Theoretical computer science · Oct 6, 2026
Matrix multiplication exponent 9/4
Proves over ℂ, giving arithmetic operations for square matrix multiplication. In characteristic zero, some inner dimension na with a > 0.465 permits rectangular multiplication. Further square bounds give ω < 2.258 outside finitely many positive characteristics and ω < 2.371054886006746 over every fixed field.
Scope and what remains
Field/ring, arithmetic-operation model, asymptotic quantifiers and independent extension proof identities matter; lower-valued targets from another approach are not interchangeable.
Contributors
OpenAI source publisher and an unnamed unreleased internal model. Exact paper-level human roles are not disclosed by the family summary.
AI systems: Unreleased OpenAI model