Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 277-01. Threshold parallel repetition for finite-dimensional entangled games
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OpenAI@2026-10-07#rem:oai-p-277-01
Authors: OpenAI. Family 277.
Title: Threshold parallel repetition for finite-dimensional entangled games.
Abstract: For every finite two-player game with entangled value v < 1, we prove exponential decay for the probability of winning at least a $v+{}delta$ fraction of k independent repetitions, uniformly over all finite-dimensional joint strategies. The result allows arbitrary correlated question distributions and holds for every $0{}lt {}delta{}lt 1-v$ and k ≥ 1. Its universal rate is proportional to ${}delta{}5/(1+{}log(|{}mathcal A||{}mathcal B|))$, where ${}mathcal A,{}mathcal B$ are the answer alphabets. For each fixed question distribution, we also obtain an explicit cubic rate in δ.
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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