Abstract

We give a finite-dimensional, reference-preserving formulation of six operational analogies associated with the Hawking narrative. The mathematical objects are a complete isometry, a declared accessible factor, its complete residual complement, destructive computational-basis readout, and classical discard. We prove complete-output restoration, the exact constant-complement criterion for full-code recovery, finite-program soundness, the sharp classical-record recovery obstruction, and the equality of readout-and-discard with partial trace. The presentation corrects several possible overstatements: an arbitrary isometry need not relocate the whole code into its residual; a nonconstant complement need not independently recover that code; unobserved residual readout cannot improve the existing accessible channel; and consumption of all named quantum registers does not prove that a complete physical complement has disappeared. A worked register-transfer schedule and a corrected quantum-computer narrative illustrate the analogies. Quantitative recovery and endpoint statements are separated from the exact results and explicitly identify their additional hypotheses. No metric, event horizon, Hawking spectrum, mass-loss dynamics, gravitational evaporation endpoint, or gravitational Page curve is derived. The contribution is an operational synthesis and separation argument, not a solution of black-hole evaporation.