{"what":"The alphatensor-q 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-q.json --sources corpus/sources re-derives each with the Python standard library alone. The claimant's code is never run.","pool":"alphatensor-q","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-q-2x2x3","pool":"alphatensor-q","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_r.npz key 2,2,3","sha256":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,2,3","dims":[2,2,3],"rank":11,"naive":12,"ring":"Q","layout":"CA","equations":144,"coefficients":[-1,0,1],"bigInt":"VERIFIED (layout CA)"},"ms":1.3},{"id":"at-q-2x2x4","pool":"alphatensor-q","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_r.npz key 2,2,4","sha256":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,2,4","dims":[2,2,4],"rank":14,"naive":16,"ring":"Q","layout":"CA","equations":256,"coefficients":[-1,0,1],"bigInt":"VERIFIED (layout CA)"},"ms":1},{"id":"at-q-2x3x3","pool":"alphatensor-q","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_r.npz key 2,3,3","sha256":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,3,3","dims":[2,3,3],"rank":15,"naive":18,"ring":"Q","layout":"CA","equations":324,"coefficients":[-1,0,1],"bigInt":"VERIFIED (layout CA)"},"ms":1},{"id":"at-q-2x2x5","pool":"alphatensor-q","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_r.npz key 2,2,5","sha256":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,2,5","dims":[2,2,5],"rank":18,"naive":20,"ring":"Q","layout":"CA","equations":400,"coefficients":[-1,0,1],"bigInt":"VERIFIED (layout CA)"},"ms":1.2},{"id":"at-q-2x2x6","pool":"alphatensor-q","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_r.npz key 2,2,6","sha256":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,2,6","dims":[2,2,6],"rank":21,"naive":24,"ring":"Q","layout":"CA","equations":576,"coefficients":[-1,0,1],"bigInt":"VERIFIED (layout CA)"},"ms":1.6},{"id":"at-q-2x3x4","pool":"alphatensor-q","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_r.npz key 2,3,4","sha256":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,3,4","dims":[2,3,4],"rank":20,"naive":24,"ring":"Q","layout":"CA","equations":576,"coefficients":[-1,0,1],"bigInt":"VERIFIED (layout CA)"},"ms":1},{"id":"at-q-2x2x7","pool":"alphatensor-q","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_r.npz key 2,2,7","sha256":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,2,7","dims":[2,2,7],"rank":25,"naive":28,"ring":"Q","layout":"CA","equations":784,"coefficients":[-2,-1,0,1,2],"bigInt":"VERIFIED (layout CA)"},"ms":1.5},{"id":"at-q-2x3x5","pool":"alphatensor-q","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_r.npz key 2,3,5","sha256":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,3,5","dims":[2,3,5],"rank":25,"naive":30,"ring":"Q","layout":"CA","equations":900,"coefficients":[-1,0,1],"bigInt":"VERIFIED (layout CA)"},"ms":1.9},{"id":"at-q-2x2x8","pool":"alphatensor-q","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_r.npz key 2,2,8","sha256":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,2,8","dims":[2,2,8],"rank":28,"naive":32,"ring":"Q","layout":"CA","equations":1024,"coefficients":[-2,-1,0,1,2],"bigInt":"VERIFIED (layout CA)"},"ms":2.3},{"id":"at-q-2x4x4","pool":"alphatensor-q","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_r.npz key 2,4,4","sha256":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,4,4","dims":[2,4,4],"rank":26,"naive":32,"ring":"Q","layout":"CA","equations":1024,"coefficients":[-1,0,1],"bigInt":"VERIFIED (layout CA)"},"ms":3.2},{"id":"at-q-3x3x4","pool":"alphatensor-q","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_r.npz key 3,3,4","sha256":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"3,3,4","dims":[3,3,4],"rank":29,"naive":36,"ring":"Q","layout":"CA","equations":1296,"coefficients":[-2,-1,0,1,2],"bigInt":"VERIFIED (layout CA)"},"ms":3.1},{"id":"at-q-2x4x5","pool":"alphatensor-q","claimant":"AlphaTensor (DeepMind, Nature 610, 2022)","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","source":"corpus/sources/alphatensor_r.npz key 