Proposition: Spectator-blind control

The guard, geometric output, particle packet, certificates, and transport $\tau$ of (eq:Grule) satisfy Contract contract:G. They are independent of the number and internal state of matter names.

Proof. The guard reads only $m,j,\nu$ and fixed geometric validity data. The output geometry is the explicitly prescribed outgoing germ. The particle packet is a fixed geometric packet. The holonomy and geometric certificates depend only on the displayed family and chart table. The transport is the fixed identity map on persistent labels.

None of these definitions reads a location occupancy count or an internal matter state. The same geometric event is defined when there are no matter names at all. Applying the same fixed map to each supplied name changes no geometric decision.