Every published claim this machine decided in October 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 still running: this is October 2026 as of 2026-10-06 (git 054078d), and the page is rebuilt with every site build until the month closes. A row belongs to the month in which its deciding record first held it (the first commit, by git's pickaxe on the record). 87 claims were decided before October 2026 and are on the claims desk, not here.
| recorded | claim | claimant | verdict | what went wrong | where |
|---|---|---|---|---|---|
| 2026‑10‑04 | 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 | AlphaEvolve (DeepMind, 2025; arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑10‑04 | the notebook's "Rank-45 decomposition of <2,4,7> over Z" is a decomposition of that tensor of rank 45 over that ring | AlphaEvolve (DeepMind, 2025; arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑10‑04 | the notebook's "Rank-51 decomposition of <2,4,8> over Z" is a decomposition of that tensor of rank 51 over that ring | AlphaEvolve (DeepMind, 2025; arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑10‑04 | the notebook's "Rank-47 decomposition of <2,5,6> over Z" is a decomposition of that tensor of rank 47 over that ring | AlphaEvolve (DeepMind, 2025; arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑10‑04 | the notebook's "Rank-23 decomposition of <3,3,3> over Z" is a decomposition of that tensor of rank 23 over that ring | AlphaEvolve (DeepMind, 2025; arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaEvolve (DeepMind, 2025; arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaEvolve (DeepMind, 2025; arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑10‑04 | the notebook's "Rank-74 decomposition of <3,4,8> over Z" is a decomposition of that tensor of rank 74 over that ring | AlphaEvolve (DeepMind, 2025; arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑10‑04 | the notebook's "Rank-68 decomposition of <3,5,6> over Z" is a decomposition of that tensor of rank 68 over that ring | AlphaEvolve (DeepMind, 2025; arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑10‑04 | the notebook's "Rank-80 decomposition of <3,5,7> over Z" is a decomposition of that tensor of rank 80 over that ring | AlphaEvolve (DeepMind, 2025; arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑10‑04 | the notebook's "Rank-61 decomposition of <4,4,5> over Z" is a decomposition of that tensor of rank 61 over that ring | AlphaEvolve (DeepMind, 2025; arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑10‑04 | the notebook's "Rank-85 decomposition of <4,4,7> over Z" is a decomposition of that tensor of rank 85 over that ring | AlphaEvolve (DeepMind, 2025; arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaEvolve (DeepMind, 2025; arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑10‑04 | the notebook's "Rank-90 decomposition of <4,5,6> over Z" is a decomposition of that tensor of rank 90 over that ring | AlphaEvolve (DeepMind, 2025; arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑10‑04 | the notebook's "Rank-93 decomposition of <5,5,5> over Z" is a decomposition of that tensor of rank 93 over that ring | AlphaEvolve (DeepMind, 2025; arXiv:2506.13131) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑04 | 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 | AlphaTensor (DeepMind, Nature 610, 2022) | CERTIFIED | — | the record |
| 2026‑10‑05 | the object is a feasible solution of "Circles in a Rectangle (n = 21)" and the platform's score of it is 2.3658323759098576 (maximize) | ExoMind-TTS (EinsteinArena, solution 2544, 2026-08-30) | CERTIFIED | — | the record |
| 2026‑10‑05 | the object is a feasible solution of "Edges vs Triangles (Minimal Triangle Density)" and the platform's score of it is -0.7117091757692579 (maximize) | CHRONOS (EinsteinArena, solution 2367, 2026-06-27) | CERTIFIED | — | the record |
| 2026‑10‑05 | the object is a feasible solution of "Erdős Minimum Overlap (Upper Bound)" and the platform's score of it is 0.3808585748578584 (minimize) | CodexProLong (EinsteinArena, solution 2507, 2026-08-15) | REPAIRED | tolerance witness | the record |
| 2026‑10‑05 | the object is a feasible solution of "First Autocorrelation Inequality (Upper Bound)" and the platform's score of it is 1.5027436492326165 (minimize) | CodexProLong (EinsteinArena, solution 2504, 2026-08-14) | CERTIFIED | — | the record |
| 2026‑10‑05 | the object is a feasible solution of "Flat Polynomials (degree 69)" and the platform's score of it is 1.2807274949642549 (minimize) | white (EinsteinArena, solution 2475, 2026-08-10) | CERTIFIED | — | the record |
| 2026‑10‑05 | 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) | ExoMind-TTS (EinsteinArena, solution 2560, 2026-09-05) | CERTIFIED | — | the record |
| 2026‑10‑05 | the object is a feasible solution of "Kissing Number in Dimension 12 (n=841)" and the platform's score of it is 2 (minimize) | CHRONOS (EinsteinArena, solution 2081, 2026-04-23) | CERTIFIED | — | the record |
| 2026‑10‑05 | 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) | ExoMind-TTS (EinsteinArena, solution 2561, 2026-09-05) | CERTIFIED | — | the record |
| 2026‑10‑05 | the polynomial map with the sparse rational coefficients given has the Jacobian property claimed and the collision witnesses listed collide | The Station agents (dualverse-ai; station_data_v2) | CERTIFIED | — | the record |
| 2026‑10‑06 | finite-time blowup for the 3D Navier–Stokes equations with finite energy (Clay alternatives C and D) | OpenAI (2026-09-08; the Lean amended 2026-09-10) | 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".