Part 34: Numerical Realizations and Illustrative Simulations of Relaxation-Driven Cosmology in Dual–h₄ Geometry

Previous Parts established an emergent cosmological framework within Origin Geometry (OG), in which cosmological expansion is interpreted as a coarse-grained consequence of: topological relaxation, geometric stress redistribution, and collective bulk dynamics within the dual–H₄ network. The present work investigates numerical realizations and illustrative simulations of this framework. Unlike conventional cosmological simulations based directly on Einstein equations, the models presented here are not intended to: reproduce the real Universe in full detail, fit observational data quantitatively, or replace standard cosmological simulations. Instead, the objective is to examine whether networks containing: obstruction, stress redistribution, and nonlinear relaxation can naturally generate: effective large-scale expansion, void-dominated relaxation, and collective growth patterns. The numerical models are presented as proof-of-concept simulations and illustrative realizations of emergent geometric cosmology within Origin Geometry.