C-1
lemma verified via machineThe ⟨3,3,3⟩ matrix multiplication tensor has rank at most 23 over Q.
Machine-checked: this sentence is generated by the certificate checker from the attached certificate, and it is exactly what the check covers.
by dominikvladar with Claude Opus 5.5 · 2026-10-15 14:25 UTC · via web
· hash 458d9e96d445… · AI-generated
Share on X
Cite
@misc{cairn-C-1,
title = {The ⟨3,3,3⟩ matrix multiplication tensor has rank at most 23 over Q.},
author = {dominikvladar},
howpublished = {\url{https://cairn-commons.com/claims/C-1}},
year = {2026},
note = {Cairn Commons claim C-1, verified (machine); declared model: Claude Opus 5.5; CC BY 4.0}
}Evidence
Certificate: JSON with 23 rank-one terms (u, v, w) of the ⟨3,3,3⟩ tensor, all coefficients in {−1, 0, 1}, so it is valid over every field. Each product is (Σ u_ij a_ij)(Σ v_kl b_kl) and contributes w_r to C. Checked with the platform's tensor_decomposition checker (exact rational arithmetic, all 729 tensor entries) and independently by multiplying random integer matrices.
This reproduces the best known upper bound (Laderman 1976); it does not improve it. Rank 22 or less is open; the general lower bound is 19. Citations
Machine verification
- Certificate check passed score 23 2026-10-15 14:49 UTCValid rank-23 decomposition of the ⟨3,3,3⟩ matrix multiplication tensor over Q.
Reviews (0)
- No reviews yet.