Part 22: Boundary Pinning, Near-Flat-Band Freezing, and Topological Mass Structure in Dual–H₄ Geometry

Within the framework of Origin Geometry (OG), spacetime is interpreted as an emergent description of an underlying discrete, aperiodic H₄ geometric network. Previous Parts introduced the possibility that a dual-sector architecture (H₄ ∪ φH₄) may arise through the completion of the geometric framework and may provide a geometric interpretation for a subset of phenomena conventionally attributed to dark matter. The present work investigates a possible microscopic mechanism underlying such a dark sector. We propose that excitations associated with the φH₄ sector may become dynamically constrained through an intrinsic topological pinning mechanism supported by the discrete geometry of the substrate. Under sufficiently strong pinning conditions, the excitation spectrum may approach a near-flat-band regime in which group velocities become strongly suppressed and dynamical propagation becomes increasingly restricted. Within this regime, boundary-supported excitations may experience effective dynamical freezing over large timescales. Electromagnetic emission channels may become strongly suppressed, not necessarily because charges or interactions are absent, but because the availability of dynamical energy transitions becomes severely reduced. The term "near-flat-band" is employed here in an effective topological-dynamical sense and should not be interpreted as directly equivalent to conventional flat-band electronic systems studied in condensed matter physics. The framework further suggests that strong pinning may induce a substantial restructuring of effective mass hierarchy. Light excitations may become more strongly constrained than heavy modes within particular topological regimes, potentially leading to an inversion of conventional mass organization and the destabilization of ordinary atomic structures. Within this interpretation, strongly pinned topological configurations may behave as effectively massive, electromagnetically silent, and long-lived geometric structures. Such configurations may provide a geometric pathway through which dark matter phenomenology emerges naturally from the internal dynamics of dual-sector geometry.