Theorem: Reference-preserving payload transport

After hop $j$, an arbitrary input ${\rho }_{S_{0}E}$ has become

Thus the logical payload channel is exactly the identity, including every reference. Arrival is $T_{\mathrm{dep}}+L/c$, and all communication dependencies lie inside the prescribed causal cone.

Proof. The first exchange moves the whole payload factor and its reference correlations into $S_1$, leaving a blank in $S_0$. Repeat inductively. Each hop covers distance $L/n$ in time $L/(nc)$, so its transfer paths are null in the developing chart and causal after pullback.