ODD Proof Series 2026-CP-02: Geometric Derivation of the Charged Lepton Mass Spectrum and Zero-Parameter Validation of the Muon-Electron Ratio

We present a first-principles, fully numerical derivation of the charged lepton mass spectrum (electron, muon, tau) within the Operator-Derived Dimension (ODD) framework. The masses are not postulated but emerge as the eigenvalues of the TransverseProjection Operator’s Hamiltonian, modulated by the geometric warp factor of the 5D bulk. The model is uniquely constrained by the topological stability index μ = 2 and requires only a single free parameter, the bulk curvature scale k, which is calibrated using the experimental electron mass. With this single input, the framework predicts the muon and tau masses. We show that the predicted values are in remarkable agreement with experimental measurements from the Particle Data Group. The small residual discrepancies are identified as the geometric prediction for higher-order radiative corrections.