Theorem: Reference-preserving regular transport

For every payload–reference input ${\rho }_{A_{0}E}$, after hop $j$ the state, under the fixed register identifications, is

The logical payload channel is exactly the identity, including arbitrary references. The finite classical report is forwarded with its complete joint law. Arrival occurs at

Every dependency route remains in the regular part.

Proof. At the first hop a SWAP exchanges the unknown payload factor, including all correlations with $E$, with the next independent blank. The previous station is left blank. Repeating gives the formula by induction.

Classical forwarding copies only diagonal record data; it is not cloning an arbitrary quantum state. The chosen tick durations make the spatial dependency edges null in the developing chart, hence causal in the supplied host geometry.