Theorem: Complete finite payload and record transport

After hop $j$, every initial payload-reference state has the form

The logical channel is exactly the identity, including references, and arrival occurs at $T_{\mathrm{dep}}+L/c$. All communication paths lie inside the supplied cone.

A classical record can be forwarded on the same route. An operation conditioned on that record at the receiver is performed only after both record and payload arrive. The resulting complete recorded residual instrument is the declared one with its payload relocated.

Proof. Each exchange transfers the whole payload factor and all of its reference correlations into the next blank factor. Induction proves the state identity. Every hop covers spatial distance $L/n$ in time $L/(nc)$, hence follows a null transfer path in the developed chart. Its pullback is causal.

Apply the payload argument with the classical record included in the reference. Forward its jointly classical blocks by classical copying and causal communication. At the receiver the code selects the same conditional maps. No copying of an unknown quantum state is used.