Theorem: Original-metric cone violation

A lossless one-tick record transport from $P$ to $Q$ gives a $P$-perturbation pair with readout laws ${\delta }_0,{\delta }_1$ at $(Q,t_0+1)$. Hence the original-metric signalling speed of the extension is at least $\ell >r$.

A lossless one-tick name transport has the same conclusion by transporting a computational-basis bit and reading it at $Q$.

Proof. Prepare the two possible bit values at $P$, use the same transport channel in both runs, and apply the common terminal readout at $Q$. Initial snapshots agree away from $P$. The signal arrives in one tick over original-metric distance $\ell$.