Theorem: Em03-D analytical release

For one normalized positive-frequency massless s-wave packet on the Schwarzschild exterior:

1. its bounded quadrature effect and inherited Unruh probability are identified;

2. real compact bulk tests converge to its scattering coefficient with the explicit covariance error (eq:packeterror);

3. a smooth compact local bilinear scalar coupling and future probe effect have the exact induced form (eq:inducedeffect);

4. the advanced evolution gives the explicit compact-observable transfer error (eq:transfererror);

5. a specified independent quasifree Hadamard probe preparation suppresses residual noise with (eq:noisebound), while its conjugate variance and readout-test effort grow as stated;

6. these constructions prove the state-class expectation comparison (eq:mainbound) and the finite resource-dependent schedule of Theorem thm:tolerance.

The construction uses full angular-shell access and a coupling zone that may grow with accuracy. Complete stationary scattering, standard local Green/scattering theory, and the bulk Unruh-state identification are the declared external inputs.

The release is a local system–probe realization of one bounded packet-observable comparison. It is not a pointlike detector, a packet-number instrument, coherent state transfer, or equivalence with Em03-C's effective Markov apparatus. No collapse-packet theorem or quantum-gravitational evaporation result is established.

Proof. Equation (eq:packetcoefficient) and Corollary cor:baseline establish (i). Theorem thm:packetbridge proves (ii), using its displayed Cauchy and spectral constructions. Specification spec:local and Theorem thm:induced prove (iii). Proposition prop:Neumann and Theorem thm:transfer prove (iv). Propositions prop:squeezedstate and prop:effort, together with (eq:noisebound), prove (v). Theorems thm:main and thm:tolerance prove (vi).

The support, species, state-class, and external-theorem restrictions are retained throughout. No excluded dynamical, instrument-level, or laboratory construction appears in these proofs.