Abstract

A microscopic derivation of black-hole evaporation must determine geometry, emission, and information transfer from stated dynamics. A fixed-background spectrum determines none of these three outputs jointly. This paper supplies a precise conditional interface rather than claiming the missing quantum-gravitational derivation. We prove a reference-preserving sequential error bound, an exact constant-complement recovery criterion, its quantitative information–disturbance consequences, and a stability theorem for residual-leakage certificates. We also construct two finite, energy-conserving emission models with identical late thermal states and energy distributions but different assisted recovery errors. A separate entropy inequality makes explicit the pair-state hypotheses relevant to small-corrections arguments. The semiclassical stress-energy problem, regulator removal, characteristic-product admission, and endpoint completion remain independent obligations. The supplied Cheung manuscripts are cited as versioned source records, not independently verified premises. No microscopic black-hole Hamiltonian, realistic endpoint, ultraviolet completion, spacetime-emergence theorem, or inherited quantum-coefficient admission is asserted.