Proposition: The genuinely record-only obstruction

Every purely classical returned channel on a $d$-dimensional diary has recovery error at least $b_d=1-1/d$. The statement applies if all receiver outputs, including $E$, are measured and only their records are returned. It does not follow merely from measuring $R$ while keeping $E$ quantum.

Proof. Every decoder after a classical-output channel is measure-and-prepare, hence entanglement breaking EntanglementBreaking. Its Bell output is separable, and every separable state has Bell overlap at most $1/d$. Testing the Bell projector gives half-diamond error at least $1-1/d$. The last assertion is established constructively below.