PART 42: GEOMETRIC BACKREACTION AND VOID-DRIVEN RESTRUCTURING IN ORIGIN GEOMETRY Hubble Tension as a Phenomenological Case Study

The Origin Geometry (OG) program proposes that spacetime emerges from the collective organization of a discrete dual–(H₄) geometric substrate. Previous studies (Parts 29–39) developed an emergent cosmology framework in which large-scale expansion is interpreted not as a fundamental background property, but as a coarse-grained manifestation of topological relaxation, geometric stress redistribution, bulk-mode propagation, and self-organizing network dynamics. The present work synthesizes these developments into a phenomenological framework for geometric backreaction. In this picture, large-scale expansion may receive additional contributions from environment-dependent restructuring processes occurring within the underlying geometric network. Regions characterized by low obstruction density, efficient relaxation pathways, and enhanced bulk transport may exhibit different effective expansion behavior than highly obstructed environments. Rather than introducing a new dark-energy component or modifying Einstein gravity directly, the framework explores the possibility that part of the observed expansion phenomenology may emerge from collective geometric reorganization. Particular attention is given to cosmic voids, which naturally function as low-obstruction relaxation channels within the OG framework. The work does not claim to solve the Hubble tension, nor does it provide a precision cosmological model. Instead, it proposes a phenomenological mechanism through which geometric backreaction may contribute to effective expansion and potentially amplify environmental differences in cosmological measurements. The Hubble tension is examined as a representative case study. More broadly, the paper establishes a theoretical prediction class involving environment-sensitive expansion signatures arising from non-equilibrium geometric evolution.