Charged Lepton Mass Hierarchy from Matter-Geometry Coupling at Conical Singularities in M-Theory Compactification on G₂-Holonomy Manifolds

The charged lepton mass spectrum is derived from first principles within the Quantum Geometric Unification (QGU) framework based on M-theory compactification on the Joyce orbifold T⁷/(Z₃ ⋉ I*) with G₂ holonomy and Betti numbers (b₂, b₃) = (27, 451). The Yukawa couplings of the tau, muon, and electron are determined by wavefunction overlap integrals at conical singularities of type I* (binary icosahedral), yielding y_τ = α_EM, y_μ = α_EM C_LIG, and y_e = α²_EM C_LIG C_QG, where α_EM = 1/137.036, C_LIG = 0.05954 (matter-geometry coupling), and C_QG = 0.665 (quantum-geometric potential strength). These constants have been established independently in ten companion publications and are not adjusted in the present work. The predicted masses m_τ = 1797 MeV (1.1%), m_μ = 107.0 MeV (1.2%), and m_e = 0.519 MeV (1.6%) reproduce experiment with percent-level accuracy. The mass ratios m_μ/m_τ = C_LIG (0.13% agreement) and m_e/m_μ = α_EM C_QG (0.34% agreement) are independent of the Higgs VEV and RGE evolution, constituting the most precise predictions. The relation y_τ = y_c = α_EM manifests b-τ Yukawa unification at the compactification scale, with y_b/y_τ = π from QCD enhancement. Combined with the quark mass predictions of the companion GSM analysis, nine charged fermion masses spanning eight orders of magnitude are expressed as algebraic functions of α_EM and two geometric constants, reducing nine independent SM Yukawa couplings to three predetermined constants