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 = αEM, y_μ = αEM CLIG, and yₑ = α²EM CLIG CQG, where αEM = 1/137. 036, CLIG = 0. 05954 (matter-geometry coupling), and CQG = 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 mₑ = 0. 519 MeV (1. 6%) reproduce experiment with percent-level accuracy. The mass ratios m_μ/m_τ = CLIG (0. 13% agreement) and mₑ/m_μ = αEM CQG (0. 34% agreement) are independent of the Higgs VEV and RGE evolution, constituting the most precise predictions. The relation y_τ = yc = αEM manifests b-τ Yukawa unification at the compactification scale, with yb/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 αEM and two geometric constants, reducing nine independent SM Yukawa couplings to three predetermined constants