Theorem: Regular reference-preserving route

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

The logical payload channel is the identity including all references. Arrival is at

The entire route lies inside the retained regular tube.

Proof. A SWAP transfers the complete payload, including its reference correlations, into the next independent blank and leaves the previous factor blank. Induction proves the state formula. Equal station spacing and developed duration give the declared null cross-port displacement. The time calibration gives the host arrival time.