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

Abstract This paper formalizes the unified non-gauge model of physical reality as a continuous, three-dimensional, monolithic elastic continuum (the Field Ocean) with reference unperturbed density ρ₀ ≈ 4.30 × 10¹⁸ kg/m³, shear modulus μ₀ ≈ 3.865 × 10³⁵ Pa, and transverse shear wave velocity c = √(μ₀/ρ₀) ≈ 2.998 × 10⁸ m/s. Matter is shown to be non-foreign inclusions, but localized topological eigenmodes of the substrate: cavitation cavities with superluminal wall circulation (vₚ ≈ 1.185c, Mach angle 57.56°) representing baryons, and continuous vortex knots (Hopf fibration, vₑ ≈ 0.198c, spin 1/2) representing leptons. A comprehensive cosmogonic framework is introduced: the Primordial Neutron Monolith. The primordial cavitation phase under extreme hydrostatic pressure creates balanced C₃-symmetric tri-blade vortex locks (Q = 0). As cosmic ambient pressure relaxes, the Kelvin-Helmholtz boundary instability drives topological uncoupling: one arm detaches, shedding a left-handed Hopf toroid (electron, Q = −1) and a transient volumetric decompression pulse («neutrino», acoustic cross-section σᵥ ∼ 10⁻⁴⁸ m²), leaving behind the right-handed precessing cavity (proton, Q = +1). This mechanism derives exact global electroneutrality (Nₚ = Nₑ₋), the 75%/25% cosmological hydrogen-to-helium ratio, the mass difference Δm = mₙ − mₚ = 1.2933 MeV, the exact Lenz mass ratio mₚ/mₑ = 6π⁵ (0.002% error), fine-structure constant α⁻¹ ≈ 137.036, and explains Einstein's relation E = mc² and Newton's inertia F = ma directly through the hydrodynamic added mass (Mₐdd) of the elastic medium without the Higgs mechanism, dark components, or extra dimensions.