Every published claim this machine decided in September 2026, read from the register: what held, what did not, and what went wrong, in one closed vocabulary. The page is a dated diff of the records — nothing on it is typed.
The month is closed. A row belongs to the month in which its deciding record first held it (the first commit, by git's pickaxe on the record). 18 claims were decided before September 2026 and are on the claims desk, not here.
| recorded | claim | claimant | verdict | what went wrong | where |
|---|---|---|---|---|---|
| 2026‑09‑03 | K(11) >= 593 — the May 2025 record | AlphaEvolve (Novikov et al., DeepMind) | CERTIFIED | — | the record |
| 2026‑09‑03 | K(4) >= 24 — exact value, Musin 2003 | classical (generated here) | CERTIFIED | — | the record |
| 2026‑09‑03 | K(8) = 240 — exact value, Levenshtein / Odlyzko–Sloane 1979 | classical (generated here) | CERTIFIED | — | the record |
| 2026‑09‑03 | K(11) >= 594 — the solved n=594 rung, score-0 winner (solution #1492) | EinsteinArena agents (Bianchi et al. platform) | CERTIFIED | — | the record |
| 2026‑09‑03 | K(11) >= 604 — the paper's headline result, credited by Cohn's reference table (2026-06-22) | EinsteinArena (Bianchi, Kwon, Pappu, Zou — arXiv:2606.10402) | CERTIFIED | — | the record |
| 2026‑09‑03 | K(11) >= 592 — the 2022 record the AI ladder started from | M. Ganzhinov (arXiv:2207.08266, Highly symmetric lines) | QUEUED | — | the record |
| 2026‑09‑03 | K(11) >= 604 — configuration 1 of three | The Station agents (dualverse-ai) | CERTIFIED | — | the record |
| 2026‑09‑03 | K(11) >= 604 — configuration 2 of three | The Station agents (dualverse-ai) | CERTIFIED | — | the record |
| 2026‑09‑03 | K(11) >= 604 — configuration 3 of three | The Station agents (dualverse-ai) | CERTIFIED | — | the record |
| 2026‑09‑03 | construction device: 604 integer D12 vectors whose oblique shadow is configuration 3 (also a valid 604-point direction set in R^12) | The Station agents (dualverse-ai) | CERTIFIED | — | the record |
| 2026‑09‑03 | K(11) >= 582 — the pre-2022 record shell, integer norm-4 maximum (Lean-proved maximal by the Station) | classical (Best 1977 class; bytes from the Station bundle) | CERTIFIED | — | the record |
| 2026‑09‑08 | f ≥ 0 as 600 values on [−1/4, 1/4]: C₁ ≤ 1.50529397 | AlphaEvolve (arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑09‑08 | f ≥ 0 as 1319 values on [−1/4, 1/4]: C₁ ≤ (no value printed for this file) | AlphaEvolve V2 (arXiv:2511.02864) | CERTIFIED | — | the record |
| 2026‑09‑08 | f ≥ 0 as 30000 values on [−1/4, 1/4]: C₁ ≤ 1.50286286 | Together AI agents (the EinsteinArena repository) | CERTIFIED | — | the record |
| 2026‑09‑08 | f ≥ 0 as 30000 values on [−1/4, 1/4]: C₁ ≤ 1.50286290 | TTT-Discover (arXiv:2601.16175) | CERTIFIED | — | the record |
| 2026‑09‑08 | n = 21 circles in a rectangle of perimeter 4 (bounding box w + h ≤ 2), no overlaps: Σ r = 2.3658321334 | AlphaEvolve V2 (Georgiev, Gómez-Serrano, Tao, Wagner — arXiv:2511.02864) | CERTIFIED | — | the record |
| 2026‑09‑08 | n = 21 circles in a rectangle of perimeter 4 (bounding box w + h ≤ 2), no overlaps: Σ r = 2.3658323759 | Together AI agents (the EinsteinArena repository) | REPAIRED | tolerance witness | the record |
| 2026‑09‑08 | 100 rows of 20 weights → (edge density, triangle density) points; the platform's envelope score = -0.712494 | AlphaEvolve V2 (arXiv:2511.02864) | CERTIFIED | — | the record |
| 2026‑09‑08 | 100 rows of 20 weights → (edge density, triangle density) points; the platform's envelope score = -0.712256 | Together AI agents (the EinsteinArena repository) | CERTIFIED | — | the record |
| 2026‑09‑08 | 70 coefficients ±1: C⁺ = max_{|z|=1} |g(z)| / √71 = 1.340925 | AlphaEvolve V2 (arXiv:2511.02864) | CERTIFIED | — | the record |
| 2026‑09‑08 | 70 coefficients ±1: C⁺ = max_{|z|=1} |g(z)| / √71 = 1.280932 | Together AI agents (the EinsteinArena repository) | CERTIFIED | — | the record |
| 2026‑09‑08 | n = 14 points, min triangle area / convex-hull area = 0.0278355715 | AlphaEvolve V2 (arXiv:2511.02864) | CERTIFIED | — | the record |
