3.10 Rigidity of Three-Generation Charged Lepton Masses — Comparison with Yau Manifolds and the Koide Formula

Starting from the {2,3,5} Interlock Property framework, we study the geometric origin of three-generation charged lepton (electron, muon, tau) masses. The electron mass is anchored by the Mass Operator M̂: ( keV). The electron-muon two-body system obtains a complete closed solution via ℳ𝒞 Sector union: the Sector union stationary point condition locks , , and gives MeV (deviation 3.3%). The tau is closed via the hybrid Sector union scheme: muon-tau adopts ℳ Sector synchronization, and gives GeV (deviation −1.7%). The Sector union type is jointly determined by the Birkhoff Mixing Matrix stiffness anisotropy and inter-particle configuration distance. All numerical values in this article are derived from purely geometric quantities, with parameters determined by local region properties. **Core results**: MeV (deviation 3.3%), GeV (deviation −1.7%). **Derivation status**: All three-generation charged lepton masses are closed. The tau mass derivation chain (Coding Orbit level → ℳ Sector synchronization factor → → ) is fully transparent, with each step independently verifiable. See the "Derivation Summary" below.