11.16 Same-order, different-order, and cross-order Hyperemergence

Hyperemergent Crossfunctionality can occur between Higher Lobes of the same Hyperfunction order or different orders. Hyperfunction order and crossfunctional role are independent coordinates.

SameOrderHEC: Expanded(L_phi,h) x Expanded(L_psi,h) -> C*

CrossOrderHEC: Expanded(L_phi,h1) x Expanded(L_psi,h2) -> C*, where h1 != h2

Same order does not mean same emergent content because function-kind differs. H100 strategy and H100 temporal perception may each be order 100 yet instantiate different function-specific emergent dimensions. Different order does not automatically create hierarchy or domination inside the crossfunction: H500 from one function may supply one narrow indispensable dimension while H20 from another supplies most of the task-relevant structure.

Anti-arithmetic rule: Do not add Hyperfunction indices to obtain the crossfunction's order. H20 x H50 is not H70, H100 x H100 is not H200, and H1000 x H1 is not definitionally H1001. Hyperfunction order belongs to the participating function-family states; Hyperemergent Crossfunctionality is a network-output relation.