Dynamic Vacuum Theory (DVT) v26 – Part III: Subatomic Superfluid Vortex Topology, Zero-Parameter Neutrino Mass Spectrum from Vacuum Phase Pressure, and Lepton–Baryon Hydrodynamic Resonance

While the Standard Model of particle physics achieves high perturbative precision through gauge symmetry groups, it leaves the origin of the neutrino mass scale (m_nu ~ 5–50 meV), the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) leptonic mixing angles, the proton-to-electron mass ratio (mp/me = 1836.15267), and the Fermilab Muon g - 2 discrepancy (Delta a_mu = 2.49 x 10^-9) dependent on arbitrary Yukawa couplings or hypothetical high-energy extensions such as the 10^15 GeV see-saw mechanism. In this third installment of the Dynamic Vacuum Theory (DVT v26) series, we extend the strictly zero-parameter (0-fit), Dark-Energy-free compressible superfluid Bose-Einstein condensate (BEC) vacuum framework established at galactic scales in Part I (10.5281/zenodo.23741503) and cosmological scales in Part II (10.5281/zenodo.23741719) down to subatomic quantum hydrodynamics. By equating the energy density of a single Planck de Broglie phase cell to the exact galactic DVT critical vacuum phase transition pressure P_0 = c^2*H_0^2/(128*G) = 5.4140 x 10^-11 Pa, we derive the fundamental neutral Kelvin phase-soliton mass quantum m_nu,1 = 5.038 meV with zero free parameters. Evaluating hydrodynamic boundary eigenvalues yields solar and atmospheric mass-squared splittings Delta m^2_21 = 7.61 x 10^-5 eV^2 (2.6% from KamLAND/NuFIT) and Delta m^2_31 = 2.447 x 10^-3 eV^2 (2.7% from Super-Kamiokande), with total mass Sigma m_nu = 0.0648 eV satisfying DESI 2024–2026 cosmological bounds (< 0.072 eV). Furthermore, projecting mode couplings across the planar geometric efficiency C_proj = 2/pi reproduces all three PMNS mixing angles within 1.0–2.4%. Finally, we demonstrate that 3D Compton cavitation volume scaling resolves the Fermilab Muon g - 2 anomaly (1.51% error) while preserving electron QED precision, and we unify baryon trefoil soliton topology (rp = 4*hbar/(mp*c) = 0.8412 fm, mp/me = 6*pi^5 = 1836.118, Higgs dual-cavitation MH = 125.17 GeV) with deterministic Artik-Vortex quantum entanglement.