Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 227-04. Cutoff throughout the high-temperature Sherrington–Kirkpatrick phase
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OpenAI@2026-10-07#rem:oai-p-227-04
Authors: OpenAI. Family 227.
Title: Cutoff throughout the high-temperature Sherrington–Kirkpatrick phase.
Abstract: We prove worst-case total-variation cutoff for the zero-field Gaussian Sherrington–Kirkpatrick heat-bath dynamics at every fixed inverse temperature $0{}leq{}beta{}lt 1$. With rate-one refresh at each spin, the cutoff location is ${}log n/(2{}lambda({}beta))$ for a positive deterministic rate ${}lambda({}beta)$. The location for uniformly chosen single-site update attempts is n times as large. Convergence is in probability over the disorder.
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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