Part 23: Scale-Mismatched Pinning, Accelerated Dark Compression, and Bulk-Mediated Relaxation in Dual–(H_4) Geometry

Within the framework of Origin Geometry (OG), matter is interpreted as a family of topological excitations embedded within a discrete, elastic, and multidimensional geometric network. Previous Parts established that the dual-sector structure H₄ ∪ φH₄ naturally supports a phase-shifted sector in which boundary electromagnetic modes may become strongly suppressed. This suppression arises from boundary-mode phase misalignment, topological pinning, Peierls-Nabarro barriers, and effective near-flat-band freezing. The present Part develops the intermediate dynamical mechanism connecting the pinned dark sector of Part 22 to the effective dark-collapse regime developed later in Part 24. The central proposal is that the φH₄ sector is not merely phase-displaced relative to the visible H₄ sector, but may also involve an effective lattice-scale mismatch. Schematically, a_φ = φa, where a denotes the effective visible-sector lattice scale and a_φ denotes the corresponding scale in the phase-shifted sector. For electron-like boundary solitons, the relevant Peierls-Nabarro pinning strength depends not on soliton width alone, but on the dimensionless ratio between the coherence width and the lattice spacing. If the boundary coherence width does not scale synchronously with the enlarged φH₄ lattice spacing, then the ratio σ/a_φ decreases and the Peierls-Nabarro barrier increases. This produces effective mass inflation of charged boundary modes, suppresses their acceleration, weakens electromagnetic radiation, contracts effective orbital structure, degrades ordinary chemical degrees of freedom, and reduces gas-pressure support. The resulting dark-sector matter can be gravitationally active while remaining electromagnetically silent. Under compression, such matter may form localized topological concentrations, or topological lumps, whose short-range geometric interactions can lead to effective topological fusion. The released configuration energy cannot efficiently relax through ordinary photon channels. Instead, the framework proposes that a substantial fraction of this energy may couple to collective bulk degrees of freedom of the underlying geometric substrate. These collective bulk excitations may propagate through the shared dual-sector geometry and admit, at a coarse-grained phenomenological level, a gravitational-wave-like description. This Part does not identify such modes with gravitational waves in General Relativity. Rather, it establishes a candidate geometric pathway through which hidden-sector structures may compress, reorganize, release energy, and relax through non-electromagnetic bulk modes. In summary, this Part proposes the sequence: scale mismatch → enhanced pinning → boundary mass inflation → electromagnetic suppression → reduced pressure support → efficient dark compression → topological fusion → bulk-mediated relaxation.