Approximate complement certificates and finite tests

We import the finite-dimensional information–disturbance consequence of the Stinespring continuity theorem KSW (Section IV). For an isometric channel $\mathcal{N}$ with its complete complement $\mathcal{E}$, define full-diamond quantities

The imported estimates are

Ancilla enlargement in a Stinespring proof is mathematical dilation bookkeeping. It is not permission to give inaccessible physical factors to the decoder.

No companion Cheung manuscript is needed as a premise for this external theorem. Its half-diamond use is also documented in CheungEn07B,CheungHawk01B,CheungHawk03A.