Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 116-01. Uniform Matrix Hitting Points in Every Positive Characteristic
Manuscript map · lines 4715–4724
OpenAI@2026-10-07#rem:oai-p-116-01
Authors: OpenAI. Family 116.
Title: Uniform Matrix Hitting Points in Every Positive Characteristic.
Abstract: 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 𝔽p 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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