The Geometric Higgs-Substrate Interface: Deriving Nuclear Rest Mass Variations from Localized Non-Linear 3D Wave Saturation

Abstract:The Higgs mechanism successfully explains the generation of inertial rest mass via a non-zero vacuum expectation value (v ≈ 246 GeV). However, standard quantum field theory models this coupling as an abstract Yukawa interaction without a localized, mechanical coordinate framework. This paper presents the Quantum Space-Time Matrix (QSM), a phenomenological model that frames the Higgs field as an ultra-stiff, 3D standing-wave substrate with a baseline bulk modulus (κ_STU) calibrated to macroscopic solar refraction metrics. We demonstrate that elemental mass variations and the nuclear mass defect are the direct geometric consequences of localized Higgs field saturation. By evaluating the spatial boundary conditions (nuclear radii) of the periodic table, we show that phase-symmetric radial damping, non-linear wave collisions, and geometric shell harmony map the local density saturation curve of the Higgs medium, yielding mass predictions within sub-percent margins of error from Hydrogen (Z=1) to Oganesson (Z=118). Notes:This manuscript is a foundational working preprint establishing the mechanical scale-invariance of the Quantum Space-Time Matrix (QSM) framework. Comments, mathematical feedback, and peer inquiries are welcome.