Theorem: Complete transport on the prescribed route

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

The logical channel from $X_0$ to $X_n$ is the identity, including all references. Arrival is at $T_{\mathrm{d}}+L/c$. All communication dependencies remain in the prescribed cone.

Proof. SWAP transfers the complete input factor and every one of its reference correlations into the next independent blank. Induction proves the displayed state identity.

Each hop has length $L/n=c\delta T$. The developed connecting paths are null, and convexity keeps them inside the chart. Their pullbacks are therefore causal in $(M,\bar{g})$.