Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 227-03. A spectral gap throughout the high-temperature Sherrington–Kirkpatrick phase
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OpenAI@2026-10-07#rem:oai-p-227-03
Authors: OpenAI. Family 227.
Title: A spectral gap throughout the high-temperature Sherrington–Kirkpatrick phase.
Abstract: For every fixed inverse temperature $0{}lt {}beta{}lt 1$, we prove that the unscaled spectral gap of single-site heat-bath dynamics for the zero-field Gaussian Sherrington–Kirkpatrick model is bounded away from zero with probability tending to one over the disorder. Equivalently, the Gibbs law satisfies a dimension-free Poincaré inequality for all functions.
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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