IV.R416 — On-Shell vs MS-bar Weinberg Angle Scheme Distinction

On-shell sin²θ_W = 1−(M_W/M_Z)² = 0.22320 differs from MS-bar sin²θ_W = 0.23122 by radiative correction Δr ≈ 0.036. Tree-level τ³ value ι_τ(1−ι_τ) = 0.22482 is closer to on-shell (0.72% gap) than to MS-bar (2.8% gap). Deriving Δr from τ³ mode structure to close the +1039 ppm gap on M_Z is an open problem.