Proposition: Operational discard does not entail annihilation

The observable equality $\mathsf{Drop}\circ \mathsf{Enter}={\mathrm{Tr}}_B$ does not imply that the complete physical input has been annihilated. Under a complete isometric realization, distinct code states remain distinct on the complete output.

Proof. Lemma lem:erasure-interface supplies an isometric realization whose omitted output retains the required coherent degrees of freedom. Theorem thm:global preserves their complete trace distances. Thus the same observable discard channel is compatible with complete preservation, and its equality with partial trace cannot entail complete annihilation.

This proves underdetermination of the physical conclusion, not a theorem that every physical gravitational evolution must be isometric.