Part 31: Bulk Collective Excitations and High-Frequency Relaxation Regimes in Dual–h₄ Cosmology

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 the collective dynamics of a dual–H₄ geometric substrate. Within this framework, bulk collective excitations play a central role in: propagating geometric stress, relaxing obstruction gradients, and coupling regions characterized by different topological structures. The present work investigates: the dynamical properties of collective bulk modes, the high-frequency regimes generated by topological relaxation, and their potential cosmological implications at the coarse-grained level. Unlike conventional gravitational waves in General Relativity (GR), bulk excitations in Origin Geometry are not necessarily tensor perturbations of a continuum metric. Instead, they are interpreted as collective modes of a dual-sector topological–geometric network. At the coarse-grained level, these excitations may admit an effective gravitational-wave-like description because they: propagate through bulk geometry, transport geometric stress, and redistribute collective energy. The present framework does not construct a complete field theory for bulk modes. Rather, it investigates them as a class of collective relaxation dynamics within the emergent cosmology program of Origin Geometry.