Abstract

We derive the finite random-state Page curve within an explicitly declared Enter-compatible model. A single logical-input-independent Haar unitary scrambles a prepared finite code; a conserving sequence then transfers quantum cells into a growing accessible radiation register. For every fixed pure input chosen independently of the unitary, the exact mean radiation entropy is

We also prove a simultaneous, all-prefix leading Page law for one sampled unitary. Destructive Enter defines a different process: its append-only records have nondecreasing Shannon entropy and cannot recover an arbitrary unknown quantum code. Their exact mean entropy is

which does not turn over.

Recovery is addressed separately. We give exact full-code recovery errors, a conservative Haar subcode-decoupling certificate, corrected flagged-transfer calibrations, and same-model endpoint and entropy comparison bounds. The Haar hypothesis, coherent access, and emission schedule are explicit additional assumptions, not consequences of Enter. The construction derives a finite Page curve and specifies a conditional route to a gravitational comparison; it does not construct a microscopic gravitational evaporation channel, an island formula, or the unresolved characteristic quantum coefficient of the supplied analytic programme.