# Spin sampler clock and regime audit

Family 227: Critical SK autocorrelation processes and dynamics across the temperature transition. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

MCMC researchers can document heat-bath update clocks and beta regime when using SK mixing statements to justify sampling budgets.

## Applicability and commercial boundary

The selected formal cutoff range is beta<1/2, versus the paper's beta<1; critical formal upper bounds are weaker than n^(2/3+o(1)), and newer autocorrelation laws are outside the inspected scope. Per-site continuous clocks and single-site discrete update counts differ by n.

## Initial business decision

Prototype evidence workflow. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Build an explicit clock conversion and scope ledger before using a mixing bound as a stopping rule.

## Evidence scope

The catalog statement was individually reviewed. Main-paper abstract passages and available family scope notes were also inspected; paper-level theorem and algorithm details still require deeper review. No independent Lean check was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Main source

[Universality of critical quench autocorrelations in the Sherrington–Kirkpatrick model](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026/main.pdf).