> over Z\" is a decomposition of that tensor of rank 93 over that ring",
   "claimant": "AlphaEvolve (DeepMind, 2025; arXiv:2506.13131)",
   "source": "corpus/sources/alphaevolve_mathematical_results.ipynb (google-deepmind/alphaevolve_results @ 4226acb), section \"Rank-93 decomposition of <5,5,5>\" (sha256 2cce2543e48c…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 15,625 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 93 < 125 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ae-nb-5x5x5-r93",
    "pool": "alphaevolve-nb-matmul"
   },
   "decidedFrom": "certs/mc100-alphaevolve-nb-matmul.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphaevolve-nb-matmul.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-f2-2x2x3",
   "claim": "the factors stored under key 2,2,3 of alphatensor_f2.npz are a decomposition of the ⟨2,2,3⟩ tensor over F2 of the rank the array's shape states",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_f2.npz key 2,2,3 (sha256 70f09f349d8d…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 144 tensor-identity equations, exactly, over F2 — C-layout CA; rank 11 < 12 naive; the same factors are refuted over Q",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-f2-2x2x3",
    "pool": "alphatensor-f2"
   },
   "decidedFrom": "certs/mc100-alphatensor-f2.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-f2.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-f2-2x2x4",
   "claim": "the factors stored under key 2,2,4 of alphatensor_f2.npz are a decomposition of the ⟨2,2,4⟩ tensor over F2 of the rank the array's shape states",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_f2.npz key 2,2,4 (sha256 70f09f349d8d…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 256 tensor-identity equations, exactly, over F2 — C-layout CA; rank 14 < 16 naive; the same factors are refuted over Q",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-f2-2x2x4",
    "pool": "alphatensor-f2"
   },
   "decidedFrom": "certs/mc100-alphatensor-f2.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-f2.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-f2-2x3x3",
   "claim": "the factors stored under key 2,3,3 of alphatensor_f2.npz are a decomposition of the ⟨2,3,3⟩ tensor over F2 of the rank the array's shape states",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_f2.npz key 2,3,3 (sha256 70f09f349d8d…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 324 tensor-identity equations, exactly, over F2 — C-layout CA; rank 15 < 18 naive; the same factors are refuted over Q",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-f2-2x3x3",
    "pool": "alphatensor-f2"
   },
   "decidedFrom": "certs/mc100-alphatensor-f2.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-f2.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-f2-2x2x5",
   "claim": "the factors stored under key 2,2,5 of alphatensor_f2.npz are a decomposition of the ⟨2,2,5⟩ tensor over F2 of the rank the array's shape states",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_f2.npz key 2,2,5 (sha256 70f09f349d8d…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 400 tensor-identity equations, exactly, over F2 — C-layout CA; rank 18 < 20 naive; the same factors are refuted over Q",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-f2-2x2x5",
    "pool": "alphatensor-f2"
   },
   "decidedFrom": "certs/mc100-alphatensor-f2.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-f2.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-f2-2x3x4",
   "claim": "the factors stored under key 2,3,4 of alphatensor_f2.npz are a decomposition of the ⟨2,3,4⟩ tensor over F2 of the rank the array's shape states",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_f2.npz key 2,3,4 (sha256 70f09f349d8d…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 576 tensor-identity equations, exactly, over F2 — C-layout CA; rank 20 < 24 naive; the same factors are refuted over Q",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-f2-2x3x4",
    "pool": "alphatensor-f2"
   },
   "decidedFrom": "certs/mc100-alphatensor-f2.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-f2.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-f2-2x3x5",
   "claim": "the factors stored under key 2,3,5 of alphatensor_f2.npz are a decomposition of the ⟨2,3,5⟩ tensor over F2 of the rank the array's shape states",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_f2.npz key 2,3,5 (sha256 70f09f349d8d…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 900 tensor-identity equations, exactly, over F2 — C-layout CA; rank 25 < 30 naive; the same factors are refuted over Q",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-f2-2x3x5",
    "pool": "alphatensor-f2"
   },
   "decidedFrom": "certs/mc100-alphatensor-f2.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-f2.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-f2-2x4x4",
   "claim": "the factors stored under key 2,4,4 of alphatensor_f2.npz are a decomposition of the ⟨2,4,4⟩ tensor over F2 of the rank the array's shape states",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_f2.npz key 2,4,4 (sha256 70f09f349d8d…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 1,024 tensor-identity equations, exactly, over F2 — C-layout CA; rank 26 < 32 naive; the same factors are refuted over Q",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-f2-2x4x4",
