Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 107-02. Complex Matrix Multiplication Below 2.258 and Rectangular Bounds
Manuscript map · lines 4575–4584
OpenAI@2026-10-07#rem:oai-p-107-02
Authors: OpenAI. Family 107.
Title: Complex Matrix Multiplication Below 2.258 and Rectangular Bounds.
Abstract: — 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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