Manuscript Oai227-A@1 · Oai227-A.tex · section · 7f45f607

Audit 3: warming in the n 2/3 window

Stage 1: finite identities and the five-stage audit › Audit 3: warming in the n 2/3 window · lines 567–588

The external warming statement concerns positive-time Gibbs-relative densities, entropy, and heat kernels at times $s T_{n}$ . Its constants are controlled on disorder events chosen to meet a prescribed confidence, and its stronger kernel bound begins beyond a deterministic rescaled time tending to zero OAI227Warming (thm:warming).

The audit must distinguish:

finite positive-time density bounds from distance to the equilibrium density 1.

A bound by a finite function of $s$ does not itself prove that the distance to equilibrium tends to zero.

The time unit $T_{n} = n^{2/3}$ is dynamical bookkeeping. No positions, spatial propagation radius, or metric are specified by it.

Displayed formulas in this passage

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$finite positive-time density bounds from distance to the equilibrium density 1.$