Input: sin²θ_W = 0.2312 Measured at Z-pole (C8) α_mf = 0.30078 Kopnin: α_mf = sin²θ_W / (1 − sin²θ_W) δ₀ = 18.48° Breit-Wigner: sin 2δ₀ = 2α_mf g² = 4 sin²δ₀ = 0.4024 Berry phase of boundary doublet e = g sin θ_W Electroweak mixing α = g² sin²θ_W / (4π) = 0.00740 Verification Tree-level result α_pred = 0.00740 (1/135.1) α_meas = 0.00730 (1/137.0) Discrepancy: +1.45% Expected from radiative corrections Cross-check: (g−2)/2 η² = α/(2π) = sin²δ₀ sin²θ_W / (2π²) η_pred = 0.0343, η_meas = 0.0341 Zero-parameter relation α, sin²θ_W, and (g−2)/2 all determined by single parameter: δ₀ = 18.48° 1/α_pred = 135.1 vs 1/α_meas = 137.0 Gap closable by vacuum polarization

The complete derivation chain from sin²θ_W to α. Left: six steps from the measured Weinberg angle through the mutual friction parameter, s-wave phase shift, SU(2) gauge coupling, electroweak mixing, to the fine structure constant. Right: numerical verification — the tree-level result gives 1/135.1 (+1.45% from measured 1/137.0), and the cross-check against (g−2)/2 is consistent to 0.8%. All three constants are determined by a single geometric parameter δ₀.