Theorem: Em04-A analytical release

Under the explicitly stated hypotheses:

1. The chain has a unique physical evolution and the exact reduction (eq:reduction).

2. Concurrence, the complete partial-transpose spectrum, logarithmic negativity, separability, purity, and coherence have the proved formulas and bounds above.

3. Protocol-B scaling uses $(\chi ,r)$, and single-$\chi$ universality fails in general.

4. The localized preparation generates entanglement, with the stated dissipative decay and conditional mixing conclusions.

5. Finite-window unitary and detuning comparisons, the two-site benchmark, and the residual interfaces hold.

6. Specified finite local instruments and readout types satisfy the proved probability, completeness, locality, no-signaling, and deferral identities.

7. Compressed oscillator position effects form a POVM, with the proved preparation, trapezoidal, tail, arithmetic, and completed-measurement error bounds.

The release is analytical. It does not assert completed source alignment, numerical regression, instantiated validated certificates, successful compilation, machine verification, or any excluded physical identification.

Proof. Lemma lem:physical and Theorem thm:reduction prove (i). Theorems thm:concurrence, thm:negativity, and Corollary cor:diagnostics prove (ii). Theorems thm:scaling and thm:shorttime prove (iii). Theorems thm:transient and thm:mixing prove (iv). Theorem thm:largechi, Propositions prop:disorder, prop:twosite, and the results of Section sec:residual prove (v). Theorems thm:instruments and thm:deferral prove (vi). The results of Section sec:bosonic prove (vii). None of those arguments requires an executed evidence package.