Proving an Arrow of Time under Universal Time: A DSFL Framework for Black-Hole Evaporation

We develop a clock-neutral framework in which “time” is universal and measured by a single operational quantity: the calibrated residual of sameness between a statistical blueprint and the physical response, both embedded in one comparison geometry. Two structural ingredients generate an intrinsic arrow of time. First, admissible evolutions—those that respect the calibration and are nonexpansive in the comparison norm—obey a Hilbert-space data-processing inequality, so the residual cannot increase under any physically allowed step. Second, a dual-scale feedback law separates an immediate, local dissipation loop from a slow, causal relay; causal boundaries throttle the relay, yielding a Lyapunov-type ringdown envelope set by the least-damped mode. All statements are invariant under reparametrization and admit an intrinsic “DSFL-time” in which decay appears with unit slope on semi-log axes. Applied to black-hole evaporation, the Hawking channel is an admissible map (stepwise contractive in the relevant norm), horizons enforce a no-relay barrier, and exterior residuals decay while global purity is carried by correlations (early/late radiation or islands). We prove global and local no-inflation inequalities, the causal barrier, and the ringdown envelope, and we outline falsifiable diagnostics—projection/data-processing checks, ringdown slopes, relay toggles, and cross-window correlation structure—suitable for simulations and data.