5.6 Recruitment law: what is variable if the whole ladder exists?

For a task T and function phi, let D_phi(T,t) be the set of Hyperfunction orders the task genuinely requires at time t. Let R_phi(T,t) be the subset of structurally available orders successfully selected/recruited by routing and metaneural control. Let X_phi(T,t) be the subset of recruited orders actually firing.

D_phi(T,t) subset of N+ ; R_phi(T,t) subset of N+ ; X_phi(T,t) subset of R_phi(T,t)

The entire structural family can be unlimited while D, R, and X remain task-specific. Therefore the developmental bottleneck is not the existence of H100 or H1000; it is whether the task-required orders are actually selected, coordinated, activated, and supplied with sufficient architectural throughput.

Define the Higher-Order Activation Gap G_H(phi,T,t)=D_phi(T,t) \ X_phi(T,t). A nonempty G_H means some task-required Higher-Lobe orders were not active even though the family exists structurally.

G_H(phi,T,t) = D_phi(T,t) minus X_phi(T,t)