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Part 15: Universality of Light Fermions as Boundary Phase Descendants in Discrete H4 Geometry

Authors: Truong, The Duy Tan;

Part 15: Universality of Light Fermions as Boundary Phase Descendants in Discrete H4 Geometry

Abstract

Having established that the electron mass arises from discretization-induced pinning of boundary phase solitons (Part 12), that this mass is exponentially suppressed by soliton delocalization (Part 13), and that the proton–electron hierarchy follows inevitably from bulk–boundary energy separation (Part 14), we now address a final structural question: Is the electron unique, or is lightness a universal property of a geometric class of excitations? We demonstrate that any excitation which: (i) avoids bulk metric deformation, (ii) propagates via boundary-supported phase degrees of freedom, and (iii) experiences discretization-induced symmetry breaking, must necessarily acquire a small but finite inertial mass governed by the same exponential suppression mechanism. Furthermore, we show that multiple light fermions arise naturally as distinct topological winding classes of boundary phase solitons, whose differing internal phase complexity fixes their effective localization and hence their mass hierarchy. This establishes light fermions in Origin Geometry as a universal geometric class—Boundary Phase Descendants—independent of particle labeling, gauge structure, or Standard Model assumptions.

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