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One Rational Matrix Hitting Point for Noncommutative Formulas

OpenAI

OpenAI Mathopenai-math/One-Rational-Matrix-Hitting-Point-for-Noncommutative-FormulasSep 24, 2026cs.CCAI-generatedscore 0

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.

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