Theorem: Regular reference-preserving route

For every input ${\rho }_{A_{0}E}$, after hop $j$ the state is

The logical channel is the identity including every reference. Classical reports can be forwarded with their full joint law. Arrival occurs at

and all routes stay in the regular part.

Proof. Each SWAP moves the complete payload factor, including its correlations with $E$, into the next independent blank and leaves the previous factor blank. Induction proves the state formula. Classical forwarding preserves diagonal record blocks and their joint correlations. Station spacing and tick duration give the certified null cross-port displacement inside the regular tube.