TBM_theta12

formal source

 111    - sin²θ₁₃ = 0 (wrong!)
 112
 113    Reality deviates from TBM by φ-corrections. -/
 114noncomputable def TBM_theta12 : ℝ := 1 / 3
 115noncomputable def TBM_theta23 : ℝ := 1 / 2
 116noncomputable def TBM_theta13 : ℝ := 0
 117
 118/-- **Hypothesis 5: Golden Ratio Mixing (GRM)**
 119
 120    sin²θ₁₂ = (2 + φ)⁻¹ = 1/3.618 ≈ 0.276
 121
 122    Or alternatively:
 123    sin θ₁₂ = 1/√(1 + φ²) = 0.526
 124    sin²θ₁₂ = 0.277
 125
 126    Still ~10% from observed. -/
 127noncomputable def GRM_theta12 : ℝ := 1 / (2 + phi)
 128
 129/-! ## RS-Corrected Mixing -/
 130
 131/-- The RS correction to tribimaximal mixing:
 132
 133    Δ(sin²θ₁₂) = 1/3 - 0.307 = 0.026 ≈ (φ - 1)² = 0.382² ≈ 0.146
 134
 135    Too large. Try:
 136    Δ(sin²θ₁₂) ≈ (φ - 1)³ ≈ 0.236 × 0.382 ≈ 0.090
 137
 138    Still too large. The correction is subtle. -/
 139noncomputable def TBM_correction_theta12 : ℝ := 1/3 - sin2_theta12_observed
 140
 141/-- The 8-tick connection:
 142
 143    With 8 phases and 3 generations, we have 24 degrees of freedom.
 144    The mixing angles partition these into mass and flavor bases.