PART 30: VOID-DEPENDENT EXPANSION PHENOMENOLOGY IN DUAL–H₄ COSMOLOGY

Part 29 proposed that cosmological expansion within the Origin Geometry (OG) framework may emerge as a coarse-grained consequence of: topological relaxation, bulk stress redistribution, and the activation of latent geometric degrees of freedom within a dual–H₄ geometric substrate. A natural consequence of this framework is that if expansion originates from geometric relaxation rather than from a perfectly homogeneous metric background, then expansion dynamics may depend upon the local topological and dynamical environment. In the present work, we investigate the possibility that: low-density void regions, filamentary dense structures, and environments characterized by different obstruction regimes may exhibit different effective relaxation rates. This framework leads naturally to: effective Hubble variations, anisotropic relaxation tendencies, and environment-dependent expansion phenomenology. The present work does not replace ΛCDM cosmology or the Friedmann–Robertson–Walker framework. Instead, it explores the possibility that large-scale expansion may admit a microscopic geometric interpretation governed by the topological and dynamical structure of a dual-sector network.