| 2026‑09‑08 | n = 14 points, min triangle area / convex-hull area = 0.0278355805 | Together AI agents (the EinsteinArena repository) | CERTIFIED | — | the record |
| 2026‑09‑08 | 12 unit hexagons inside a hexagon of side 3.9419123, no overlaps, all inside: score = the outer side | AlphaEvolve V2 (arXiv:2511.02864) | CERTIFIED | — | the record |
| 2026‑09‑08 | 12 unit hexagons inside a hexagon of side 3.9416523, no overlaps, all inside: score = the outer side | Together AI agents (the EinsteinArena repository) | CERTIFIED | — | the record |
| 2026‑09‑08 | n = 16 points, (max distance / min distance)² = 12.889266 | AlphaEvolve (Novikov et al. — arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑09‑08 | n = 16 points, (max distance / min distance)² = 12.889230 | Together AI agents (the EinsteinArena repository) | CERTIFIED | — | the record |
| 2026‑09‑08 | a step function h with 95 steps, 0 ≤ h ≤ 1, Σh = n/2: upper bound 0.380924 | AlphaEvolve (arXiv:2506.13131) | REPAIRED | tolerance witness | the record |
| 2026‑09‑08 | a step function h with 51 steps, 0 ≤ h ≤ 1, Σh = n/2: upper bound 0.380927 | J. K. Haugland (arXiv:1609.08000) | CERTIFIED | — | the record |
| 2026‑09‑08 | a step function h with 600 steps, 0 ≤ h ≤ 1, Σh = n/2: upper bound 0.380871 | Together AI agents (the EinsteinArena repository) | REPAIRED | tolerance witness | the record |
| 2026‑09‑08 | a step function h with 600 steps, 0 ≤ h ≤ 1, Σh = n/2: upper bound 0.380876 | TTT-Discover (Yuksekgonul et al. — arXiv:2601.16175) | REPAIRED | tolerance witness | the record |
| 2026‑09‑15 | the exceedance counts printed for the environmental-contour benchmark's 150 contours | the benchmark's contributing teams (Haselsteiner et al., Ocean Eng. 2021) | MIXED | not from the published data | the record |
| 2026‑09‑21 | the worked solutions of GSM8K's 8,792 test and train keys | GSM8K (Cobbe et al., 2021) | MIXED | arithmetic slip | the record |
| 2026‑09‑22 | the time-horizon coefficients and 50% horizons METR prints for 23 models | METR (Time Horizon 1.1) | MIXED | not the optimum | the record |
| 2026‑09‑27 | the 15 Hs marginal fits the benchmark teams printed for buoys A, B and C | the environmental-contour benchmark's contributing teams | MIXED | wrong quantity | the record |
| 2026‑09‑28 | the annual-maximum Hs fits of 20 printed rows for five South Atlantic lease areas | Bhaskaran et al. (Energies 16, 6935, 2023) | NEEDS DATA | data not public | the record |
| 2026‑09‑29 | Borcea-Branden AIM problems | GPT-5 (Pro), GPT-5.6 (Pro), Opus 5 (S. Sra's counterexample library) | PARTIAL | narrower scope | the record |
| 2026‑09‑29 | Courtade's volume conjecture for Minkowski sums is false | Suvrit Sra, by hand (S. Sra's counterexample library) | CERTIFIED | — | the record |
| 2026‑09‑29 | Feasible Picard steps for DPP likelihood | GPT-5.6 (S. Sra's counterexample library) | PARTIAL | depends on reading | the record |
| 2026‑09‑29 | Failure of the proposed Hamiltonian NEPv Rayleigh identity | OpenAI Codex (S. Sra's counterexample library) | CERTIFIED | — | the record |
| 2026‑09‑29 | Log-volume midpoint gap and its Lorentzian generalization | GPT-5.6 Pro (S. Sra's counterexample library) | PARTIAL | narrower scope | the record |
| 2026‑09‑29 | Macdonald lattice Schur-convexity | GPT-5.6 (Pro) (S. Sra's counterexample library) | CERTIFIED | — | the record |
| 2026‑09‑29 | No dimension-free constant in O'Donnell's matrix conjecture | GPT-5.6 Pro (S. Sra's counterexample library) | PARTIAL | narrower scope | the record |
| 2026‑09‑29 | An oblivious subspace injection need not give relative-error sketch-and-solve | OpenAI Codex (S. Sra's counterexample library) | CERTIFIED | — | the record |
| 2026‑09‑29 | Exact QRCP can miss the orthonormal-row conditioning bound | OpenAI Codex (S. Sra's counterexample library) | CERTIFIED | — | the record |
| 2026‑09‑29 | Quantum coupon collection: positivity of an alternating sum of inverses | GPT Pro (S. Sra's counterexample library) | CERTIFIED | — | the record |
| 2026‑09‑29 | A mixed-norm Cauchy-Schwarz question of Sah, Sawhney, Stoner and Zhao | GPT-5.6 Sol (Pro), Opus 5 (S. Sra's counterexample library) | CERTIFIED | — | the record |
