The Profile Calculus: An Axiomatic Certification Framework for the $\omega \le 9/4$ Matrix-Multiplication Exponent

This record contains The Profile Calculus, an axiomatic certification framework and independent mathematical audit establishing the bound $\omega \le 9/4$ for the exponent of complex matrix multiplication. Reconstructing and consolidating the foundational developments of the OpenAI Mathematics Collection, this work formalizes the asymptotic proof into a reusable, modular calculus.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-17
DOI
https://doi.org/10.5281/zenodo.23440228
Primary Topic
Complexity and Algorithms in Graphs
Type
preprint
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preprint

The Profile Calculus: An Axiomatic Certification Framework for the $\omega \le 9/4$ Matrix-Multiplication Exponent

Mark Winston
Zenodo (CERN European Organization for Nuclear Research)
Complexity and Algorithms in Graphs
preprint

The Profile Calculus: An Axiomatic Certification Framework for the $\omega \le 9/4$ Matrix-Multiplication Exponent

Mark Winston
preprint en

Abstract

This record contains The Profile Calculus, an axiomatic certification framework and independent mathematical audit establishing the bound $\omega \le 9/4$ for the exponent of complex matrix multiplication. Reconstructing and consolidating the foundational developments of the OpenAI Mathematics Collection, this work formalizes the asymptotic proof into a reusable, modular calculus.

Zenodo (CERN European Organization for Nuclear Research)
Complexity and Algorithms in Graphs
DOIOpen Access PDFOpenAlex
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