What was already known
Polynomial decay was known for arbitrary entangled games, and exponential decay for anchored games. The unanchored general two-player case remained open.
AI involvement
OpenAI credits Astra with the argument and later Lean formalization; people selected problems and prepared the manuscript with the model. Sienicki and Sienicki checked a Chapter 6 conditioning expression and withdrew an earlier PDF-extraction objection.
OpenAI explicitly credits Astra with the argument and Lean formalization; humans selected problems and prepared the manuscript with the model.
Importance
The reported theorem extends exponential parallel repetition to general finite two-player entangled games.
Limitations
The statement concerns the specified finite entangled-game model. The Lean certificate is source-reported; no independent rebuild is documented. Human review documented for a conditioning lemma does not amount to a complete human check.
Technical verification
The source reports a complete Lean certificate for the selected theorem. A human audit checked only a conditioning lemma; neither the build nor semantic alignment was independently reproduced here.
Independent checking
Sienicki and Sienicki checked the Chapter 6 conditioning expression and withdrew an objection caused by a lost overbar; this is a partial human check.
- Checker
- Mikołaj Sienicki and Krzysztof Sienicki
- Scope
- Chapter 6 greedy conditioning lemma only
- Basis
- Reported by the linked checker
Formal checking
Lean manifest lists QuantumParallelRepetition.distributionUniformExponential with zero sorry and standard axioms.
- Checker
- OpenAI ten-proofs project, Lean 4 kernel and Comparator
- Scope
- Uniform exponential bound for finite two-player entangled games with value below one
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Sienicki and Sienicki explain and inspect the conditioning lemma; no complete human explanation of the later sampleability mechanism is documented.
Correction and publication history
Chapter 6 all-win repetition result has a distinct source and proof from the published threshold theorem.
Read this published revision