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Uniform Matrix Hitting Points in Every Positive Characteristic

OpenAI

OpenAI Mathopenai-math/Uniform-Matrix-Hitting-Points-in-Every-Positive-CharacteristicOct 4, 2026cs.CCAI-generatedscore 0

We construct a single matrix substitution that detects every nonzero size- s division-free noncommutative formula in n variables over every field of a given positive characteristic. One deterministic machine, given a promised prime p in binary and n , s in unary, outputs matrices over 𝔽 p of dimension $O(n^3s^6)$ in polynomial bit time. The same tuple works with arbitrary extension-field coefficients, including in characteristic two. The construction also applies to the stated acyclic algebraic path programs.

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