Theorem: U excludes ordinary bidirectional relays

U and well-founded causal executability are incompatible with bidirectional lossless one-tick transport between any two distinct sites, including sites at distance at most $r$.

Proof. Let $\phi (P)=1$ and $\phi (x)=0$ for $x\ne P$. It is $r$-compatible. The ${\beta }_{\phi }$-image of $P\to Q$ has duration $0$; the ${\beta }_{-\phi }$-image of $Q\to P$ also has duration $0$. U admits their composition $(P,s)\to (Q,s)\to (P,s)$, a directed dependency cycle. No topological ordering exists.