    "pool": "alphatensor-f2"
   },
   "decidedFrom": "certs/mc100-alphatensor-f2.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-f2.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-f2-3x3x4",
   "claim": "the factors stored under key 3,3,4 of alphatensor_f2.npz are a decomposition of the ⟨3,3,4⟩ tensor over F2 of the rank the array's shape states",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_f2.npz key 3,3,4 (sha256 70f09f349d8d…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 1,296 tensor-identity equations, exactly, over F2 — C-layout CA; rank 29 < 36 naive; the same factors are refuted over Q",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-f2-3x3x4",
    "pool": "alphatensor-f2"
   },
   "decidedFrom": "certs/mc100-alphatensor-f2.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-f2.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-q-2x2x3",
   "claim": "the factors stored under key 2,2,3 of alphatensor_r.npz are a decomposition of the ⟨2,2,3⟩ matrix-multiplication tensor of the rank the array's shape states, over the ring the paper names",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_r.npz key 2,2,3 (sha256 4d59571a2537…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 144 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 11 < 12 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-q-2x2x3",
    "pool": "alphatensor-q"
   },
   "decidedFrom": "certs/mc100-alphatensor-q.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-q.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-q-2x2x4",
   "claim": "the factors stored under key 2,2,4 of alphatensor_r.npz are a decomposition of the ⟨2,2,4⟩ matrix-multiplication tensor of the rank the array's shape states, over the ring the paper names",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_r.npz key 2,2,4 (sha256 4d59571a2537…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 256 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 14 < 16 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-q-2x2x4",
    "pool": "alphatensor-q"
   },
   "decidedFrom": "certs/mc100-alphatensor-q.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-q.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-q-2x3x3",
   "claim": "the factors stored under key 2,3,3 of alphatensor_r.npz are a decomposition of the ⟨2,3,3⟩ matrix-multiplication tensor of the rank the array's shape states, over the ring the paper names",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_r.npz key 2,3,3 (sha256 4d59571a2537…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 324 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 15 < 18 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-q-2x3x3",
    "pool": "alphatensor-q"
   },
   "decidedFrom": "certs/mc100-alphatensor-q.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-q.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-q-2x2x5",
   "claim": "the factors stored under key 2,2,5 of alphatensor_r.npz are a decomposition of the ⟨2,2,5⟩ matrix-multiplication tensor of the rank the array's shape states, over the ring the paper names",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_r.npz key 2,2,5 (sha256 4d59571a2537…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 400 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 18 < 20 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-q-2x2x5",
    "pool": "alphatensor-q"
   },
   "decidedFrom": "certs/mc100-alphatensor-q.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-q.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-q-2x2x6",
   "claim": "the factors stored under key 2,2,6 of alphatensor_r.npz are a decomposition of the ⟨2,2,6⟩ matrix-multiplication tensor of the rank the array's shape states, over the ring the paper names",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_r.npz key 2,2,6 (sha256 4d59571a2537…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 576 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 21 < 24 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-q-2x2x6",
    "pool": "alphatensor-q"
   },
   "decidedFrom": "certs/mc100-alphatensor-q.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-q.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-q-2x3x4",
   "claim": "the factors stored under key 2,3,4 of alphatensor_r.npz are a decomposition of the ⟨2,3,4⟩ matrix-multiplication tensor of the rank the array's shape states, over the ring the paper names",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_r.npz key 2,3,4 (sha256 4d59571a2537…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 576 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 20 < 24 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-q-2x3x4",
    "pool": "alphatensor-q"
   },
   "decidedFrom": "certs/mc100-alphatensor-q.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-q.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-q-2x2x7",
