Functional universality of critical SK autocorrelations

We prove that the stationary spin autocorrelation of the zero-field Sherrington–Kirkpatrick model at inverse temperature β = 1 has a common functional scaling limit for Gaussian and Rademacher couplings. With rate-one heat-bath clocks at every site, time is scaled by n${}^{2/3}$ and the mean spin autocorrelation is multiplied by n${}^{1/3}$. The functions converge in law uniformly on compact positive-time intervals. Their limiting law is not a point mass: it retains sample-to-sample randomness, and its functions decay to zero at large times.