Overview Within the framework of Origin Geometry (OG), matter is interpreted as a family of topological excitations embedded within a discrete, elastic, aperiodic, and multidimensional geometric substrate. Previous Parts developed a dual-sector architecture 13, 16, 17, represented schematically by H4 ∪ φH4, in which the visible (H4) sector and the phase-shifted (φH4) sector coexist within a shared geometric bulk while exhibiting strongly suppressed boundary-mode overlap. This suppression was previously associated with boundary phase displacement, topological pinning, Peierls–Nabarro-type barriers, and effective near-flat-band freezing. The present Part develops an intermediate dynamical mechanism connecting the pinned dark sector of Part 22 to later dark-collapse and phase-collapse regimes. The central proposal is that the (φH4) sector may differ from the visible sector not only by phase displacement, but also by an effective lattice-scale mismatch associated with golden-ratio projection 3, 13, 18–20. Schematically, one may write: a_φ = φa where (a) denotes an effective visible-sector lattice scale and (a_φ) denotes the corresponding scale in the phase-shifted sector. Scale Mismatch and Boundary Mass Inflation The key point is not that a larger lattice scale automatically increases pinning. If the coherence width of a boundary soliton scaled synchronously with the lattice spacing, the dimensionless width (σ/a) would remain unchanged. Enhanced pinning arises only under a non-synchronous coherence condition 17, 25–29: (σ_φ / a_φ) 0 then the process releases configuration energy. Bulk-Oscillation Relaxation Channels Because electromagnetic relaxation channels are strongly suppressed in the pinned dark sector, this energy may not be efficiently transported by photon-like boundary modes. Instead, the framework proposes that a substantial fraction of the released 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 14, 15, 32–35. The present Part does not identify these modes with gravitational waves in General Relativity. It does not derive their waveform, spectrum, polarization structure, propagation law, or observational amplitude. 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, the Part proposes the conditional sequence: Scale mismatch → enhanced pinning → boundary mass inflation → electromagnetic suppression → reduced support pressure.
The Duy Tan Truong (Wed,) studied this question.