What ``under both disorders'' means in the certificate

We certify the same statement separately under each disorder: for the same realization $J$, stationary and quench autocorrelations are close on the stated compact. Our proof is stronger in this particular finite model: it holds for every $J\in \mathbb{R}$.

We do not identify Gaussian and Rademacher finite-size autocorrelation laws. Proposition prop:finite-laws shows that those laws are different. A cross-disorder finite-law approximation would require its own chosen metric, tolerance, and theorem.