Abstract

We construct the finite certificate requested by the Family 227 audit plan without assuming its functional scaling-limit theorem. For critical zero-field Sherrington–Kirkpatrick heat-bath dynamics with rate-one clocks per spin, we freeze

where physical waiting time and lag are $2^{2/3}s$ and $2^{2/3}t$, and mean autocorrelations are multiplied by $2^{1/3}$. An exact four-state calculation proves, for every real coupling, that the rescaled stationary autocorrelation exceeds the rescaled uniform-quench autocorrelation by less than $1/65536$, uniformly on this compact. Consequently the same certificate holds with probability one under both Gaussian and Rademacher disorder, without truncating Gaussian couplings.

We distinguish this within-realization comparison from finite-size universality: at two spins the Rademacher autocorrelation functions are deterministic, whereas their Gaussian counterparts are nondegenerate. We also provide finite-state normalization checks, compact interpolation bounds, sampling and clock-history allowances, and a rate-perturbation ledger. The external stationary-edge, warming, entrance-selection, and functional replacement assertions are audited but not imported. Several ambiguities in the proposed plan are corrected, including the difference between a common limiting law and identical stationary and quench functions, and the existence of an implicit semigroup representation of the proposed limit. No thermodynamic-limit theorem, quantum SK theorem, QAOA identification, Page curve, or gravitational conclusion is proved.