Enter, Hawk05-B, 2026, pp. 1-21
Hawk05-B A Finite Page-Curve Derivation under the Enter Discipline
Ngo Cheung
15 October 2026
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 S̅_k = (H_{s^N} − H_{s^{max (k, N − k)}} − (s^{min (k, N − k)} − 1)/(2s^{max (k, N − k)}))/(ln 2). 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 H̅_k = (H_{s^N} − H_{s^{N − k}})/(ln 2), 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.
Bibliographic record
- Title
- Hawk05-B A Finite Page-Curve Derivation under the Enter Discipline
- Author
- Cheung, Ngo
- Publication date
- 2026/10/15
- Institution
- Enter
- Report number
- Hawk05-B
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 21
- Language
- en