A Collective Vacuum Domain Interpretation of Lepton Geometry and Mass Hierarchies

This preprint develops a phenomenological model in which the physical vacuum is treated as a neutral collective medium with a characteristic present-day structural scale. The observed charged-lepton mass hierarchy is used to define a dimensionless geometric parameter, which is then anchored to the reduced electron Compton wavelength to obtain a characteristic separation of approximately 4.97 pm and a reciprocal structural energy scale of about 39.7 keV. Within the model, the electron and positron are interpreted as rare localized charged defects of the neutral vacuum, while the muon and tau correspond to higher collision-induced geometrical excitations of the same charged topology. The neutrino sector is treated as a neutral propagating excitation, and the same geometric framework is tested against charged-lepton, neutrino, atomic and quark-sector relations. Additional appendices examine the relation between the proposed vacuum scale and the Bohr radius, the neutrino mass-squared hierarchy, an exploratory extension to running quark Yukawa couplings, and a possible interstitial neutral sector as a phenomenological dark-matter mechanism. The construction is explicitly presented as a phenomenological toy model rather than a complete quantum field theory. It does not replace the Standard Model, QED or QCD, but explores whether several apparently unrelated particle and length scales may reflect a common collective vacuum geometry.