Abstract

We give a finite-dimensional, reference-preserving formulation of the Enter/Page analogy and correct several incompatible claims in its original narrative. Complete isometric evolution preserves an unknown quantum code, but recovery from a declared accessible output is equivalent to constancy of that output's complete complementary channel. Destructive Enter returns a classical record, not the consumed quantum input. A channel retaining only such a record has optimal whole-code recovery error at least $1-1/d$, at every stage, including the endpoint. Moreover, the Shannon entropy of an unedited cumulative classical record cannot decrease as outcomes are appended.

An explicit energy-conserving transfer schedule has a rise-and-fall quantum radiation entropy for pure unreferenced inputs, while its recovery error decreases monotonically. The same schedule after destructive readout does not purify the accumulated classical record. We prove exact recovery, leakage, and readout-error formulas; construct matched entropy histories with opposite endpoint recoverability; establish the readout-and-drop identity; and formulate a same-model endpoint certificate with quantitative error bounds. The result is a corrected operational analogy, not a gravitational Page-curve derivation or a construction of the unresolved characteristic quantum coefficient in the supplied analytic programme.