Light Quark Masses from Informational Axioms: Channel Isolation and Measure-Theoretic Ratios

We derive the three light quark masses (u, d, s) from informational axioms with zero free parameters. The MS-bar masses at 2 GeV are: m_u = α · g_A · v₃ · (1 − απ/4) = 2.144 MeV, m_d = m_u · (2 + 1/(2π)) = 4.628 MeV, m_s = 20m_d = 92.57 MeV, where α is the fine-structure constant (self-consistent solution of Theorem 22, 1/α = 137.036), g_A = 4/π is the axial coupling (derived from the Hopf fibration of SU(2)_L; experimental: 1.2762 ± 0.0005, error −0.23%), and v₃ = M_Pl · α^g(3) is the QCD scale from the universal cascade. All three masses agree with PDG 2024 to within 1.1σ. The QED self-energy correction δ_QED = απ/4 ≈ 0.57%, whose coefficient π/4 = I_ψ/2 is the Hopf fiber integral, propagates to the neutron-proton mass difference and the neutron lifetime. All four formulas (absolute mass, QED coefficient, and both mass ratios) are derived from the axioms. The PDG 2024 values are: m_u = 2.16 ± 0.07 MeV (−0.76% error, 0.24σ), m_d = 4.67 ± 0.09 MeV (−0.90% error, 0.47σ), m_s = 93.4 ± 0.8 MeV (−0.89% error, 1.0σ). Neither the intra-generational ratio m_d/m_u ≈ 2.16 nor the inter-generational ratio m_s/m_d ≈ 20 has a Standard Model explanation; both are derived here from the Haar measure of U(1)_Y and the arithmetic cascade structure. A complete Python validation script reproducing all numerical results is provided in the appendix.