Theorem: Em03-E finite dynamical release

For the explicitly specified finite model:

1. a message qubit is encoded into a degenerate source-energy sector with independent initial environments;

2. explicit bounded internal and emission Hamiltonians generate the two radiation prefixes and conserve the declared free energy;

3. the complete radiation channel, all message matrix-unit outputs, and the complementary channel are calculated;

4. individual cells are exactly message-independent, while collective radiation has the distinguishability values of Proposition prop:distinguish;

5. an explicit complete decoder attains the optimal referenced recovery error and Bell-test fidelity (eq:optimalrecovery);

6. the named complementary-channel replacement distance is exactly (eq:leakage);

7. calibrated finite occupation emissions have the state, count, mean, and replacement-channel comparisons in Theorem thm:matching;

8. newly constructed finite coherent access and complete decoder controls give the end-to-end budget (eq:endrecovery);

9. destructive verification has complete-record and independent-trial certificates, while classical measure-and-prepare processing has the stated quantum-recovery obstruction;

10. the exact entropy and reference-information trajectories are those of Theorem thm:entropy.

These conclusions are finite model statements. They do not derive the interactions from quantum gravity, identify the payloads with scalar Hawking packets, construct local black-hole evaporation, derive a Page curve, restore black-hole unitarity, resolve the firewall question, or determine an evaporation endpoint.

Proof. The encoding and model specification establish (i). Theorem thm:evolution proves (ii). Theorems thm:channel and thm:complement prove (iii). Corollary cor:private and Proposition prop:distinguish prove (iv). Theorem thm:recovery proves (v). Theorem thm:leakage proves (vi). Theorem thm:matching proves (vii). Proposition prop:access, Lemma lem:stability, and Theorem thm:endrecovery prove (viii). Lemma lem:readout, Theorem thm:recordgap, the printed concentration argument, and Proposition prop:EB prove (ix). Theorem thm:entropy proves (x).

No named gravitational microscopic dynamics or local field–probe correspondence is among the model inputs. The separate comparison maps explicitly concern selected occupation factors. The excluded physical conclusions therefore are not additional assertions of the release.