Breakthrough Tracker record
An AI-generated preprint claims matrix multiplication exponent at most 9/4
An OpenAI preprint proves an asymptotic arithmetic upper bound omega at most 9/4 over the complex numbers. A later independent manuscript improves a shared-leg step and extends the 9/4 conclusion over algebraic closures in every characteristic.
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- Stable ID
cs-matrix-multiplication-exponent-nine-quarters-2026- Revision
cs-matrix-multiplication-exponent-nine-quarters-2026.v1- Field
- Mathematics and theoretical computer science · Algebraic complexity, tensors and formal verification
- Evidence
- Tier 1 · Peer reviewed: No
- Record state
- Provisional · Formalization-backed provisional upper bound
- Last checked
AI role
OpenAI attributes the released mathematics catalogue, including this result, to an internal frontier model. The public paper is collectively authored as OpenAI; humans remain responsible for release and evaluation.
Record details
- Problem or result
- Upper bound for the square matrix-multiplication exponent
- Authors
- OpenAI; independent extension by Houxi Lü
- Institutions
- OpenAI; Lü's affiliation was not stated in the inspected arXiv author block
- Result date
- Preprint dated October 2; announced October 6; independent extension submitted October 12, 2026
Why it matters
The claimed 9/4 bound would be a major simplification and improvement in algebraic-complexity theory, with a separate manuscript already probing and strengthening one of its central constructions.
Limits
This is an asymptotic arithmetic-operation result, not a practical implementation, bit-complexity bound or claim that ordinary matrix multiplication now runs near n^2. The manuscripts are unrefereed; formal checking certifies encoded statements and does not replace semantic or historical-priority review.
Sources
- Primary: OpenAI 9/4 matrix-multiplication preprint
- Author announcement: OpenAI mathematics release and methodology note
- Independent follow-up: Lü arbitrary-characteristic extension
- Independent formal extension: Lean formalization for the arbitrary-field extension
Correction and revision history
- 2026-10-19 — Added after primary-source, scope, status, AI-role and limitation review.
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