Resolution of the Neutrino Mass Hierarchy and Oscillation Mechanism: Sub-eV Transverse Shear Wavepackets and Modal Dispersion in a Pre-Stressed Elastic Continuum

In the minimal Standard Model, neutrinos are strictly massless, yet oscillation experiments establish non-vanishing mass squared differences (Δm_21^2 ≈ 7.5 × 10^-5 eV^2, |Δm_31^2| ≈ 2.5 × 10^-3 eV^2) and sub-eV mass bounds (∑ m_ν < 0.12 eV). To explain this extreme suppression relative to charged leptons without fine-tuning Yukawa couplings to 10^-12, theoretical physics invokes the Type-I See-Saw mechanism, postulating unobserved Grand Unified (GUT) scale Majorana fermions (M_R ~ 10^14–10^15 GeV). Building upon our foundational series on the physical vacuum as an elastically pre-stressed continuum, we show that neutrino masses and oscillations are deterministic manifestations of transverse acoustic shear wavepackets in the substrate. Unlike charged leptons, which are closed topological vortex knots with volumetric dilation (electric charge), neutrinos are pure non-dilational shear packets (∇ · u_ν = 0) carrying zero Coulomb self-energy. We derive their sub-eV mass scale as the minimal boundary strain energy m_ν c^2 ≈ (ħ ω_EW)^2 / (G_v ℓ_0^3) ≈ 0.082 eV, damped naturally by the lattice-to-envelope volume ratio without heavy Majorana states. Flavor mixing and spatial oscillations are shown to be the classical beat phenomena of coupled acoustic modes propagating along slightly anisotropic vacuum stress axes, with the PMNS matrix representing the geometric rotation tensor between internal soliton symmetry planes and substrate axes. Furthermore, the MSW resonance in dense matter is derived as a localized hydrostatic compression modifying the acoustic sound speed. We strictly predict the absence of neutrinoless double-beta decay (T_1/2^0νββ -> ∞) and normal mass ordering.