Theorem: Reference-preserving null endpoint transport

After tick $j$, every payload-reference input has state

The logical transfer is exactly ${\mathrm{id}}_d$, all other payload registers finish blank, arrival time is $T_{\mathrm{d}}+L/c$, and all tick-boundary dependencies are causal.

Proof. Each SWAP exchanges the entire current payload factor, including its reference correlations, with the next independent blank. Induction gives the state identity. Each hop has length $c$ times its tick duration, so Lemma lem:causal applies.