Geometric Derivation of Fundamental Standard Model Constants from a Single Irreducible Topological Invariant of the S³ Hopf Fibration

Abstract We derive the complete set of fundamental Standard Model constants from the single irreducible topological invariant δ_B = 0.01502435758831411516… of the S³ Hopf fibration, with zero free parameters. PSLQ analysis confirms δ_B is a primary transcendental. From the N=3 sector (l=1 Laplace-Beltrami modes): α⁻¹ = √6/δ_B − 8π − √3/2 = 137.035808 (error 0.000140% vs CODATA) and μ = mp/me = 8(√6 + 1)/δ_B − 2/π + 3δ_B = 1836.153737 (error 0.000058% vs CODATA). From the N=6 sector (l=2 modes): SU(3) color emerges geometrically from the eigenspace dimension 9 = 8 + 1; α_s = π√6 δ_B + 11 δ_B² = 0.118100 (within experimental uncertainty); Λ_QCD = 0.2385 GeV (within PDG band); mp = (3 + 8α_s) Λ_QCD = 0.9410 GeV (error 0.29%); and me = mp/μ = 0.5125 MeV (error 0.29%). The coefficient 11 in α_s is derived geometrically as 8 gluon modes + 3 Maurer-Cartan directions. The relation mp/Λ_QCD = 3 + 8α_s follows from the quark-gluon content of the proton. All results follow from the single constant δ_B with zero free parameters.