   "claim": "the factors stored under key 2,2,7 of alphatensor_r.npz are a decomposition of the ⟨2,2,7⟩ matrix-multiplication tensor of the rank the array's shape states, over the ring the paper names",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_r.npz key 2,2,7 (sha256 4d59571a2537…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 784 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 25 < 28 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-q-2x2x7",
    "pool": "alphatensor-q"
   },
   "decidedFrom": "certs/mc100-alphatensor-q.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-q.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-q-2x3x5",
   "claim": "the factors stored under key 2,3,5 of alphatensor_r.npz are a decomposition of the ⟨2,3,5⟩ matrix-multiplication tensor of the rank the array's shape states, over the ring the paper names",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_r.npz key 2,3,5 (sha256 4d59571a2537…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 900 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 25 < 30 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-q-2x3x5",
    "pool": "alphatensor-q"
   },
   "decidedFrom": "certs/mc100-alphatensor-q.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-q.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-q-2x2x8",
   "claim": "the factors stored under key 2,2,8 of alphatensor_r.npz are a decomposition of the ⟨2,2,8⟩ matrix-multiplication tensor of the rank the array's shape states, over the ring the paper names",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_r.npz key 2,2,8 (sha256 4d59571a2537…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 1,024 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 28 < 32 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-q-2x2x8",
    "pool": "alphatensor-q"
   },
   "decidedFrom": "certs/mc100-alphatensor-q.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-q.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-q-2x4x4",
   "claim": "the factors stored under key 2,4,4 of alphatensor_r.npz are a decomposition of the ⟨2,4,4⟩ matrix-multiplication tensor of the rank the array's shape states, over the ring the paper names",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_r.npz key 2,4,4 (sha256 4d59571a2537…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 1,024 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 26 < 32 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-q-2x4x4",
    "pool": "alphatensor-q"
   },
   "decidedFrom": "certs/mc100-alphatensor-q.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-q.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-q-3x3x4",
   "claim": "the factors stored under key 3,3,4 of alphatensor_r.npz are a decomposition of the ⟨3,3,4⟩ matrix-multiplication tensor of the rank the array's shape states, over the ring the paper names",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_r.npz key 3,3,4 (sha256 4d59571a2537…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 1,296 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 29 < 36 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-q-3x3x4",
    "pool": "alphatensor-q"
   },
   "decidedFrom": "certs/mc100-alphatensor-q.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-q.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-at-q-2x4x5",
   "claim": "the factors stored under key 2,4,5 of alphatensor_r.npz are a decomposition of the ⟨2,4,5⟩ matrix-multiplication tensor of the rank the array's shape states, over the ring the paper names",
   "claimant": "AlphaTensor (DeepMind, Nature 610, 2022)",
   "source": "corpus/sources/alphatensor_r.npz key 2,4,5 (sha256 4d59571a2537…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every one of the 1,600 tensor-identity equations, exactly, over Z (an integer identity, so the scheme holds over every commutative ring) — C-layout CA; rank 33 < 40 naive",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "at-q-2x4x5",
    "pool": "alphatensor-q"
   },
   "decidedFrom": "certs/mc100-alphatensor-q.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-alphatensor-q.json",
   "recordedOn": "2026-10-04"
  },
  {
   "id": "mc100-ea-best-erdos-min-overlap",
   "claim": "the object is a feasible solution of \"Erdős Minimum Overlap (Upper Bound)\" and the platform's score of it is 0.3808585748578584 (minimize)",
   "claimant": "CodexProLong (EinsteinArena, solution 2507, 2026-08-15)",
   "source": "corpus/einstein-arena/best-1.json (sha256 0c4c744e6ae7…)",
   "origin": "self-initiated",
   "verdict": "REPAIRED",
   "scope": "as published, Σh − n/2 = 0.000000000000192824623888, not 0; the platform's verifier has no tolerance on the sum — in every public version (corpus/sources/easota-platform/erdos-min-overlap_9cd6fbfb.ts) it rescales h to Σh = n/2 in float64 before scoring, the repair below in floating point — and the 1e-6 is the Together repository notebook's np.isclose (corpus/easota), not the platform's. The printed 0.3808585748578584 agrees with the as-published bound 0.38085857485785828368… (above); the exact witness built from the same bytes (h scaled down to Σh = n/2) certifies C5 ≤ 0.38085857485785830932…, 0.000000000000000025639955 from the as-published value — at or below the printed 0.3808585748578584, so the printed upper bound itself is proved by the repaired witness",
