{"what":"The alphatensor-f2 pool of the hundred pre-registered machine claims (corpus/machine-claims-100.json, registered 2026-10-02 before any was decided), decided by tools/run-mc100-tensors.js: every row the manifest names, its bytes re-hashed against the pin, its factors transcribed exactly and every tensor-identity equation decided by instruments/strassen/tensor.js and re-decided in BigInt. `entries` is the detached certificate of every CERTIFIED row: python3 tools/verify_strassen.py certs/mc100-alphatensor-f2.json --sources corpus/sources re-derives each with the Python standard library alone. The claimant's code is never run.","pool":"alphatensor-f2","manifest":"corpus/machine-claims-100.json","registered":"2026-10-02","decider":"instruments/strassen/tensor.js (audit, auditZi; BigInt cross-check in full) · second implementation: tools/verify_strassen.py on this file","transcriber":"tools/convert_alphatensor.py --emit","rows":[{"id":"at-f2-2x2x3","pool":"alphatensor-f2","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_f2.npz key 2,2,3","sha256":"70f09f349d8d2874ef0e0e089459c7320f5aa3eef277df5ffa67f573709db2da","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,2,3","dims":[2,2,3],"rank":11,"naive":12,"ring":"F2","layout":"CA","equations":144,"coefficients":[0,1],"bigInt":"VERIFIED (layout CA)","overQ":"REFUTED over Q — the scheme needs characteristic 2 (identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=0, k=1): sum 2, target 0)"},"ms":0.6},{"id":"at-f2-2x2x4","pool":"alphatensor-f2","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_f2.npz key 2,2,4","sha256":"70f09f349d8d2874ef0e0e089459c7320f5aa3eef277df5ffa67f573709db2da","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,2,4","dims":[2,2,4],"rank":14,"naive":16,"ring":"F2","layout":"CA","equations":256,"coefficients":[0,1],"bigInt":"VERIFIED (layout CA)","overQ":"REFUTED over Q — the scheme needs characteristic 2 (identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=2, k=6): sum 2, target 0)"},"ms":0.9},{"id":"at-f2-2x3x3","pool":"alphatensor-f2","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_f2.npz key 2,3,3","sha256":"70f09f349d8d2874ef0e0e089459c7320f5aa3eef277df5ffa67f573709db2da","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,3,3","dims":[2,3,3],"rank":15,"naive":18,"ring":"F2","layout":"CA","equations":324,"coefficients":[0,1],"bigInt":"VERIFIED (layout CA)","overQ":"REFUTED over Q — the scheme needs characteristic 2 (identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=0, k=2): sum 2, target 0)"},"ms":1.1},{"id":"at-f2-2x2x5","pool":"alphatensor-f2","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_f2.npz key 2,2,5","sha256":"70f09f349d8d2874ef0e0e089459c7320f5aa3eef277df5ffa67f573709db2da","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,2,5","dims":[2,2,5],"rank":18,"naive":20,"ring":"F2","layout":"CA","equations":400,"coefficients":[0,1],"bigInt":"VERIFIED (layout CA)","overQ":"REFUTED over Q — the scheme needs characteristic 2 (identity fails under BOTH C-layouts; last failure: equation (ab=1, bc=0, k=0): sum 2, target 0)"},"ms":0.8},{"id":"at-f2-2x3x4","pool":"alphatensor-f2","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_f2.npz key 2,3,4","sha256":"70f09f349d8d2874ef0e0e089459c7320f5aa3eef277df5ffa67f573709db2da","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,3,4","dims":[2,3,4],"rank":20,"naive":24,"ring":"F2","layout":"CA","equations":576,"coefficients":[0,1],"bigInt":"VERIFIED (layout CA)","overQ":"REFUTED over Q — the scheme needs characteristic 2 (identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=0, k=5): sum 2, target 0)"},"ms":1.5},{"id":"at-f2-2x3x5","pool":"alphatensor-f2","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_f2.npz key 2,3,5","sha256":"70f09f349d8d2874ef0e0e089459c7320f5aa3eef277df5ffa67f573709db2da","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,3,5","dims":[2,3,5],"rank":25,"naive":30,"ring":"F2","layout":"CA","equations":900,"coefficients":[0,1],"bigInt":"VERIFIED (layout CA)","overQ":"REFUTED over Q — the scheme needs characteristic 2 (identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=1, k=3): sum 2, target 0)"},"ms":1.7},{"id":"at-f2-2x4x4","pool":"alphatensor-f2","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_f2.npz key 2,4,4","sha256":"70f09f349d8d2874ef0e0e089459c7320f5aa3eef277df5ffa67f573709db2da","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,4,4","dims":[2,4,4],"rank":26,"naive":32,"ring":"F2","layout":"CA","equations":1024,"coefficients":[0,1],"bigInt":"VERIFIED (layout CA)","overQ":"REFUTED over Q — the scheme needs characteristic 2 (identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=0, k=1): sum 2, target 0)"},"ms":2},{"id":"at-f2-3x3x4","pool":"alphatensor-f2","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_f2.npz key 3,3,4","sha256":"70f09f349d8d2874ef0e0e089459c7320f5aa3eef277df5ffa67f573709db2da","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"3,3,4","dims":[3,3,4],"rank":29,"naive":36,"ring":"F2","layout":"CA","equations":1296,"coefficients":[0,1],"bigInt":"VERIFIED (layout CA)","overQ":"REFUTED over Q — the scheme needs characteristic 2 (identity fails under BOTH C-layouts; last failure: equation (ab=0, bc=1, k=0): sum 2, target 0)"},"ms":2.8}],"count":8,"byVerdict":{"CERTIFIED":8},"byKind":{"none":8},"timing":{"runMs":70.2,"rowMsTotal":11.4},"layoutNote":"layout AC: k = a*p + c; layout CA: k = c*n + a.","sourcePins":{"alphatensor_f2.npz":"70f09f349d8d2874ef0e0e089459c7320f5aa3eef277df5ffa67f573709db2da"},"entries":[{"id":"at-f2-2x2x3","source":"AlphaTensor (DeepMind, Nature 610, 2022), key 2,2,3 of alphatensor_f2.npz","dims":[2,2,3],"rank":11,"naive":12,"ring":"F2","layout":"CA","statement":"at-f2-2x2x3: 2x2 times 2x3 in 11 multiplications VERIFIED over F2 — all 144 tensor-identity equations hold exactly (layout 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