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.