Scope, provenance, and the corrected question

The physical information problem arises from the relation between black-hole emission and the quantum evolution of the complete initial state Hawking1975,Hawking1976. This paper addresses only the following finite-code question:

This is not the assertion that every physical black-hole question reduces to finite-dimensional channel theory. It is the recovery obligation for the finite interface specified below. A physical application must justify that interface in its own model.

The documentary predecessors are Cheung's Hawk04-A, Hawk04-B, and En07-A CheungHawk04A,CheungHawk04B,CheungEn07A. The present proofs do not assume their theorem statements. Where a standard mathematical theorem is imported, it is named explicitly and cited to an external source.

“complete” means. The inaccessible output must include every output omitted from the observer's accessible description: the remaining source, preparation purifiers, discarded field modes, unused cells, apparatus environments, and any other unreturned quantum registers. A mixed preparation is not made complete by ignoring its purification. A selected residual marginal is not necessarily the complementary channel.

“self-contained” means here. The exact statements and elementary certificates are proved below. We use the usual finite-dimensional Kraus/Stinespring structure and standard diamond-norm facts Stinespring,Watrous. Approximate information–disturbance conversion uses the external KSW theorem KSW; its normalization and consequences are proved here, but its continuity theorem is not reproved.

boundary. The supplied manuscript identifiers and versions are cited as provided records. Their citations do not assert journal publication, independent proof verification, or a scan of the entire Enter series. In particular, statements about an unconstructed analytic object are not converted into nonexistence theorems.