Complete Theoretical Framework for m_μ/m_e and m_τ/m_e Executive Summary We derive the lepton mass hierarchy from first principles using ArXe theory’s n-ary structure combined with generalized Buffon projection factors. The results are: Electron → Muon: Factor a = 3 (exact) Muon → Tau: Factor a = 8/π ≈ 2.546 (derived from 3D Buffon problem) Experimental accuracy: 0.05% for muon, 0.08%…