{"id":"openai-math/Uniform-Matrix-Hitting-Points-in-Every-Positive-Characteristic","pdf":"https://github.com/openai/math/blob/main/preprints/Uniform-Matrix-Hitting-Points-in-Every-Positive-Characteristic-October-4-2026/uniform-matrix-hitting-points-positive-characteristic.pdf","url":"https://github.com/openai/math/tree/main/preprints/Uniform-Matrix-Hitting-Points-in-Every-Positive-Characteristic-October-4-2026","tags":["algebraic-complexity","formulas","positive-characteristic"],"score":0,"title":"Uniform Matrix Hitting Points in Every Positive Characteristic","domain":"Theoretical computer science","family":"116","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"cs.CC","summary":"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.","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"discussed":0,"published":"2026-10-04","reactions":{},"formalized":false,"family_title":"Uniform black-box noncommutative identity testing across characteristics"}