FIELD DYNAMICS OF THE ELASTIC SUBSTRATE: Topological Continuum Mechanics, Mass Spectra, and Fundamental Interactions (EUP Model)

Abstract:This work presents a closed, non-gauge model of physical space as a continuous, three-dimensional, monolithic elastic substrate (the Field Ocean) with a density of ρ₀ ≈ 4.30 × 10¹⁸ kg/m³ and a shear modulus of μ₀ ≈ 3.865 × 10³⁵ Pa. Matter is described not as foreign inclusions, but as dynamic topological states of the Field itself: cavitation cavities with superluminal wall circulation (vₚ ≈ 1.185c, Mach cone 57.56°) representing baryons, and smooth Hopf fibration vortex solitons representing leptons (electron). The model provides an analytical derivation of the proton-to-electron mass ratio (mₚ/mₑ = 6π⁵, 0.002% error), muon resonance mass (<0.8%), elementary charge e, fine-structure constant α, and derives E = mc² and Newton's inertia (F = ma) directly as the hydrodynamic added mass (Mₐdd) of an incompressible elastic continuum without invoking the Higgs mechanism or abstract gauge fields.