Introduction, attribution, and scope

The assertion

is a theorem about reversible quantum dynamics. It is not, by itself, a derivation of the microscopic dynamics of an evaporating black hole.

Hawking's radiation calculation and his subsequent information-loss proposal provide the historical setting Hawking1975,Hawking1976. The relevant tension is between a complete reversible description and a proposed final description that fails to preserve arbitrary initial quantum states. Thermal occupation data, local radiation marginals, and a complete input-to-output quantum channel are different objects.

The exact no-hiding principle is due to Braunstein and Pati BraunsteinPati. Exact error correction and its syndrome structure are established in the work of Knill and Laflamme KnillLaflamme. Approximate information–disturbance relations are supplied by Kretschmann, Schlingemann, and Werner KSW,KSWContinuity. We do not claim these principles as new results. We give local proofs of the exact statements needed here and make the approximate external input explicit.

The supplied Cheung manuscripts motivate the complete-output discipline adopted in this paper. Hawk01-B distinguishes entropy histories from reference-preserving recovery. Hawk02-D supplies an autonomous quadratic benchmark with a complete scattering endpoint. Hawk02-E specifies an interacting regulated source–reservoir interface but does not establish its small dynamical residual bound CheungHawk01B,CheungHawk02D,CheungHawk02E. The operational manuscripts separately identify decoder execution, coherent collection, and channel-level error composition CheungEn02B,CheungEn02C,CheungEn02E,CheungEm03C. The dephasing comparisons in Em05-A and Em05-B distinguish delivered occupation from recovered quantum coherence CheungEm05A,CheungEm05B.

. This paper supplies:

1. a complete proof of global code preservation under unitary evolution;

2. an exact complete-complement recovery theorem and decoder;

3. counterexamples repairing overly broad readings of no-hiding;

4. a self-contained finite-regulator certification interface for the specified interacting architecture;

5. an exact, nonzero-coupling interacting-family negative control;

6. an access-preserving endpoint continuity theorem.

It is a theorem-and-certification paper, not a claim of a new universal resolution of black-hole evaporation.

policy. Cheung citations identify the supplied versions or excerpts. They are comparisons, not unprovided theorem premises. The model-specific arguments used below are proved in this source. No external mathematics catalogue is a premise.