cube3_faces

formal source

  76
  77theorem cube3_vertices : cube_vertices 3 = 8 := by native_decide
  78theorem cube3_edges : cube_edges_count 3 = 12 := by native_decide
  79theorem cube3_faces : cube_faces 3 = 6 := rfl
  80
  81/-! ## Derivation of the Coefficient 6 (Atmospheric) -/
  82
  83/-- The atmospheric correction coefficient is the face count of a 3-cube.
  84
  85    **Physical interpretation**: Each of the 6 faces of the cubic ledger
  86    contributes one unit of vacuum polarization to the atmospheric mixing.
  87    The μ-τ sector, being maximally mixed (sin²θ₂₃ ≈ 1/2), receives a
  88    symmetric correction from all faces. -/
  89def atmospheric_coefficient : ℕ := cube_faces 3
  90
  91theorem atmospheric_coefficient_eq_6 : atmospheric_coefficient = 6 := rfl
  92
  93/-- The atmospheric radiative correction is 6α. -/
  94noncomputable def atmospheric_correction : ℝ := (atmospheric_coefficient : ℝ) * alpha
  95
  96theorem atmospheric_correction_eq : atmospheric_correction = 6 * alpha := by
  97  unfold atmospheric_correction atmospheric_coefficient
  98  rfl
  99
 100/-! ## Derivation of the Coefficient 10 (Solar) -/
 101
 102/-- The solar correction coefficient is edges minus the active pair.
 103
 104    **Physical interpretation**: The solar sector involves 2-step torsion
 105    (φ⁻² weight), coupling via edges. The 12 edges minus the 2 active
 106    modes (e and ν_e in the 1-2 sector) gives 10 passive contributions. -/
 107def solar_coefficient : ℕ := cube_edges_count 3 - 2
 108
 109theorem solar_coefficient_eq_10 : solar_coefficient = 10 := rfl