Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 227-02. Functional universality of critical SK autocorrelations
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OpenAI@2026-10-07#rem:oai-p-227-02
Authors: OpenAI. Family 227.
Title: Functional universality of critical SK autocorrelations.
Abstract: We prove that the stationary spin autocorrelation of the zero-field Sherrington–Kirkpatrick model at inverse temperature β = 1 has a common functional scaling limit for Gaussian and Rademacher couplings. With rate-one heat-bath clocks at every site, time is scaled by n2/3 and the mean spin autocorrelation is multiplied by n1/3. The functions converge in law uniformly on compact positive-time intervals. Their limiting law is not a point mass: it retains sample-to-sample randomness, and its functions decay to zero at large times.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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