A target-adapted route

Choose sender and receiver $x_A,x_B\in \mathcal{V}$ with

and a straight developed segment inside the regular convex laboratory. Install sites

Each site has a two-qubit payload register $X_j$. Initialize $X_1,\dots ,X_n$ in a fixed pure blank $\omega$.

At hop $j$, transmit the contents of $X_{j-1}$ to $X_j$ and the blank contents back to $X_{j-1}$, giving the endpoint SWAP channel. Allocate duration

to that hop. Both directions have causal ports; equivalently, this is an admitted finite communication block with all input-output dependencies causally certified.