A mathematical reference is not a delivered control

A record $R$ can be included in $E$ when proving (eq:route). This proves preservation of its correlations with the transported payload. It does not move $R$ to the receiver.

For a diagonal classical register, copying has the canonical channel

On a classical–quantum input it preserves the full correlation with the quantum residual while creating a new classical copy. Delivery of that copy requires a separately permitted causal wire.