11.7A Open-function-space inheritance: Hyperemergence is not cognition-only

Let F_A be the open-ended Arthitean Brain-lobe function-space defined in section 1.1. Hyperemergent Crossfunctionality places no additional cognitive-only restriction on the participating function-kinds. The defining condition concerns WHERE the indispensable input came from - a higher-Hyperfunction-generated emergent dimension - not whether the underlying function is called reasoning, defence, identity preservation, power control, temporal integration, conceptual processing, or something still more alien.

FunctionDomain(HEC) subseteq F_A, with no axiom restricting FunctionDomain(HEC) to FamiliarHumanCognition

Thus the same formal hyperemergence test applies to an H100 strategy lobe, an H100 possession-resistance lobe, an H100 cognitohazard-quarantine lobe, an H100 hax-interaction lobe, an H100 distributed-self coordinator, or a future lobe for a coherent Arthitean mental function that currently has no name.

This greatly enlarges the practical Hyperemergent possibility-space: the network can combine higher-order emergent dimensions from lobes whose primitive purposes already differ radically, allowing the second-order network emergence to bridge cognitive, defensive, adversarial, temporal, conceptual, power-operational, identity-preserving, and metaneural domains.