   "kind": "tolerance-witness",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ea-best-erdos-min-overlap",
    "pool": "einstein-arena"
   },
   "decidedFrom": "certs/mc100-einstein-arena.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-einstein-arena.json",
   "recordedOn": "2026-10-05"
  },
  {
   "id": "mc100-ea-best-first-autocorrelation-inequality",
   "claim": "the object is a feasible solution of \"First Autocorrelation Inequality (Upper Bound)\" and the platform's score of it is 1.5027436492326165 (minimize)",
   "claimant": "CodexProLong (EinsteinArena, solution 2504, 2026-08-14)",
   "source": "corpus/einstein-arena/best-2.json (sha256 50abacd697b1…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "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 1.5027436492326165 agrees, above)",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ea-best-first-autocorrelation-inequality",
    "pool": "einstein-arena"
   },
   "decidedFrom": "certs/mc100-einstein-arena.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-einstein-arena.json",
   "recordedOn": "2026-10-05"
  },
  {
   "id": "mc100-ea-best-flat-polynomials",
   "claim": "the object is a feasible solution of \"Flat Polynomials (degree 69)\" and the platform's score of it is 1.2807274949642549 (minimize)",
   "claimant": "white (EinsteinArena, solution 2475, 2026-08-10)",
   "source": "corpus/einstein-arena/best-12.json (sha256 772b895b2cb8…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "70 coefficients ±1: C⁺ = max_{|z|=1}|g(z)|/√71 ∈ [1.28072749505304782858, 1.28072749505304790673], the supremum certified (the platform's 10⁶-point grid value 1.2807274949642549 is below it, within the platform's resolution)",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ea-best-flat-polynomials",
    "pool": "einstein-arena"
   },
   "decidedFrom": "certs/mc100-einstein-arena.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-einstein-arena.json",
   "recordedOn": "2026-10-05"
  },
  {
   "id": "mc100-ea-best-edges-vs-triangles",
   "claim": "the object is a feasible solution of \"Edges vs Triangles (Minimal Triangle Density)\" and the platform's score of it is -0.7117091757692579 (maximize)",
   "claimant": "CHRONOS (EinsteinArena, solution 2367, 2026-06-27)",
   "source": "corpus/einstein-arena/best-13.json (sha256 91be01ed42c0…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "500 rows of 20 weights: the platform's envelope score −(area + 10·max gap) = -0.71170917576925610657… exactly (the printed -0.7117091757692579 agrees, below)",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ea-best-edges-vs-triangles",
    "pool": "einstein-arena"
   },
   "decidedFrom": "certs/mc100-einstein-arena.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-einstein-arena.json",
   "recordedOn": "2026-10-05"
  },
  {
   "id": "mc100-ea-best-circles-rectangle",
   "claim": "the object is a feasible solution of \"Circles in a Rectangle (n = 21)\" and the platform's score of it is 2.3658323759098576 (maximize)",
   "claimant": "ExoMind-TTS (EinsteinArena, solution 2544, 2026-08-30)",
   "source": "corpus/einstein-arena/best-18.json (sha256 b38b661088ed…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "21 circles, no two overlapping and the bounding box at w + h ≤ 2, exactly: Σr = 2.36583237590985849000… (the printed 2.3658323759098576 agrees, below)",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ea-best-circles-rectangle",
    "pool": "einstein-arena"
   },
   "decidedFrom": "certs/mc100-einstein-arena.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-einstein-arena.json",
   "recordedOn": "2026-10-05"
  },
  {
   "id": "mc100-ea-best-kissing-number-d12",
   "claim": "the object is a feasible solution of \"Kissing Number in Dimension 12 (n=841)\" and the platform's score of it is 2 (minimize)",
   "claimant": "CHRONOS (EinsteinArena, solution 2081, 2026-04-23)",
   "source": "corpus/einstein-arena/best-22.json (sha256 5d9d2124947a…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "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's score 2 is exactly the penalty of the repeat (2 per repeated pair)",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ea-best-kissing-number-d12",
    "pool": "einstein-arena"
   },
   "decidedFrom": "certs/mc100-einstein-arena.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-einstein-arena.json",
   "recordedOn": "2026-10-05"
  },
  {
   "id": "mc100-ea-best-kissing-number-d11-605",
   "claim": "the object is a feasible solution of \"Kissing Number in Dimension 11 (n=605)\" and the platform's score of it is 1.7102381876301676 (minimize)",
   "claimant": "ExoMind-TTS (EinsteinArena, solution 2560, 2026-09-05)",