| 2026‑09‑29 | Strict diagonal dominance does not ensure diminishing Nyström error reductions | OpenAI Codex (S. Sra's counterexample library) | CERTIFIED | — | the record |
| 2026‑09‑29 | Derivatives of the Jacobi-theta kernel | GPT-5.5 (Pro) (S. Sra's counterexample library) | CERTIFIED | — | the record |
| 2026‑09‑29 | Variance-sensitive Matrix Spencer | GPT-5.5 (Pro) (S. Sra's counterexample library) | PARTIAL | narrower scope | the record |
| 2026‑09‑29 | 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) | ChatGPT 5.6 Sol, printed by Gupta, Ndiaye, Norin and Wei as preliminary and unverified (arXiv 2407.19026v2) | CERTIFIED | — | the record |
| 2026‑09‑29 | three closed forms that "pass the compliance check and match the high-precision reference" | GPT-5.6 Sol Max (HorizonMath, arXiv 2603.15617v2) | NEEDS DATA | data not public | the record |
| 2026‑09‑29 | Area(E) = 0.1091479892... < 0.1148103258186177 (the AlphaEvolve baseline) | GPT-5.4 Pro, reproduced by GPT-5.6 Sol Max (HorizonMath, arXiv 2603.15617v2, Appendix A.2) | CERTIFIED | — | the record |
| 2026‑09‑29 | R(k,k) <= 3.6960839126^(k+o(k)), improving 3.7992 (Gupta–Ndiaye–Norin–Wei), by a certificate that satisfies their Theorem 14 | GPT-5.4 Pro, reproduced by GPT-5.6 Sol Max (HorizonMath, arXiv 2603.15617v2, Appendix A.3) | REFUTED | checker wider than definition | the record |
| 2026‑09‑29 | C3b >= 1.77898884 (the registry's asterisked lower bound) | Mosaic Intelligence (2026) | CERTIFIED | — | the record |
| 2026‑09‑29 | C3c >= 1.6747338950414058 (the registry's asterisked lower bound) | Y. Lin (2026) | CERTIFIED | — | the record |
| 2026‑09‑29 | C3c >= 1.6747338950208249 (superseded in the registry) | Mosaic Intelligence (2026) | CERTIFIED | — | the record |
| 2026‑09‑29 | C42 <= 0.6906538 (the registry's asterisked upper bound) | S. Griego (github. | PARTIAL | narrower scope | the record |
| 2026‑09‑29 | C42 <= 0.688983 (an open pull request to the registry) | A. Röhrig with Codex (teorth/ | PARTIAL | narrower scope | the record |
| 2026‑09‑29 | C71 > 6.521845710923046575 (the registry's asterisked lower bound) | Numaro (numaro.tech, "AI Autoresearch"), Zenodo 10.5281/zenodo.21497769 | CERTIFIED | — | the record |
| 2026‑09‑29 | C84b <= 1.999281 (c >= 0.000719) (the registry's asterisked upper bound) | I. Althoefer with ChatGPT 5.5 (the note, 28 May 2026), as the registry quotes it | REPAIRED | arithmetic slip | the record |
| 2026‑09‑29 | 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) | Castañeda, Honorato, Valenzuela-Henríquez (arXiv 2608.05392); the map first published in a gist that says ChatGPT generated it | CERTIFIED | — | the record |
| 2026‑09‑29 | 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 | Castañeda, Honorato, Valenzuela-Henríquez (arXiv 2608.05392) | CERTIFIED | — | the record |
| 2026‑09‑29 | 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 | Castañeda, Honorato, Valenzuela-Henríquez (arXiv 2608.05392) | CERTIFIED | — | the record |
| 2026‑09‑29 | 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 | S. Gao, with Claude Fable 5 assisting (arXiv 2608.00222) | CERTIFIED | — | the record |
| 2026‑09‑29 | 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 | S. Gao, with Claude Fable 5 assisting (arXiv 2608.00222) | CERTIFIED | — | the record |
| 2026‑09‑29 | F6: the map the printed construction defines (n = 5), det J = -290, not injective | S. Gao, with Claude Fable 5 assisting (arXiv 2608.00222) | CERTIFIED | — | the record |
| 2026‑09‑29 | F7: the map the printed construction defines (n = 5), det J = 119377, not injective | S. Gao, with Claude Fable 5 assisting (arXiv 2608.00222) | PARTIAL | narrower scope | the record |
| 2026‑09‑29 | G: a polynomial map of C^3 with det J = 2 that is not injective (a counterexample to the Jacobian conjecture), printed in full | S. Gao, with Claude Fable 5 assisting (arXiv 2608.00222) | CERTIFIED | — | the record |
The vocabulary is closed: 14 kinds, defined once in tools/run-claims-ledger.js. A defect that fits none of them refuses the register until the vocabulary is decided on, never "other".