Corollary: Conditional evaporation implication

If one physical gravitational model justifies the four obligations in Definition def:four, with an interface to which the preceding theorem applies, its declared outgoing endpoint recovers the finite code exactly, or within the stated approximate allowance. A subsequent terminal record is distinct from this quantum recovery.

Proof. Apply Theorem thm:endpoint to that justified complete interface. Apply Lemma lem:erasure-interface and Theorem thm:classical to any subsequent destructive record interface, with its actual surviving registers.