{"id":"openai-math/Complex-Matrix-Multiplication-Below-2.258-and-Rectangular-Bounds","pdf":"https://github.com/openai/math/blob/main/preprints/Complex-Matrix-Multiplication-Below-2.258-and-Rectangular-Bounds-September-24-2026/Complex-Matrix-Multiplication-Below-2.258-and-Rectangular-Bounds-September-24-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/Complex-Matrix-Multiplication-Below-2.258-and-Rectangular-Bounds-September-24-2026","tags":["matrix-multiplication","computational-complexity","algebra"],"score":0,"title":"Complex Matrix Multiplication Below 2.258 and Rectangular Bounds","domain":"Theoretical computer science","family":"107","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"cs.CC","summary":"— secondary writeup Over every field of characteristic zero, we prove that the square matrix-multiplication exponent satisfies ω < 2.258, the dual exponent satisfies α > 0.465, and $`\\omega(1,0.709,1)\\lt 2.092`$. The strict square and k = 0.709 rectangular bounds also hold over every field except possibly in one finite set of positive characteristics, in the arithmetic-operation model.","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"Matrix multiplication with exponent at most 9/4"}