Part 21: Dark Matter as Geometry: Dual–H₄ Cosmology and the Emergent Large-Scale Structure of the Universe

Previous Parts of the Origin Geometry (OG) research program developed a framework in which continuous spacetime, fields, and particle-like structures emerge as effective descriptions of an underlying discrete, aperiodic, elastically connected geometric network. Within this framework, mass hierarchy, spectral organization, topological confinement-like behavior, and emergent Lorentz symmetry arise as consequences of geometric structure rather than fundamental physical postulates. A central development of the program concerns the completion of the H₄ geometric framework through spinorial closure, leading to a minimal algebraic extension associated with E₈. Under golden-ratio projection, this completion naturally generates a dual-sector structure represented by (H₄ ∪ φH₄). The two sectors coexist within a common geometric bulk while remaining phase-shifted at boundary-supported modes. This phase displacement suppresses effective boundary-mode interactions while preserving collective responses to geometric deformation. The present work investigates the cosmological implications of this dual-sector architecture. We propose that phenomena conventionally attributed to dark matter may admit an alternative geometric interpretation associated with the φH₄ sector. Within this picture, effective mass emerges from topological defects, geometric stress distributions, and pinned network configurations rather than from an independently postulated particle population. Large-scale cosmic structure is interpreted as a manifestation of stress organization within the dual-sector geometric substrate. Halos, filaments, and cluster-scale structures may arise as emergent stress configurations of the underlying network, while visible matter behaves as a population of boundary-supported excitations propagating within this evolving geometric environment. The framework remains intentionally conservative. No complete replacement of the ΛCDM cosmological model is proposed. No claim is made that dark matter has been identified conclusively as a geometric phenomenon. Instead, the present Part investigates whether a dual-sector geometric architecture associated with E₈ completion may provide a viable geometric interpretation for a subset of cosmological phenomena currently attributed to dark matter and large-scale structure formation.