Author

Rafael Pass

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Preprint Oct 2026

Matrix Multiplication from Polynomial Packings: A Constructive and Elementary Proof of $\omega\le9/4$

We give a self-contained constructive proof that the matrix multiplication exponent satisfies $\omega\le9/4$. This bound was recently claimed by OpenAI~\cite{original} through non-constructive arguments in Strassen's asymptotic spectral framework, counting exact scalar arithmetic operations over the complex numbers. We...

Rafael Pass · 0 citations

Preprint Aug 2026

The Value of a Prompt: An LLM-Relative Kolmogorov-Complexity Approach

In a world where valuable artifacts are increasingly created, completed, or processed by LLMs, the central economic question is not only what the LLM can produce, but what \emph{value} remains in the inputs (i.e., the prompts) we provide to it. Given a prompt, hint, critique, problem statement, or partial solution that...

Rafael Pass · 0 citations