Proposition: Private observations before communication

Consider two local quantum programs with disjoint quantum ownership. Suppose their geometric actions leave the other party's private readable cells fixed, and neither program inspects shared link status, uses a cross-party communication primitive, or has its local enablement changed by the other's geometric actions. Then:

1. the specified Born semantics has program-independent unconditioned remote classical laws;

2. an operationally admissible unknown strategy has the same independence by ${\text{(NS)}}_N$;

3. the remote private geometric observation is unchanged.

Proof. Part (i) is the path-map marginalization in Lemma lem:born-inhabitation. Part (ii) is the operational requirement, applied to the stated local experiments. Part (iii) follows because no transition writes a remotely readable private cell or changes its local enablement.