What was already known
Bläser’s classical general lower bound was 19, while Laderman gave a 23-product algorithm. Later 21, 22 and exact-rank-23 results over F₂, and their integer-coefficient consequences, do not establish those bounds over arbitrary fields.
What changed and why it matters
The field-uniform lower bound narrows the gap for a longstanding small-format algebraic-complexity problem. It is a different scope from field-specific searches and from asymptotic exponent bounds.
The AI contribution
Ivanov is the responsible author and directed the research. He discloses substantial ChatGPT/Codex assistance with mathematical exploration, Lean implementation, proof refactoring and documentation; exact historical model versions and a full prompt archive were not retained.
Limitations
This does not determine the exact rank over every field and makes no border-rank or general-circuit claim. The pinned source revision is dated 12 October and Palomar registered it on 13 October; an earlier DOI release is acknowledged, but its original release date was unavailable during this review. Registration is not a new discovery date. AIProofWatch has not rebuilt the project or audited its proof or statement equivalence. No independent human peer review is claimed.
Verification evidence
Evidence labels show what supports the claim. Importance rates its impact if correct.
Author claim
Pinned source states the unrestricted all-field bilinear lower bound and prior-work distinctions.
Accessible artifact / proof
The exact AB interface and its proved translation to the internal row-action formulation are available.
Formal checking
The immutable registry records Comparator, Lean and independent-kernel checking; this was not rerun by AIProofWatch.
Checker: Palomar Comparator, Lean, NanoDa and con-ron (reported)
Scope: MMRank.Palomar.lower_bound at commit cb1557b7ea80ea66fae4714628663d8c1df7a48d, with only the declared three standard axioms.
Basis: Reported by the linked checker
Check date: 2026-10-12
Checking a formal statement does not establish that it matches the original problem.
Correction and publication history
Daily 13 October source-statement review: newly reviewed all-field lower-bound record, absent from complete local/live publications. Preserve the earlier release caveat and field-specific prior bounds.
Read this published revision