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Part 10: Geometric Origin of Mass Hierarchy from Hierarchical Inertia in Discrete H4 Lattices

Authors: Truong, The Duy Tan;

Part 10: Geometric Origin of Mass Hierarchy from Hierarchical Inertia in Discrete H4 Lattices

Abstract

Building upon the geometric definition of inertial mass established in Part 9, we investigate how discrete H₄ geometry generically produces extreme inertial hierarchies without introducing particle identity, coupling constants, or symmetry-breaking fields. We show that inertia within the Origin Geometry framework is naturally stratified into three geometrically distinct regimes: bulk metric inertia, boundary phase inertia, and projection-induced attenuation. These regimes are determined solely by how an excitation participates in the underlying lattice structure. To formalize this stratification, we introduce a Hierarchical Inertia Operator that combines graph-theoretic stiffness with topology-defined inertial weights. The resulting spectrum is predicted to separate into distinct inertial bands associated with volumetric, boundary-supported, and projection-mediated excitations. The framework establishes a purely geometric precondition for mass hierarchy, independent of dynamics, interactions, or phenomenological inputs. It provides the structural foundation for subsequent identification of heavy and light excitation regimes while remaining agnostic regarding particle identity and interaction structure.

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