# Entangled-game soundness planning reference

Family 277: Threshold repetition for entangled games. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Quantum protocol researchers can relate repeated-game thresholds to exponential rejection probabilities under finite game and entanglement assumptions.

## Applicability and commercial boundary

Constants depend on the game and margin; a qualitative exponential bound may not give practical sample counts. Laboratory imperfections or protocol composition need separate analysis.

## Initial business decision

Conditional research. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Extract an effective rate for one finite game and compare with existing finite-block soundness analysis.

## Evidence scope

The catalog statement was individually reviewed. This record does not imply a manuscript proof review or formal-scope comparison. No independent Lean check was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Main source

[Threshold parallel repetition for finite-dimensional entangled games](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Threshold-parallel-repetition-for-finite-dimensional-entangled-games-September-25-2026/paper.pdf).