Scope, sources, and the question actually answered

A recovery certificate and successful recovery are different results. For a black-hole application, successful recovery must additionally refer to a specified physical code, a specified radiation access algebra, and a complete residual output.

The supplied versions of Cheung's manuscripts already maintain these distinctions: Hawk01-B separates entropy histories from code-wide recovery; Hawk02-A separates a transfer interface from its gravitational derivation; and Hawk02-C supplies an autonomous source–boson comparison while explicitly withholding a black-hole identification CheungHawk01B,CheungHawk02A,CheungHawk02C. Hawk03-A distinguishes an encoded radiation algebra from an independent interior tensor factor CheungHawk03A. The operational manuscripts distinguish information availability, decoder existence, executable access, and coherent cutoff errors CheungEn02B,CheungEn02C,CheungEn02E,CheungEm03C.

The construction here follows that discipline. It proves actual dynamical recovery and an asymptotic endpoint in a fully specified quadratic fermionic model. It does not identify that model with the interacting SYK–Majorana evaporation proposal.

The relevant external SYK literature supplies substantial but different results. Chen, Qi, and Zhang study a SYK system coupled to Majorana chains, with thermofield-double preparation, replicated entropy dynamics, and information associated with a classical control bit ChenQiZhang. Kourkoulou and Maldacena construct pure SYK states with a nearly-${\mathrm{AdS}}_2$ interpretation KourkoulouMaldacena. Nakayama, Miyata, and Ugajin study a two-dimensional operator-insertion code and recovery maps in SYK NakayamaMiyataUgajin. These are not silently identified with the code and channel below.

Likewise, gravitational reconstruction results are not denied. The JT-plus-bath analysis of Almheiri, Engelhardt, Marolf, and Maxfield and the gravitational Petz reconstruction argument of Penington, Shenker, Stanford, and Yang contain additional geometric and algebraic structure AEMM,PSSY. An entropy-only counterexample is not a counterexample to those results.

status. References to Cheung identify the manuscript codes, versions, and excerpts supplied with the development request. Full publication metadata and independent verification were not supplied. No theorem below relies on an unprovided theorem from those manuscripts. Model-specific statements used in the benchmark are proved locally.

is not claimed. The terms “source” and “reservoir” below describe lattice degrees of freedom. They do not mean “black hole” and “Hawking radiation.” The title therefore deliberately does not claim a solution of black-hole evaporation.