What was already known
Dupont and collaborators obtained ω<2.371177 with combination-loss optimization and AlphaEvolve. This work shares extraction across recursion levels of the asymmetric laser method rather than optimizing only level-by-level extraction.
What changed and why it matters
An improvement within the laser-method line of asymptotic matrix-multiplication bounds, accompanied by an independently developed formal proof pipeline. It is separate from a faster small-size algorithm or measured hardware speedup.
The AI contribution
The authors state that GPT-6 Astra and Claude systems largely produced the shared-extraction idea, proof and Lean development under their direction; Meta Muse Spark handled the final numerical search. Proudfoot and Perrault chose the problem, directed the work, audited the statement and reproduced the build.
Limitations
OpenAI separately reports the stronger ω≤9/4 bound; this record does not claim to improve that result or hold the current overall record. The authors’ clean rebuild was performed by coauthor Andrew Perrault, not an outside mathematical referee. They did not verify every natural-language proof step. AIProofWatch has not compiled the project, replayed its numerical certificate or audited the equivalence of its tensor-rank definition with other exponent definitions. The 7 October date is the documented registry release; the earlier first-publication time is not established.
Verification evidence
Evidence labels show what supports the claim. Importance rates its impact if correct.
Author claim
Pinned statement, exact rank-based definition and human/AI roles.
Accessible artifact / proof
The declaration exponent_lt exposes the exact all-commutative-ring bound.
Formal checking
Registry-reported Comparator and kernel checks of the independent statement; no local reproduction claimed.
Checker: Palomar Comparator, Lean, NanoDa and con-ron (reported)
Scope: MatrixBounds.Numeric.SuppliedCertifiedPipeline.exponent_lt at commit 93492a4dd1ee90fd98cd7b339af77bb8bbc8be55; exact tensor-rank exponent and declared project dependencies.
Basis: Reported by the linked checker
Check date: 2026-10-06
Checking a formal statement does not establish that it matches the original problem.
Correction and publication history
Daily 13 October primary review of the distinct source newly added to a discovery index on 12 October. Compare the full mathematical statement, prior bound, AI roles and stronger separate OpenAI claim; no duplicated AlphaEvolve or OpenAI discovery.
Read this published revision