From Marginal Entropy to Calibrated Sameness: Reframing the Black-Hole Information Paradox with DSFL

We recast the black-hole information problem in a single comparison geometry where “information” is an operational, quadratic observable: the calibrated residual of sameness between a statistical blueprint and the physical response. Two structural principles drive the analysis. 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 physically allowed coarse-grainings or channel compositions. Second, a dual-scale feedback law separates immediate local dissipation from slow causal relay; horizons throttle the slow loop, yielding a Lyapunov (ringdown) envelope for the exterior residual. Modeling Hawking emission as an admissible channel gives stepwise nonincrease of the exterior residual, compatible with locally thermal flux, while global purification proceeds via correlations (early/late radiation or island wedges). The paradox dissolves when we track what semiclassics actually constrains—calibrated sameness—rather than marginal entropy. We prove global and exterior inequalities, a causal “no-relay” barrier, a ringdown envelope, and propose falsifiable diagnostics.