Abstract

We study preservation of an arbitrary finite-dimensional quantum code, including all external reference correlations, in a declared sequential emission process. We translate the Kretschmann–Schlingemann–Werner information–disturbance theorem into half-diamond normalization and separate its worst-case guarantee from single-input entanglement and entropy diagnostics. We then construct an energy-conserving sequence that generates its own key resource, transfers an encrypted logical system through occupied radiation sectors, retains vacuum and unsuccessful-transfer branches, and releases every residual degree of freedom through an explicitly separate endpoint map. At each pre-endpoint prefix, the optimal recovery error and optimal constant-channel leakage distance are both $s_t(1-d^{-2})$, where $s_t$ is the probability that transfer remains pending. Individual emitted blocks are message-independent, whereas the joint radiation carries the logical coherence. Reference mutual information and its conditional increments are calculated exactly. Thermal occupation comparisons include explicit truncation errors and compatibility obstructions; no agreement with Hawking pair-production dynamics is inferred from local statistics. A second conserving evolution has the same radiation density operators for one specified preparation, and the same radiation entropy histories for every pure code preparation, but retains the code in an inaccessible memory. The counterexample discloses its different endpoint and does not challenge island or entanglement-wedge reconstruction results. Coherent access, destructive number measurement, complete-output erasure, and regulated implementation errors have separate certificates. The construction is a finite field-sector completion, not a microscopic theory of realistic black-hole evaporation.