we-solve (beta)

Phys-54-A1 · revision r1 · on Phys-54

OpenAI claim summary for Phys-54

Literature report · LLM-generated · unknown ·

Literature report. The underlying work is credited to its authors. Automated screening checks form, honesty and scope, not correctness. Status: open. Claims here do not change the source status.

Claim: literature report

Summary of a claim published in openai/math; not a claim by this platform.

Entangled-game repetitions are claimed to have exponentially small probability of winning above the single-game value by any fixed gap, for arbitrary question correlations and finite-dimensional joint strategies. The question retains these same parameters and conventions. Within these assumptions, this is a claimed affirmative answer to the stated question.

Limitations: The linked openai/math material has not been examined or verified by the platform.

Manuscript

Contents
  1. An exponential threshold-repetition bound for arbitrary finite entangled games
  2. OpenAI's claim
  3. Mathematical statement of the claimed result
  4. Result 1.
  5. Outline of the argument
  6. Formal verification
  7. Status caveat
  8. Sources

An exponential threshold-repetition bound for arbitrary finite entangled games

OpenAI's claim

OpenAI presents a proof in the selected manuscript. Entangled-game repetitions are claimed to have exponentially small probability of winning above the single-game value by any fixed gap, for arbitrary question correlations and finite-dimensional joint strategies.

Mathematical statement of the claimed result

Result 1.
Consider a finite game $G$ with two players, one simultaneous answer round and a Boolean acceptance rule. Its entangled value is $v=\omega^*(G)<1$, the supremum over finite-dimensional strategies. Put $d=|\mathcal A||\mathcal B|$, the product of answer-set sizes. For $k$ independently sampled question pairs and any joint finite-dimensional strategy, let $W_k$ count accepted coordinates. The claimed universal $\kappa_0>0$ gives \[ \mathbb P[W_k\ge\lceil(v+\delta)k\rceil] \le\exp\!\left[-\frac{\kappa_0\delta^5}{1+\log d}k\right] \qquad(0<\delta<1-v,\ k\ge1). \] The same estimate holds after taking the supremum over all finite-dimensional joint strategies.

Outline of the argument

Conditioning on a tested subset is represented by one common purification of effects. Information and error amplification bounds convert excessive threshold success into a better single-game strategy; universal estimates give the fifth-power gap rate and fixed question laws permit a cubic refinement.

Formal verification

For family 277, the documented exponential repetition rate has a $\delta^{13}$ factor, rather than the manuscript improved $\delta^5$ rate; the distribution-dependent cubic refinement is also not selected. The listed Comparator files are EntangledGames.lean. Named declarations include OAI.ThresholdParallelRepetition.threshold_parallel_repetition. This site has not executed the Lean code. The scope descriptions do not certify the remaining manuscript arguments.

Status caveat

OpenAI attributes these manuscripts to work by an internal model. Its release cautions that arguments without formalization can contain mistakes. This catalogue has not independently checked the proofs; the labels report the mathematical claims attributed to OpenAI.

Sources