Topological Geometry of the Lepton Sector: Derivation of Charged Lepton Masses and Neutrino PMNS Mixing Angles from the 9-Cell Flat Unfolding of the Clifford Torus (Formally Verified in Lean 4)
Year: 2026
Type: preprint
Abstract: In the Standard Model of particle physics, charged lepton masses and neutrino mixing parameters (the PMNS matrix) are governed by free phenomenological constants without theoretical explanation. We propose a parameter-free phenomenological geometric framework modeling leptons as closed phase solitons on a Clifford torus (R/r = sqrt(2)) undergoing topological eversion. Distributing the normalized minimal Willmore energy (W / pi^2 = 2) over a 9-cell flat unfolding lattice (Z_3 x Z_3 = Fin 3 x Fin 3) uniquely fixes the Koide phase shift theta_0 = 2/9 rad. Furthermore, modeling neutrinos as zero-amplitude phase remnants tunneling across the 9 unfolding cells yields analytical predictions for the three PMNS mixing angles (theta_13 = sqrt(2)/9, theta_23 = pi/4 + 1/18, theta_12 = arcsin(1/sqrt(3)) - 2/81) and an exponential mass suppression factor exp(-18). This predicts normal neutrino mass ordering with a non-zero lightest neutrino mass (m_1 ~ 0.0021 eV, sum(m_nu) ~ 0.0625 eV). All algebraic identities, numerical mass bounds, and PMNS unitarity are formally verified without gaps (sorry) in Lean 4.
Author: Saltykov
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225828341
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