Abstract

We construct a time-independent, excitation-conserving source–boson Hamiltonian with a finite logical code and derive its complete emission isometry. The prepared one-excitation sector is a regular Friedrichs model with identical, orthogonal logical-label channels. Its survival amplitude and emitted wavefunction determine the accessible channel and its complete complement.

For collection in a prescribed finite packet subspace, let $q(T)$ be source survival and ${\ell }_N(T)$ the uncollected one-particle weight. Both optimal recovery error and complete residual leakage, in half-diamond distance, are exactly $(1-d^{-2})[q(T)+{\ell }_N(T)]$. An identified complete packet approximation has distance at most $\sqrt{2{\ell }_N(T)}$, proved from its isometries rather than from discarded probability alone.

A positive-frequency semicircle form factor gives a bound-state-free prepared spectral measure, an explicit survival law, a finite-time survival bound, and predetermined Chebyshev packets with a factorial collection-tail certificate. A finite autonomous chain supplies a separate predictive complete-output approximation. Checked invariant-sector perturbations give a Duhamel allowance. These estimates provide a nonempty finite-time regime with implemented recovery error at most any prescribed $\epsilon \in (0,1)$.

The supplied execution manifest reports completion of all 18 finite-proxy predicates at $d=2$, $c=1$, ${\omega }_0=3$, $T=1$, with eight collected packets and a 24-packet reference chain. Its reported recovery/leakage formula is $0.2494586279164458$. The record supports selected finite-matrix identities and norm comparisons; it is not continuum simulation, numerical diamond-norm optimization, or machine proof verification. An arithmetic-aware interface separates exact truncation bounds from floating-point execution evidence.

The bridge is an engineered source–field model, not a gravitational Hawking-emission mechanism, microscopic black-hole Hamiltonian, Page curve, or spacetime-emergence theorem.