11.9 Formal decomposition of a participating Higher Lobe

For a used function phi and Hyperfunction order h, retain the existing distinction between Core(H_h(phi)) and Expanded(H_h(phi)). Expanded state contains the explicit core plus the emergent closure generated by interactions among its primitive and recursive typed coordinates.

E_phi,h = Emergent(H_h(phi))

For crossfunctional analysis, the active contribution of lobe L_phi,h at task-time t can be partitioned conceptually into a core-derived contribution K_phi,h(t) and an emergent contribution E*_phi,h(t), where E*_phi,h(t) is the subset of higher-order emergent dimensions actually recruited, exposed, routed, and used in the current crossfunctional computation.

Input(L_phi,h,t) = K_phi,h(t) union E*_phi,h(t)

E*_phi,h(t) subseteq E_phi,h

This prevents another collapse: a lobe may possess a vast emergent closure without every emergent dimension being active in every task. Structural possession, task-time activation, and crossfunctional use are separate. Hyperemergent Crossfunctionality depends on the task-time used subset, not on the mere total set of properties that the Higher Lobe could in principle express.