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Part 9: Geometric Inertia and the Origin of Mass in Discrete H4 Lattices

Authors: Truong, The Duy Tan;

Part 9: Geometric Inertia and the Origin of Mass in Discrete H4 Lattices

Abstract

Overview We investigate the geometric origin of inertial mass within the Origin Geometry (OG) framework, in which effective spacetime is modeled as an emergent description of an underlying discrete four-dimensional aperiodic geometric substrate. In this setting, mass is not introduced as a primitive particle attribute, a phenomenological coupling, or a fitted parameter. Instead, we propose that inertial resistance arises as a structural response of the geometric substrate to metric deformation. The Pre-Dynamical Nature of Inertia The central claim is deliberately pre-dynamical. An excitation is inertial when its existence, propagation, or stabilization requires persistent distortion of inter-site geometric relations across a finite region of the underlying lattice. Metric deformations modify edge lengths, local distances, effective volumes, or higher-order connectivity relations. Such deformations require elastic participation of the substrate. By contrast, approximately isometric, orientation-preserving, or phase-like motions preserve local metric relations and therefore remain energetically transparent in the ideal geometric limit. Volumetric Participation and Mass Hierarchy Within this framework, mass is identified not with motion itself, but with the minimal geometric cost required to sustain metric deformation. Volumetric participation becomes the primary structural source of large inertial resistance: excitations that engage four-dimensional bulk deformation are expected to be heavy in the geometric sense, whereas excitations that remain boundary-supported, phase-like, or approximately isometric are expected to possess much lower geometric inertia. Scope and Limitations This Part does not compute the masses of known particles. It does not identify fermions or bosons. It does not introduce gauge dynamics, Higgs-like mechanisms, or phenomenological fitting. It establishes a geometric precondition for mass: inertial behavior becomes meaningful only when the substrate must participate metrically in the excitation. The resulting definition provides the conceptual foundation for later investigations of mass hierarchy, boundary lightness, bulk participation, and effective low-energy mass terms.

Keywords

Boundary Modes, Isometric Motion, Metric Deformation, Geometric Substrate, Emergent Mass, Volumetric Participation, Elastic Response, Mass Hierarchies, Origin of Mass, Foundational Physics, Discrete Geometry, Inertial Resistance, Continuum Limit, Geometric Stiffness, Origin Geometry, Isometric Deformation, Elastic Lattice Dynamics, 600-Cell Geometry, Aperiodic Geometry, Geometric Inertia, Bulk Deformation, H4 Geometry, Structural Mass, Pre-Dynamical Mass, Elastic Eigenmodes, Discrete Spacetime

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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