PMNSParameters

formal source

  65
  66where c_ij = cos θ_ij and s_ij = sin θ_ij
  67-/
  68structure PMNSParameters where
  69  theta12 : ℝ  -- Solar angle
  70  theta23 : ℝ  -- Atmospheric angle
  71  theta13 : ℝ  -- Reactor angle
  72  deltaCP : ℝ  -- CP phase
  73
  74/-- The best-fit PMNS parameters. -/
  75noncomputable def bestFitPMNS : PMNSParameters := {
  76  theta12 := theta12_degrees * Real.pi / 180,
  77  theta23 := theta23_degrees * Real.pi / 180,
  78  theta13 := theta13_degrees * Real.pi / 180,
  79  deltaCP := deltaCP_degrees * Real.pi / 180
  80}
  81
  82/-! ## φ-Connection Hypotheses -/
  83
  84/-- **Hypothesis 1: Golden Ratio Mixing**
  85
  86    sin²θ₁₂ = 1/(1 + φ²) = 1/(1 + 2.618) = 1/3.618 ≈ 0.276
  87
  88    Compared to observed 0.307, this is ~10% off. -/
  89noncomputable def phi_prediction_theta12 : ℝ := 1 / (1 + phi^2)
  90
  91/-- **Hypothesis 2: Maximal θ₂₃ from symmetry**
  92
  93    sin²θ₂₃ = 1/2 (maximal mixing)
  94
  95    Observed ≈ 0.545, close to maximal but slightly off.
  96    A small φ-correction could explain the deviation. -/
  97noncomputable def maximal_theta23 : ℝ := 1 / 2
  98