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

The frozen external assertion

Stage 0: freeze the classical model and the external claim › The frozen external assertion · lines 365–409

Oai227-A@1#record:main

The external claim is that

Law_{D} (A_{n, J}, B_{n, J}) ⟹ Law_{g} (A_{g}, B_{g}), D \in {D_{G}, D_{R}},

C_{loc} ((0, \infty)) \times C_{loc} ((0, \infty)^{2}),

with the same limiting pair law for the two disorders. The stationary limiting law is not a point mass.

The quench starts from $U_{n}$ . Its selected entrance family has positive-time probability densities $h_{s}^{g}$ , satisfies a semigroup relation, and relaxes to equilibrium. In particular, the stated conclusion includes

a \leq t \leq b sup ∣ B_{g} (s, t) - A_{g} (t) ∣ ⟶ 0

in probability over $g$ as $s \to \infty$ , for $0 < a < b < \infty$ OAI227Quench,OAI227Stationary.

This record is not a premise of any local theorem below.

records. The family also records a high-temperature gap and cutoff, critical slowing, low-temperature barriers, and a critical mixing exponent. Their statements concern different quantities or temperature regimes Lean227,Catalogue. They are not premises of our finite certificate. This does not assert that the external quench manuscript has no dependencies on its companions: its own source explicitly cites stationary, spectral, and mixing inputs OAI227Background,OAI227Edge,OAI227Warming.

Displayed formulas in this passage

unlabeled · line 370
$Law_{D} (A_{n, J}, B_{n, J}) ⟹ Law_{g} (A_{g}, B_{g}), D \in {D_{G}, D_{R}},$
unlabeled · line 377
$C_{loc} ((0, \infty)) \times C_{loc} ((0, \infty)^{2}),$
unlabeled · line 388
$a \leq t \leq b sup ∣ B_{g} (s, t) - A_{g} (t) ∣ ⟶ 0$