11.20 Recursive Hyperemergent Crossfunctionality

A Hyperemergent Crossfunction can itself become an input to another crossfunctional operation. When the later operation depends on the earlier hyperemergent output, Hyperemergent Crossfunctionality becomes recursively compositional.

HC_1 = Cross(X1,...,Xm) with HEC(HC_1)=1

HC_2 = Cross(HC_1, Y1,...,Yr)

HC_(c+1) = Cross(HC_c, additional task-relevant neural outputs)

Define c as Hyperemergent crossfunction-recursion depth. c is a network-composition index, not a Hyperfunction order, not an Antilobe monitoring-recovery depth, and not a sublobar specialization depth.

c != h != a != s

At c=1, higher-order lobe-derived emergence participates in one crossfunctional integration. At c=2, the output of that integration becomes material for another integration. At c=3, the second-order hyperemergent output is further integrated, and so on. If the architecture permits unbounded recursive network composition, c need not have a terminal structural depth. Task-time recruitment still determines how much of that possibility-space is actually used.

Recursive Hyperemergent Crossfunctionality is therefore a new recursion axis. Hyperfunction recursion recursively enriches a function-family state; Antilobe recursion recursively monitors failure of lower anti-monitors; sublobar recursion recursively specializes a function; Hyperemergent recursion recursively composes crossfunctional outputs. These recursions can interact while remaining non-identical.