Overview Previous Parts of the Origin Geometry research program developed a framework in which continuous spacetime, fields, particle-like excitations, inertial mass, spin-like topology, charge-like organization, confinement-like behavior, and Lorentzian continuum structure emerge as effective descriptions of an underlying discrete, aperiodic, elastically connected geometric substrate 1–7, 11–15. Within this framework, mass is not introduced first as a primitive particle parameter. It is interpreted as a geometric cost associated with deformation, participation, pinning, and stress organization of the substrate. Dual-Sector Architecture and E8 Completion A central structural result of the program is the spinorial completion of the H4-based geometric framework. Under Clifford-type closure, the H4 structure admits a natural exceptional completion associated with E8. Under golden-ratio projection, this completion supports a dual-sector architecture represented schematically as: H4 ∪ φH4 The two sectors are not interpreted as two disconnected universes 4, 8–10. They coexist within a common geometric bulk. Their boundary-supported phase modes may be relatively displaced or phase-incoherent, suppressing direct boundary-mode communication, while collective bulk deformation remains shared. Dark Matter as Geometric Stress The present Part investigates the cosmological consequence of this dual-sector architecture. We propose that phenomena conventionally attributed to dark matter may admit a geometric interpretation associated with the φH4 sector 22–25. In this picture, the dark component is not necessarily a population of hidden particles. It may instead be an effective macroscopic manifestation of geometric stress, topological defects, pinned configurations, and long-lived deformation structures in the shared substrate. This interpretation proceeds at three levels: Micro-geometric level: The φH4 sector is a projected geometric sector arising from algebraic completion. Stress-defect level: This sector supports deformation energy, pinned topology, and stress concentrations. Cosmological effective level: These structures appear to visible H4-sector observers as gravitationally active but electromagnetically inaccessible mass distributions. Large-scale cosmic structure is then interpreted as a manifestation of stress organization within the dual-sector substrate. Halos, filaments, nodes, and cluster-scale structures arise not merely as aggregations of unseen particles, but as effective stress configurations of the underlying network 26–29. Visible matter behaves as boundary-supported excitation flow guided by this stress landscape. Scope and Limitations The framework remains intentionally conservative. No complete replacement of ΛCDM is proposed. No claim is made that dark matter particles cannot exist. No derivation of the matter power spectrum, CMB acoustic structure, cluster lensing, or galaxy formation is attempted here. The present Part establishes a structural cosmological layer of Origin Geometry: if E8-compatible completion naturally generates a dual-H4 architecture, then at least part of dark matter phenomenology may be interpreted as hidden geometric stress rather than hidden material substance.
The Duy Tan Truong (Wed,) studied this question.