Corollary: Metric support and signalling upper bound

For finite $Y$,

Equal initial state restrictions on the algebra of that metric neighborhood, and common included complete device actions, give equal terminal snapshots.

Any admitted matched local signalling pair whose changes are excluded from this backward region has zero unconditioned law gap. For ticks of physical duration $\Delta t$, the resulting scalar metric propagation upper bound is $r/\Delta t$. No lower attainment statement follows.

Proof. If $x$ is added through a block meeting $N_{s+1}(Y)$ at $y$, then

Backward induction proves (eq:metricenvelope). Isotony permits restriction from the larger metric-neighborhood algebra to the ancestor algebra. Theorem thm:matched gives the snapshot statement. The speed assertion is the same upper-bound comparison in physical units.