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)

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.