Geometric Phase Structure in Social-Balance Dynamics: Structural Universality with Substrate-Dependent Morphology

Five experiments extend the geometric phase structure framework — developed across transformer attention, EEG brain dynamics, and ODE dynamical systems — to a continuous-opinion variant of the social-balance dynamics of Pham et al. (2020). Three foundational existence claims are confirmed: a curvature sign change marks the fragmentation transition with topology-class structure, trajectory-level dynamics exhibit coordinate-asymmetric sign reversal via connectivity-induced rate heterogeneity, and topologically distinct moderates form a connected boundary structure (foam topology) between committed blocs. The morphological details of each phenomenon diverge from the framework's discrete-bloc defaults through legible, substrate-specific mechanisms: the timing-commitment correlation sign depends on time parametrization, the foam thickens rather than thins with density, co-descent coupling does not generalize because the geometry observable saturates at the substrate's natural dimension, and the geometric phase boundary is direction-asymmetric in the homophily-density control plane. These results establish a two-level universality claim: substrate-independent existence (Level 1) holds; substrate-dependent morphology (Level 2) varies through characterizable mechanisms. The relationship to the analytical social-balance literature is complementary — the analytical framework derives transitions; the geometric framework measures their structural character.