Theorem: Regular reference-preserving report route

For every initial payload–reference state ${\rho }_{A_{0}E}$, after hop $j$ the complete route state is

The logical channel is the identity, including every reference and all correlations between reports and quantum residuals. Arrival is at

The route remains regular and future causal.

Proof. A SWAP exchanges the entire current payload factor, including its reference correlations, with the next independent blank. It leaves the old factor blank. Induction gives the stated tensor identity.

Station separation and developed duration both equal $\ell /n$, so cross-port dependencies have straight null certificates in the developed chart. Same-station dependencies are timelike. The signature and time ledger converts the developed arrival time into the host time.