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

Certificate manifest

Stage 6: the one explicit finite certificate › Certificate manifest · lines 1421–1457

Item	Frozen value or verified statement
Size and temperature	$n = 2$ , zero field, $β = 1$ .
Clock convention	Independent rate-one clock at each of the two sites; holds retained.
Disorder quantifier	Every $J \in R$ , hence separately probability one under $N (0, 1)$ and symmetric ${- 1, 1}$ .
Initializations	Stationary law $π_{a}$ and independent fair-spin law $U_{2}$ .
Rescaling	Amplitude $v = 2^{1/3}$ ; physical waiting and lag $T s, T t$ , where $T = 2^{2/3}$ .
Compact	$[4, 5] \times [1, 2]$ , entirely inside positive times.
Exact difference	$v a e^{- 2 T s - T t} sinh (a T t)$ .
Uniform tolerance	Strictly less than $1/98304$ , hence less than $1/65536$ .
Finite arithmetic	$32 > 27$ , $64 > 54$ , $131 > 128$ , and $98304 > 65536$ .

This manifest, the four-state generator, and the proof above are the finite certificate. No unexecuted numerical assertion is needed to establish its inequalities.