The Dual-Spin Gyroscope and the Constraint Triangle Dual-spin gyroscope Body 2 (shell) I₂ , ω₂ ≈ −ω₁ Body 1 I₁ , ω₁ K_r (reactive) K_d (dissipative) L₁ L₂ S = ℏ/2 L₁ + L₂ = S η = (I₁ − I₂) / (I₁ + I₂) ≈ 0.034 The C6 / C8 / C9 constraint triangle δ₀ = 18.44° C8: sin²θ_W ≈ 0.231 (Weinberg angle) C6: α ≈ 1/137 (fine structure) C9: (g−2)/2 ≈ 0.00116 (anomalous) α_mf = ½ sin 2δ₀ g² = 4 sin²δ₀ α = g²sin²θ_W / 4π η² = α/(2π) (g−2)/2 = η² linked through α one phase shift → three constants The 3.4% asymmetry between core and boundary moments of inertia connects the Weinberg angle, α, and (g−2)/2.