Theorem: Exact metric cone

Two runs on the same schedule have equal terminal snapshots at $(A,T)$ if:

1. their initial snapshots agree on $B_d(A,r(T-t_0))$;

2. their block channels agree at each tick $s<T$ on every block contained in $I_s$.

Every common terminal readout then has the same law. The result is independent of all data and gates outside the cone, including gates on straddling blocks.

Proof. Every ancestor block lies in the corresponding $I_s$, by backward induction using the preceding block geometry. Equation (eq:metricenvelope) places the initial ancestors in the initial ball. Restrict the equal snapshots to that ancestor region and apply Theorem thm:order.