HAL Program Paper 32: Derivation of the Electroweak Mixing Angle and Gauge Couplings from the HAL Quartic Coupling

Numerical identification of electroweak couplings from HAL quantities. Central result: sin^2(theta_W) = lambda/(4*pi) + alpha_em = 2/9 + alpha_em = 0.22951, agreeing with PDG value 0.23122 to 0.74%. g3^2 = 2*pi/27 = alpha_em * exp(+6*gamma_E) exact to 0.000%. g2 = 0.6318 (SM: 0.6494, 2.7% error), g1 = 0.3448 (3.5% error). Note: these are numerical identifications at the UV scale; RG running to MZ remains an open problem. L_total reduces free inputs. Part of HAL programme papers 1-31 (Zenodo DOI 20849243-20941535).