Part 32: Coarse-Grained Dynamical Framework for Emergent Cosmology in Dual–h₄ Geometry

Previous Parts of the Origin Geometry (OG) research program have proposed that cosmological expansion may emerge as a coarse-grained consequence of: topological relaxation, geometric stress redistribution, and collective bulk dynamics within a dual–H₄ geometric substrate. The present work develops a coarse-grained dynamical framework for this process. Rather than treating spacetime as a fundamentally continuous metric manifold, the Origin Geometry framework considers: geometric stress, obstruction density, phase accessibility, and bulk collective modes as effective dynamical variables of an underlying topological–geometric network. Within this perspective, a phenomenological system of equations is introduced to describe: the redistribution of topological obstruction, the propagation of bulk stress, and the growth of effective geometric separation. The present framework is not intended to replace Einstein's equations or Friedmann–Robertson–Walker (FRW) cosmology. Instead, its purpose is to establish an effective dynamical language for emergent geometric cosmology within the Origin Geometry program.