Proposition: Geometric rule and blind control

The event is a certified $(G)$-rule. Its guard, support selection, output geometry, and permission accounting use only declared geometric and control data. Transport is the fixed map ${\tau }_B$, independent of state and name cardinality. Under separately reserved spectator location/history storage, ass:sched holds.

Proof. The preceding geometric propositions certify the outgoing germ and continuation. The guard reads only $s,\mathsf{mode},\mathsf{perm}$ and the fixed family certificate. Applying a fixed label map does not depend on how many names are transported. Separate reservation prevents additional spectator storage from changing the geometric budget.