2,4,5","sha256":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33","verdict":"CERTIFIED","kind":"none","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","decision":{"npzKey":"2,4,5","dims":[2,4,5],"rank":33,"naive":40,"ring":"Q","layout":"CA","equations":1600,"coefficients":[-1,0,1,3],"bigInt":"VERIFIED (layout CA)"},"ms":3.9}],"count":12,"byVerdict":{"CERTIFIED":12},"byKind":{"none":12},"timing":{"runMs":118.2,"rowMsTotal":23},"layoutNote":"layout AC: k = a*p + c; layout CA: k = c*n + a.","sourcePins":{"alphatensor_r.npz":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33"},"entries":[{"id":"at-q-2x2x3","source":"AlphaTensor (DeepMind, Nature 610, 2022), key 2,2,3 of alphatensor_r.npz","dims":[2,2,3],"rank":11,"naive":12,"ring":"Q","layout":"CA","statement":"at-q-2x2x3: 2x2 times 2x3 in 11 multiplications VERIFIED over Q — all 144 tensor-identity equations hold exactly (layout CA)","U":[[0,0,0,0,1,1,1,0,0,0,0],[0,0,1,1,1,0,0,1,0,1,0],[1,1,1,0,0,-1,0,0,1,0,0],[0,1,0,0,0,0,0,-1,-1,0,1]],"V":[[0,0,0,0,0,0,1,0,1,0,1],[1,0,0,0,0,1,0,0,0,0,0],[0,0,1,1,1,1,-1,0,0,1,0],[0,0,0,0,0,0,0,0,0,-1,1],[-1,1,1,0,0,0,0,1,0,0,0],[0,0,0,-1,0,0,0,1,0,0,0]],"W":[[0,0,0,0,1,0,1,0,0,-1,0],[0,0,0,0,0,0,0,0,1,0,1],[1,0,1,0,-1,1,0,0,0,0,0],[1,1,0,0,0,0,0,0,0,0,0],[0,0,0,-1,1,0,0,0,0,0,0],[0,-1,1,-1,0,0,0,-1,0,0,0]],"sourcePin":{"file":"alphatensor_r.npz","sha256":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33"}},{"id":"at-q-2x2x4","source":"AlphaTensor (DeepMind, Nature 610, 2022), key 2,2,4 of alphatensor_r.npz","dims":[2,2,4],"rank":14,"naive":16,"ring":"Q","layout":"CA","statement":"at-q-2x2x4: 2x2 times 2x4 in 14 multiplications VERIFIED over Q — all 256 tensor-identity equations hold exactly (layout CA)","U":[[1,1,1,0,1,1,1,0,1,0,1,0,0,0],[0,-1,0,0,0,-1,-1,1,-1,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0,1,1,1,0],[0,0,1,1,0,0,-1,1,-1,1,0,-1,0,1]],"V":[[0,0,1,1,0,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,1,1,1,0,0,0,1,1],[0,0,0,0,1,0,1,1,1,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0,0,0,0,0,1],[0,0,0,-1,0,0,0,1,0,1,0,0,0,1],[0,0,0,0,1,1,1,1,0,0,0,0,0,1],[1,1,-1,0,0,0,0,0,0,0,0,0,0,1]],"W":[[0,1,1,-1,0,0,0,-1,0,-1,0,0,0,1],[0,0,0,1,0,0,0,0,0,1,0,1,0,0],[0,0,0,0,-1,0,1,1,0,-1,0,0,0,0],[0,0,0,0,0,0,0,0,0,1,0,0,1,0],[0,0,0,0,1,-1,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,-1,0,1,0,0,0,-1,0],[1,-1,0,0,0,0,0,0,0,0,0,0,0,0],[-1,0,-1,0,0,0,0,0,0,0,1,-1,0,0]],"sourcePin":{"file":"alphatensor_r.npz","sha256":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33"}},{"id":"at-q-2x3x3","source":"AlphaTensor (DeepMind, Nature 610, 2022), key 2,3,3 of alphatensor_r.npz","dims":[2,3,3],"rank":15,"naive":18,"ring":"Q","layout":"CA","statement":"at-q-2x3x3: 2x3 times 3x3 in 15 multiplications VERIFIED over Q — all 324 tensor-identity equations hold exactly (layout CA)","U":[[0,1,1,1,0,0,0,1,0,0,0,0,1,0,1],[0,0,0,0,0,1,1,0,0,1,1,0,-1,0,0],[0,0,0,-1,1,0,-1,0,0,-1,-1,0,0,0,0],[0,0,0,0,0,0,0,-1,1,0,0,0,-1,1,-1],[0,0,0,0,0,0,0,1,-1,-1,0,1,1,0,0],[1,-1,0,0,-1,0,1,0,0,1,0,0,0,-1,0]],"V":[[1,1,0,0,0,0,0,0,0,0,0,0,0,1,1],[0,0,1,0,0,0,0,1,1,0,0,1,0,0,0],[0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1],[0,0,0,0,1,0,1,0,0,1,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,-1,0,1,0,0,0,0,1,0,-1],[1,0,0,0,1,0,0,0,0,0,0,0,0,0,0],[1,0,0,0,0,1,-1,0,0,0,1,0,0,0,0],[0,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0]],"W":[[1,1,0,-1,1,0,1,0,0,0,1,0,0,0,0],[1,0,0,0,0,0,1,0,0,-1,1,0,0,1,0],[0,0,0,0,0,1,0,1,1,0,-1,0,-1,0,0],[0,0,0,0,0,0,-1,0,1,1,-1,1,0,0,0],[0,0,-1,-1,0,0,0,1,1,0,0,0,-1,0,0],[0,-1,-1,0,0,0,0,1,1,0,0,0,0,1,1]],"sourcePin":{"file":"alphatensor_r.npz","sha256":"4d59571a2537a9472e8229176d5ebe2925f3e041ad403c095b41853026caec33"}},{"id":"at-q-2x2x5","source":"AlphaTensor (DeepMind, Nature 610, 2022), key 2,2,5 of alphatensor_r.npz","dims":[2,2,5],"rank":18,"naive":20,"ring":"Q","layout":"CA","statement":"at-q-2x2x5: 2x2 times 2x5 in 18 multiplications VERIFIED over Q — all 400 tensor-identity equations hold exactly (layout 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