Theorem: Em03-B version 2 release

Under the explicitly stated radiation input and apparatus model:

1. the normal geometric packet marginal and finite carrier–record interface are constructed;

2. a smooth finite-switching passive capture interaction has the exact kernel (eq:captureann), and its referenced certificate (eq:capbudget) includes nonvacuum mode mismatch, preparation, and justified vacuum loss;

3. coherent oscillator–register extraction is implemented by the explicit swap pulses, with exact sharp-tail comparison (eq:sharpK);

4. global bounded perturbations and support-only control certificates yield their distinct proved tail regimes;

5. a complete pointer instrument with quantum noise, assignment noise, spectator coupling, preparation imperfections, and visible failures has the derived budget (eq:readbudget);

6. the derived transfer and readout budgets give the complete referenced record comparison and the mean and count-law bounds of Theorem thm:model;

7. the tolerance schedule is constructive within its stated parameter family, with its resource growth and possible error floors retained.

These statements establish a specified apparatus-model realization, not a local Schwarzschild detector or a laboratory realization. No global radiation Fock density, collapse packet limit, nondestructive field instrument, evaporation mechanism, or quantum-gravitational correction is established.

Proof. Theorem thm:marginal, Proposition prop:carrier, and Theorem thm:record prove (i). Theorem thm:capturekernel, Lemmas lem:window–lem:modeerror, and Theorem thm:captureerror prove (ii). Theorem thm:extraction and Proposition prop:compile prove (iii). Lemma lem:Duhamel and Proposition prop:controlregimes prove (iv). Theorems thm:assignment and thm:readbudget prove (v). Theorems thm:transfer and thm:model prove (vi). Theorem thm:tolerance and Section sec:resources prove (vii).

The specifications include no local Schwarzschild system–probe coupling or experimental correspondence theorem. None of the excluded conclusions is an additional implication of the constructed finite interfaces.