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Sign inarXiv:2610.11823 claims that the tensor rank of 3×3 matrix multiplication over the field with two elements is exactly 23, so Laderman's algorithm is optimal there and among all bilinear algorithms with integer coefficients. The lower bound builds on a lower bound of 22 that the preprint attributes to Rudich and Rousseau (no public source found), uses the substitution method (sharpening bounds on 111 of Wang's 496 subspace classes) and a 27×27 flattening, and an exact search shows that no candidate set of 22 first factors completes to a decomposition. The result does not settle the rank over the rationals or complex numbers.
Posted 8 October 2026 and revised 12 October 2026; not refereed. The paper links Lean 4 artefacts, including a kernel-only version depending on the three standard axioms; no independent rebuild is recorded yet.
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The abstract says the kernel-only proof (GitHub tejasvi/rank333-f2-kernel, Zenodo 10.5281/zenodo.23304899) depends only on the three standard axioms; it needs an independent rebuild.
Expert review of the argument (111 of 496 subspace classes, 27×27 flattening) and of the completeness of the exact search.
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Compare with the earlier F2 lower-bound preprints: 20 (arXiv:2603.07280) and 21 (arXiv:2609.06725; structural proof arXiv:2609.18722).