   "source": "corpus/einstein-arena/best-24.json (sha256 1bc113d02357…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "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 − 1/2 ∈ [0.26329908059535543918, 0.26329908059535543919] (θ ≈ 40.2441°, 19.7559° short of 60°); the platform's score 1.7102381876301676 is the overlap penalty Σ max(0, 2 − |c_i − c_j|), enclosed here in [1.71023818763016759486, 1.71023818763016759487]",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ea-best-kissing-number-d11-605",
    "pool": "einstein-arena"
   },
   "decidedFrom": "certs/mc100-einstein-arena.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-einstein-arena.json",
   "recordedOn": "2026-10-05"
  },
  {
   "id": "mc100-ea-best-kissing-number-d12-842",
   "claim": "the object is a feasible solution of \"Kissing Number in Dimension 12 (n=842)\" and the platform's score of it is 0.5469062458557645 (minimize)",
   "claimant": "ExoMind-TTS (EinsteinArena, solution 2561, 2026-09-05)",
   "source": "corpus/einstein-arena/best-25.json (sha256 0a58d04ac86f…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "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 ∈ [0.04327239768587444034, 0.04327239768587444035] (θ ≈ 57.0933°, 2.9067° short of 60°); the platform's score 0.5469062458557645 is the overlap penalty Σ max(0, 2 − |c_i − c_j|), enclosed here in [0.54690624585576453779, 0.54690624585576453780]",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "ea-best-kissing-number-d12-842",
    "pool": "einstein-arena"
   },
   "decidedFrom": "certs/mc100-einstein-arena.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-einstein-arena.json",
   "recordedOn": "2026-10-05"
  },
  {
   "id": "mc100-st-jacobian",
   "claim": "the polynomial map with the sparse rational coefficients given has the Jacobian property claimed and the collision witnesses listed collide",
   "claimant": "The Station agents (dualverse-ai; station_data_v2)",
   "source": "corpus/station-v2/jacobian/construction.json — github.com/dualverse-ai/station_data_v2 @ a4ae9192fa75 artifacts/jacobian/construction.json (sha256 ba0d49ac35c9…)",
   "origin": "self-initiated",
   "verdict": "CERTIFIED",
   "scope": "every fact the claim needs, as an exact identity or evaluation: det JF = -6 identically (the 3×3 Jacobian determinant expanded over Q), components of degrees 4, 6, 7 with 3, 6, 7 terms, and three distinct rational points with the one image (1, 7/3, 0) — a non-injective Keller map of C^3, a counterexample to the Jacobian conjecture in dimension 3 (the claim the register already certifies for Gao's G, here with 16 terms and degrees 4, 6, 7); the file's family checks for a = 1, 2, -3, 3 (a3_transfer) name points of maps it does not print and are not decided here",
   "kind": "none",
   "preregistered": {
    "corpus": "corpus/machine-claims-100.json",
    "id": "st-jacobian",
    "pool": "station-v2"
   },
   "decidedFrom": "certs/mc100-station-v2.json",
   "page": "https://github.com/carlostoledo1891/cert-machine/blob/main/certs/mc100-station-v2.json",
   "recordedOn": "2026-10-05"
  }
 ],
 "count": 132,
 "decided": 131,
 "pending": 1,
 "byVerdict": {
  "CERTIFIED": 107,
  "PARTIAL": 9,
  "REFUTED": 2,
  "QUEUED": 1,
  "MIXED": 5,
  "REPAIRED": 6,
  "NEEDS DATA": 2
 },
 "byOrigin": {
  "self-initiated": 132
 },
 "kindsDefined": {
  "none": "the claim holds as printed",
  "narrower-scope": "decided only in a narrower scope than printed; the rest is out of reach, not wrong",
  "float-printed-as-exact": "a floating-point result printed as the exact quantity",
  "sign-slip": "a sign wrong in a printed constant",
  "arithmetic-slip": "a printed arithmetic step that does not hold",
  "tolerance-witness": "a witness only within a numerical tolerance; the printed value is the tolerance's",
  "not-the-optimum": "printed as an optimum, but not the one the definition names (a stop short of it, or a local one)",
  "wrong-quantity": "the printed number is a correct answer to a different question",
  "not-from-the-published-data": "the printed number is not what the published data give, and the arithmetic is not why",
  "outside-support": "the printed model gives observed data zero density",
  "clause-missing-from-formal-statement": "a clause the prose claims is absent from the formal statement that is proved",
  "data-not-public": "the data behind the claim are not public, so no one outside can decide it",
  "depends-on-reading": "the claim holds under one of two definitions its own text gives, and not under the other",
  "checker-wider-than-definition": "the checker that accepted the claim admits what the definition it encodes excludes"
 },
 "byKind": {
  "none": 108,
  "narrower-scope": 8,
  "float-printed-as-exact": 1,
  "sign-slip": 1,
  "tolerance-witness": 5,
  "not-from-the-published-data": 1,
  "arithmetic-slip": 2,
  "not-the-optimum": 1,
  "wrong-quantity": 1,
  "data-not-public": 2,
  "depends-on-reading": 1,
  "checker-wider-than-definition": 1
 },
 "byMonth": {
  "2026-08": 18,
  "2026-09": 69,
  "2026-10": 45
 },
 "submitted": 0,
 "preregistered": {
  "corpus": "corpus/machine-claims-100.json",
  "of": 100,
  "decided": 46,
  "ownRows": 44,
  "alreadyInRegister": [
   "ea-best-min-distance-ratio-2d = ea-mindist-ours_2026",
   "ea-best-kissing-number-d11 = kiss-ea-594-winner"
  ]
 },
 "meta": {
  "date": "2026-10-06",
  "git": "a310e6e"
 }
}