Axiodynamics v5.12 — Group-Scale Axiological Dynamics (N > 5): Vectorized Axiological Distance, Adaptive Networks and Emergent Collective Dynamics

Axiodynamics is a formal, computational-level theory of affect–cognition dynamics between valuing agents, developed from the dyadic (v5.10) and triadic (v5.11) levels. The present paper extends the framework to groups of size N > 5, where attentional channels saturate, coalitions cease to reduce to sums of dyads, and genuinely collective phenomena — polarization, exclusion cascades, endogenous reformation of the collective telos, leader emergence — exceed the reach of any finite triadic formalism. The extension rests on two complementary pillars: the vectorized axiological distance (BRC-1) as the geometric engine driving the update of directed relational edge weights w_ij(t), and an audited analytic armature from the non-exchangeable, co-evolutionary lineage of graph-limit and mean-field theory (Kuehn–Xu; Jabin–Poyato–Soler; Gkogkas–Kuehn–Xu; Cabrera-Nyst & Poyato; Ayi–Pouradier Duteil–Poyato), which supplies the formal conditions for existence, uniqueness and large-scale limit descriptions under explicitly stated hypotheses. The classical unlabelled exchangeable mean-field route is rejected as inadequate to the retained type- and label-dependent architecture: axiological heterogeneity makes agents distinguishable (type-conditional exchangeable formulations are not thereby excluded). Fast directed affective channels inherited from the triadic formalism are integrated by adiabatic elimination — under a stated, testable spectral-gap hypothesis — so that only the slow state — directed edge weights, accumulated inertias, and the slow agent-level variables required for closure — is transported through the limit, at finite horizon, under a proved finite-horizon inertia bound (H-BORN-T). Consistent with the programme's Lakatosian discipline, the present contribution is formal coherence conditional on the stated hypotheses and open adequacy conditions, simulability and falsifiability, not demonstrated predictive success; statements whose interpretation depends materially on scale or proof status are marked by explicit level tags (dense-limit object, finite-N simulation, or heuristic), and empirical predictions are pre-registered before testing.