Example: The complete diary is in the residual

For

radiation is constant and has recovery error $a_d$. The complete residual exactly recovers the diary. Its computational record alone cannot do so: Theorem thm:classical applies. Readout-and-drop leaves radiation unchanged.

Proof. The channels are a replacement channel and the identity, up to local isometric dictionaries. Equation (eq:ad) gives the radiation error. The readout assertions follow from Theorem thm:classical and Lemma lem:erasure-interface.