OpenAI reports universal critical SK quench autocorrelation limits

For zero-field Sherrington–Kirkpatrick heat-bath dynamics at β=1, stationary and fair-spin quench autocorrelations converge jointly as random functions after multiplying correlations by n^{1/3} and scaling waiting times and lags by n^{2/3}; Gaussian and Rademacher couplings have the same limiting law, and the quench limit relaxes to the stationary limit as waiting time grows.

Sources for this record

What was already known

Finite-size critical stationary autocorrelation scaling had numerical support and a companion stationary theorem; earlier soft-spin and spherical quench results used different models or asymptotic regimes.

AI involvement AI-led

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 Notable

Identifies a common random finite-size critical relaxation process for two coupling laws.

Limitations

The result uses rate-one clocks at every site and positive waiting times and lags. The linked Lean scope checks separate high-temperature or mixing-barrier claims, not this critical quench functional limit.

Technical verification Reported

Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.

Human understanding Few

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

2026-10-18 · publication

Primary manuscript, attribution, prior-work, and precise Lean-scope or conditional-input review for non-notifying local inclusion.

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