Abstract

We construct an excitation-conserving sequential-emission model and derive its complete emission isometry from finite-dimensional Hamiltonians. A $d$-dimensional code occupies a degenerate excited memory sector and exchanges its excitation with initially vacant radiation cells through prescribed pulses. After $N$ pulses the survival probability is $q_N={{\prod }_{j=1}}^N{\cos }^2{\theta }_j$. The optimal single-cell recovery error in half-diamond distance is $q_N(1-d^{-2})$, and the complete single-cell residual leakage has the same exact value. For $K$ emission mechanisms carrying an arbitrarily entangled $K$-cell code, the exact recovery error is $1-[1-q_N(1-d^{-2}){]}^K$, hence at most $K{q}_N$. A Duhamel estimate supplies a compatible finite-time implementation budget.

Emission-time dephasing alone does not destroy the logical code: time-resolved, label-coherent recovery remains optimal. Internal-label dephasing, destructive label-blind records, incomplete collection, and decoder-mode mismatch have different operational consequences. Entropy turnover is calculated but is not used to certify recovery.

A supplied execution record reports successful completion of all 32 predicates in the finite-matrix diagnostic script at $d=2$, $N=3$, ${\theta }_j=\pi /4$, with a memory-label detuning of strength $10^{-4}$ and numerical tolerance $2\times 10^{-10}$. The corrected exact targets are $q_N=1/8$, single-cell recovery and leakage $3/32$, and two-cell recovery $183/1024$. These reported checks support the selected matrix identities and Bell witnesses; they do not replace the analytical proofs or constitute diamond-norm optimization. The model is an externally scheduled, bare-energy-conserving evaporation analogue, not gravitational Hawking radiation or an autonomous microscopic black-hole model.