What was already known
Entangled players can coordinate across repeated games, so independent-trial concentration does not apply. A uniform threshold parallel-repetition bound for arbitrary finite games and correlated question distributions remained open in the manuscript’s account.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Gives universal exponential threshold decay for finite-dimensional entangled strategies.
Limitations
The pinned Lean rate has δ to the thirteenth power; the manuscript states a stronger fifth-power rate that is outside this selected formalization. Answer alphabets are A and B, and strategy dimension is unrestricted but finite.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note proves the displayed δ¹³ bound uniformly over every joint finite-dimensional strategy and its supremum.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For every finite two-player game with finite-dimensional entangled value v<1 and arbitrary correlated questions, the maximum probability of winning at least a fraction v+δ of k repetitions decays at least as exp(−κδ¹³k/(1+log(|A||B|))) for one universal κ>0 and 0<δ<1−v.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision