This paper presents a unified theoretical framework in which particle mass and structure arise from the spatial convergence of wavefronts. A central τ-function encodes energy localization using a vector operator and a Gaussian-smeared delta kernel, yielding an energy density that drives mass formation. The energy-to-mass relation is expressed as \( m = \epsilon \cdot V / c^2 \), where τ has units of energy. Wave synchronization is captured by a function Σ, which applies only to stable particles, while transient wave convergence yields virtual particles.
Spacetime curvature is incorporated through the Ricci scalar R, which modulates the energy convergence probability. We derive all key equations, compute Standard Model particle masses, and perform a χ² analysis against experimental values. The model reproduces particle masses with an error of less than 1%. TikZ diagrams illustrate the physical difference between stable and virtual particle convergence mechanisms. This work connects quantum coherence, wave interference, and general relativity in a novel mass-generation framework.
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