Overview Within the Origin Geometry framework, spacetime is not treated as a fundamental continuum, but as an emergent large-scale description of a deeper discrete, aperiodic, multi-sector topological–geometric substrate. Previous Parts developed the dual–H4 architecture, dark-sector stress dynamics, topological pinning, bulk-mediated relaxation, phase-collapse regions, and cross-sector energy transfer 1–9. These results motivate a further cosmological question: What is the microscopic geometric origin of cosmic expansion? In standard cosmology, expansion is described with great empirical success through a scale factor in an effective continuum metric 10–12. However, if the continuum itself is emergent, then the growth of large-scale separation should admit a deeper substrate-level interpretation. The present Part proposes such an interpretation. Cosmological expansion is modeled not as the literal stretching of a pre-existing continuous space, nor as the action of a fundamental repulsive force, but as the effective macroscopic consequence of discrete geometric proliferation within an evolving dual–H4 network. The Geometric Pathway to Expansion The central mechanism is a causal chain. Topological relaxation events in the phase-shifted φH4 sector release configuration energy into collective bulk stress modes. These modes are not identified with ordinary electromagnetic radiation and are not assumed to be gravitational waves of General Relativity. They are gravitational-wave-like only in the coarse-grained sense that they carry geometric stress through the shared substrate. As these high-frequency bulk modes propagate through the cosmic network, low-density void regions provide preferred environments for coherent accumulation because they possess reduced topological obstruction, weaker collective scattering, and greater phase accessibility. In such void-dominated environments, the aperiodic structure of the H4-derived network may support Anderson-like nonlinear localization of bulk stress modes 15, 22–25. Localized stress concentrations, called stress droplets, can then form. When the local stress energy exceeds a critical geometric threshold, the network may undergo a projection accessibility transition: previously latent coordinates in the E8-compatible parent structure become realized within the effective H4-projected network 1, 17–21. This process is called lattice proliferation. Lattice proliferation does not mean creation of spacetime from nothing. It means the effective realization of geometric degrees of freedom already encoded in the parent structure but not previously active in the projected H4 network. As additional network elements become realized, the number of effective geometric units between distant excitations increases. In the macroscopic continuum limit, this appears as growth of the effective scale factor and produces cosmological redshift. Scope and Limitations The present work is intentionally cautious. It does not claim to replace Friedmann–Robertson–Walker cosmology or ΛCDM. It does not derive the Friedmann equations, calculate the observed Hubble constant, or produce a precision model of cosmic acceleration. Instead, it proposes a microscopic geometric pathway through which expansion-like behavior may emerge from dark-sector relaxation, nonlinear stress localization, and latent coordinate realization in a dual–H4 substrate. The framework remains conditional, falsifiable, and dependent on future mathematical and numerical development.
The Duy Tan Truong (Tue,) studied this question.