Parts 37 and 38 proposed that cosmological evolution within Origin Geometry (OG) may proceed through cycles of geometric growth, saturation, frustration accumulation, phason activation, topological restructuring, and geometric renewal. A natural consequence of the renewal process is the emergence of newly realized H₄ domains generated through projection reorganization within the parent E₈ substrate. The formation of a new cosmological cycle raises an important dynamical question. Can a newly emerging dual–H₄ realization establish global coherence instantaneously? If information propagates at finite speed through the network, the answer is generally no. Different regions may independently select slightly different phason configurations before large-scale synchronization becomes possible. This situation closely resembles the conditions underlying the Kibble–Zurek mechanism (KZM), originally developed in condensed matter physics and later applied to cosmological phase transitions. In the present work, we investigate the possibility that phason-mediated transitions within dual–H₄ geometry naturally generate: topological freeze-out, defect formation, chirality selection, primitive mass localization, matter–antimatter asymmetry seeds, dark-sector precursors, and primordial geometric perturbations. The framework does not claim that Standard Model particles are fully derived. Instead, it develops a geometric pathway through which the earliest cosmological structures may emerge from non-equilibrium phason dynamics. The resulting picture suggests that matter genesis may be interpreted as a consequence of geometric coherence failure during the birth of a new H₄ realization.
The Duy Tan Truong (Wed,) studied this question.