OpenAI · 227-06 · 2026-09-24 · Probability and statistical mechanics
Stretched-exponential barriers for typical SK initial states
preprints/Stretched-exponential-barriers-for-typical-SK-initial-states-September-24-2026
Family 227. The dynamical phase transition in the Sherrington–Kirkpatrick model.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
For zero-field Gaussian SK heat-bath dynamics with rate-one updates per spin, proves worst-start cutoff on the scale for fixed , mixing time at , and stretched-exponential mixing from a Gibbs-sampled fixed starting configuration for , in probability over disorder. At criticality, rescaled stationary and quench autocorrelation processes have universal random limits for Gaussian and Rademacher disorder; the quench limit relaxes to the stationary limit.
At every fixed inverse temperature β > 1, we prove a stretched-exponential obstruction to mixing for the zero-field Sherrington–Kirkpatrick model from typical equilibrium configurations held fixed as initial states. The Gibbs mass of states whose total-variation distance from equilibrium at time exceeds 1/4 tends to one in probability over the disorder. This holds for rate-one-per-site heat-bath dynamics and after the same stated number of discrete update attempts.
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
This preprint is named in the Lean scope note for 227: Critical SK autocorrelation processes and dynamics across the temperature transition. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.
SKHighTemperature.lean · SKHighTemperature.lean
SKRatio.lean · SKRatio.lean
CriticalSKMixing.lean · CriticalSKMixing.lean
CriticalSK.lean · CriticalSK.lean
SKBarriers.lean · SKBarriers.lean
Page curve
A finite SK autocorrelation is not a Page curve
Family 227 records a classical critical SK quench and a claimed common functional limit. Oai227-A records a two-spin stationary--quench certificate at beta=1 on [4,5] times [1,2] and does not verify 227-01. The difference is less than 1/65536 for every real coupling. Gaussian and Rademacher finite-size laws are not identified. SKRatio.lean and CriticalSKMixing.lean end in sorry and are not this certificate. A classical autocorrelation is not a Page curve. A separable spin law is not gravity-generated entanglement and not an exclusion of classical gravity. QAOA is not this heat-bath dynamics. The authors of the external preprint are OpenAI. The companion does not verify those proofs.
Page curveOai227-A finite SK certificateEm04-A XY reductionHawk02-E regulated SYK