A Geometric Interpretation of Lepton and Neutrino Mass Hierarchies via Defect Tunneling in a Close-Packed Lattice

I present a speculative geometric framework to explore the mass hierarchies of charged leptons (e, µ, τ) and neutrinos (νe, νµ, ντ). By modeling the physical vacuum as a dynamical electron–positron pair condensate, material leptons are interpreted as localized defects or collective excitations of this underlying structure. Three characteristic defect configurations are associated with the fundamental crystallographic directions, [100],[110], and [111]. Incorporating a single anisotropic deformation corresponding to the close-packing constraint √(2/3) along the Z-axis, the model obtains effective geometric distances governed by an exponential mass ansatz, m ∝ e^(αd). Using only the electron and muon masses as inputs, the construction gives a tau mass of approximately 1765.62 MeV, within 0.63% of the measured value. Applied phenomenologically to the neutral sector, the same geometric structure gives an estimated neutrino mass sum of approximately 0.0529 eV. The model is explicitly presented as a minimalist toy model and does not attempt to derive/explain the Standard Model or its microscopic dynamics.