Scheduled ancestry versus influence versus geometry

This gives a schedule upper bound, not equality with actual influence. For an oracle primitive, its entire declared support must be included. No bounded spatial diameter is supplied merely by bounding its address length.

Conversely, a coherent Boolean oracle can have operational influence when its registers are exposed to interventions: $f(x)=x$ implements CNOT. The correct statement is therefore not that an oracle has no influence. It is that a supplied oracle is not, by itself, an extracted causal relation or a cone-selection principle.

These distinctions are the three-relation discipline of VII-J and En08-A CheungVIIJ,CheungEn08A.