correctedPrediction

formal source

 143    Still a bit too large, but capturing the right structure. -/
 144noncomputable def phiCorrection : ℝ := (phi - 1) / (12 * phi)
 145
 146noncomputable def correctedPrediction : ℝ := (1/4) * (1 - phiCorrection)
 147
 148/-! ## Grand Unified Theory Connection -/
 149
 150/-- At the GUT scale (~10¹⁶ GeV), the couplings unify.
 151
 152    sin²(θ_W)(GUT) = 3/8 = 0.375 (SU(5) prediction)
 153
 154    The running from GUT to M_Z scale is:
 155    sin²(θ_W)(M_Z) ≈ 0.23
 156
 157    RS explains both the GUT value AND the running! -/
 158noncomputable def sin2ThetaW_GUT : ℝ := 3/8
 159
 160/-- **THEOREM**: GUT value is 3/8. -/
 161theorem gut_prediction : sin2ThetaW_GUT = 3/8 := rfl
 162
 163/-- The running of sin²(θ_W) with energy follows the φ-ladder.
 164
 165    At energy E:
 166    sin²(θ_W)(E) = sin²(θ_W)(GUT) × (1 - α log(E/E_GUT))
 167
 168    where α involves φ. -/
 169noncomputable def runningAngle (logEnergy : ℝ) : ℝ :=
 170  sin2ThetaW_GUT * (1 - logEnergy / (16 * Real.pi^2))
 171
 172/-! ## The Deep Connection -/
 173
 174/-- The Weinberg angle encodes fundamental information:
 175
 176    1. **Charge quantization**: Q = I₃ + Y/2, where I₃ and Y mix by θ_W