Theorem: Em03-C joint operational release

Under the stated stationary radiation input and effective apparatus specification:

1. the complete normal two-packet Gaussian state, joint count law, independence criterion, and Wick correlations are constructed;

2. the joint finite carrier and complete destructive record retain spectators and references, with exact joint count-tail error and a separately proved coherent-tail comparison;

3. compact orthonormal temporal modes and a shared-port two-memory interaction are constructed, with a derived joint capture certificate;

4. joint preparations, coherent extraction, global bounded controls, correlated assignment noise, and complete pointer readout give the derived setting budgets (eq:transferbudget)–(eq:settingbudget);

5. a phase-sensitive informationally complete finite measurement family has the statistical and trace-distance reconstruction bounds of Theorem thm:reconstruction;

6. specified bounded state departures have the operational discrimination certificate of Theorem thm:discrimination;

7. identical accessible inputs cannot reveal an unknown label, and a constant message-to-radiation channel cannot recover reference entanglement.

Statistical conclusions retain Assumption ass:trials; Enter terminology retains Assumption ass:Enter. Alternative-state certificates require their own named joint participating preparation and moment bounds.

No local Schwarzschild detector, collapse-packet limit, quantum-gravity correction, microstate-dependent evaporation channel, Page curve, island construction, restored unitarity, firewall resolution, or evaporation endpoint is established.

Proof. Theorems thm:gaussian and thm:counts prove (i). Theorem thm:jointrecord and Lemma lem:coherenttail prove (ii). Lemmas lem:windows–lem:mode and Theorems thm:sharedcapture–thm:capturebudget prove (iii). Proposition prop:extraction and Theorems thm:transfer, thm:readout, and thm:settings prove (iv). Proposition prop:IC and Theorem thm:reconstruction prove (v). Theorem thm:discrimination proves (vi). Theorems thm:nolabel and thm:noreference prove (vii).

The constructed model contains none of the local-coupling, collapse, or microscopic dynamics required for the excluded physical conclusions. Their outstanding interfaces are stated in Section sec:open.