 114    The mixing angle comes from the geometric arrangement.
 115
 116    Key insight: The "golden cut" of the 8-tick circle gives the mixing angle. -/
 117structure EightTickGeometry where
 118  /-- Number of phases in SU(2) sector -/
 119  su2_phases : ℕ := 3
 120  /-- Number of phases in U(1) sector -/
 121  u1_phases : ℕ := 1
 122  /-- Total phases -/
 123  total : ℕ := 8
 124
 125/-- The geometric mixing angle from 8-tick structure. -/
 126noncomputable def geometricMixing (g : EightTickGeometry) : ℝ :=
 127  (g.u1_phases : ℝ) / ((g.su2_phases : ℝ) + (g.u1_phases : ℝ))
 128
 129/-- **THEOREM**: Simple geometric ratio gives sin²(θ_W) = 1/4 = 0.25.
 130
 131    This is close but not exact. The correction comes from φ. -/
 132theorem simple_geometric_ratio : geometricMixing ⟨3, 1, 8⟩ = 1/4 := by
 133  unfold geometricMixing
 134  norm_num
 135
 136/-- The φ-correction to the geometric ratio.
 137
 138    sin²(θ_W) = 1/4 × (1 - ε)
 139    where ε = (φ - 1) / (12φ) ≈ 0.032
 140
 141    This gives: 0.25 × (1 - 0.032) = 0.242 × 0.968 = 0.234
 142
 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

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.