Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 116. Uniform identity testing for noncommutative formulas
Family claims › Theoretical computer science · lines 869–874
OpenAI@2026-10-07#rem:oai-116
For each characteristic, constructs in deterministic polynomial bit time a polynomial-dimensional matrix tuple detecting every nonzero division-free noncommutative formula of bounded size over any field of that characteristic. Rational formulas over also admit polynomial-size hitting lists whenever they have a defined rational-matrix evaluation.
The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.
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- remark: Remark: Family 103. Derandomization of logarithmic space: L= (RL)= (BPL)
- remark: Remark: Family 104. Quasipolynomial algorithms for mean-payoff, stochastic and parity games
- remark: Remark: Family 105. The 2-to-1 Games Conjecture with perfect completeness
- remark: Remark: Family 106. Hardness of coloring three-colorable graphs
- remark: Remark: Family 107. Matrix multiplication with exponent at most 9/4
- remark: Remark: Family 108. A cubic permanent–determinant lower bound
- remark: Remark: Family 109. Integer multiplication below n n