A Parameter-Free Derivation of the Neutron-to-Proton Mass Ratio from a Mechanistic Vacuum-Field Model

This preprint presents a mechanistic vacuum-field model of the neutron–proton mass ratio within the framework of Resonant Vacuum Theory (RVT). The proton and neutron are modeled as Borromean-ring solitons of a nonlinear scalar field with a Mexican-hat vacuum potential. The mass splitting is attributed to a cubic vacuum asymmetry term, V‴(Ψ₀) = 6λΨ₀, arising from spontaneous breaking of the Ψ → −Ψ symmetry by the nonzero vacuum condensate. The model derives the neutron-to-proton mass ratio mn/mp ≈ 1.00137, against the experimental value 1.001378, corresponding to a mass difference ΔM ≈ 1.29 MeV, close to the experimental 1.293 MeV. The absolute mass scale is calibrated to the proton mass, but this calibration cancels in the ratio; no parameter is tuned separately for proton and neutron. The central mechanical concept is the triadic flywheel: three phase-locked vortex rings forming a persistent rotor whose phase circulation suppresses the condensate amplitude at the soliton core. The surrounding coherence halo is interpreted as the time-averaged wave-like envelope of the precessing triad. The paper also derives the 2π/3 phase offsets between the rings from far-field stability and single-valuedness, and relates proton–neutron charge asymmetry to the net long-range phase gradients of their respective winding configurations. The work is intended as a mechanistic complement to quantum field theory rather than a replacement for its empirical formalism. It explicitly identifies as open problems whether the minimal RVT Lagrangian admits the proposed Borromean configurations as true field-theoretic minima, and whether the qualitative RVT bridges to Pauli exclusion, Coulomb interaction, nuclear attraction, atomic shell structure, double-slit interference, and uncertainty can be promoted to quantitative derivations. This version is submitted as a preprint to document the calculation, assumptions, and open questions for further review and development.