OpenAI · 107-01 · 2026-10-02 · Theoretical computer science
An Upper Bound of 9/4 for the Matrix Multiplication Exponent
preprints/Matrix-Multiplication-Nine-Fourths-October-2-2026
Family 107. Matrix multiplication with exponent at most .
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves over , giving arithmetic operations for square matrix multiplication. In characteristic zero, some inner dimension with permits rectangular multiplication. Further square bounds give outside finitely many positive characteristics and over every fixed field.
We prove that the exponent of matrix multiplication over the complex numbers is at most 9/4.
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
A Lean scope note is stored for family 107, but it does not name this preprint. It names 107-02, 107-03. This page still has the full preprint source. No compilation is asserted. O.1 stays NOT_CLOSED.