Definition: Signalling speeds

On a fixed schedule, an $x$-perturbation pair has equal initial snapshots on all finite regions excluding $x$, and equal block channels on all blocks excluding $x$. Let $c_{\mathrm{lat}}(\mathcal{P})$ be the supremum of $d(x,A)/\tau$, $\tau \ge 1$, over pairs that change a common readout at $(A,t_0+\tau )$. For a schedule class $\mathfrak{S}$, take the supremum over $\mathcal{P}\in \mathfrak{S}$. An empty positive-distance supremum is $0$.