Abstract

We develop a proof-based extrapolation framework for the finite Enter interfaces of Hawk04-C. The operational core consists of a complete isometry, declared accessible and inaccessible outputs, quantum-return decoders, destructive readout, and explicit classical discard. We prove exact calibration formulas for a partial-SWAP schedule and a flagged sequential-transfer model, including their different information targets. We establish fixed-code approximation and growing-code certification statements, reconstruct a finite-band reservoir regulator, and give an independent thermal-pair truncation certificate. The regulator is not transferred to a collapsing-shell Bogoliubov model without a separate comparison theorem.

A supplied luminosity law is treated as an additional physical hypothesis. Under fixed massless-species and greybody scaling assumptions, we derive the inverse-square power law and the resulting cubic cutoff-lifetime formula, together with perturbation and discretization bounds. These conclusions stop at a positive validity cutoff and do not determine Planck-scale behavior. Entropy turnover, approximately thermal observations, complementary decoupling, and full-code recovery are separated by explicit counterexamples and dimension constraints. An access-preserving endpoint package yields a fixed-decoder certificate; terminal residual readout-and-discard leaves the existing radiation channel unchanged.

The resulting predictions are conditional on independently supplied dynamics, access, approximation, luminosity, and endpoint hypotheses. No gravitational evaporation channel, universal Page-time recovery transition, final-burst spectrum, or absence of physical remnants is derived. The contribution is a coherent certification architecture and a set of calibrated tests, not a solution of black-hole evaporation.