Corollary: What an endpoint can and cannot certify

A certified constant complete complement proves quantum recovery, not purity of an arbitrary raw record. A purely classical endpoint with $d\ge 2$ cannot satisfy exact obligation (E4).

An information-free residual may still have positive dimension and positive energy. For example,

has zero leakage and residual energy $ϵ$.

Proof. Use Remark rem:purity and Corollary cor:classicalendpoint. The displayed residual channel is replacement by $|1⟩⟨1|$, so Theorem thm:exact applies directly.