Appendix A.2 Open Brain-lobe Function-Space and Hyperemergent Domain

F_A = {phi | phi is a sufficiently distinct Arthitean mind/neural-system-performable function}

FamiliarHumanCognition is a proper subregion of F_A; F_A is not defined by human-neurological familiarity.

Used(phi) AND phi in F_A -> L_phi,h exists structurally for h = 1,2,3,... without terminal order

HEC inputs may draw from any phi_i in F_A; there is no CognitiveOnly(phi_i) axiom.

HEC(C)=1 iff at least one task-time output-relevant input e belongs to Emergent(H_hi(phi_i)) for some phi_i in F_A and removing/downgrading e changes the relevant output property.

Hyperemergent recursion depth c is independent: c != h != a != s

Success(all participating lobes) does not imply Success(HEC)

new HEC function-kind -> optional dedicated lobe generation -> new Higher-Lobe family -> further HEC