Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 227-05. Critical slowing down in the Sherrington–Kirkpatrick model
Manuscript map · lines 6715–6724
OpenAI@2026-10-07#rem:oai-p-227-05
Authors: OpenAI. Family 227.
Title: Critical slowing down in the Sherrington–Kirkpatrick model.
Abstract: At the critical inverse temperature β = 1, we prove slow mixing for zero-field Gaussian Sherrington–Kirkpatrick heat-bath dynamics from typical equilibrium configurations held fixed as initial states. For every deterministic sequence $t_n=o(n{}{2/3})$ in rate-one-per-site time, the Gibbs mass of initial states whose time-tn total-variation distance from equilibrium exceeds 1/4 tends to one in probability over the disorder. The same statement holds for every deterministic integer sequence $k_n=o(n{}{5/3})$ of uniform-site update attempts.
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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