{"id":"openai-math/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas","pdf":"https://github.com/openai/math/blob/main/preprints/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026","tags":["computational-complexity","algebraic-complexity","polynomial-identity-testing"],"score":0,"title":"One Rational Matrix Hitting Point for Noncommutative Formulas","domain":"Theoretical computer science","family":"116","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"cs.CC","summary":"We construct, in deterministic polynomial bit time, one tuple of rational matrices that detects every nonzero polynomial computed by a noncommutative division-free formula of a prescribed size. The matrices have dimension $`O(ns^2)`$ for n variables and formula size s , and the same tuple works over every field of characteristic zero.","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Uniform black-box noncommutative identity testing across characteristics"}