correction_D_quad2

formal source

  74noncomputable def correction_D_quad1 (d : ℕ) : ℝ := (d : ℝ) * ((d : ℝ) - 1) / 4
  75
  76/-- Candidate 5: D²/6 (another quadratic) -/
  77noncomputable def correction_D_quad2 (d : ℕ) : ℝ := ((d : ℝ) ^ 2) / 6
  78
  79/-! ## Part 3: All Candidates Equal 1.5 in D=3 -/
  80
  81theorem D_half_at_3 : correction_D_half 3 = 3/2 := by
  82  unfold correction_D_half
  83  norm_num
  84
  85theorem F_quarter_at_3 : correction_F_quarter 3 = 3/2 := by
  86  unfold correction_F_quarter
  87  simp [cube_faces]
  88  norm_num
  89
  90theorem E_eighth_at_3 : correction_E_eighth 3 = 3/2 := by
  91  unfold correction_E_eighth
  92  simp [cube_edges]
  93  norm_num
  94
  95theorem D_quad1_at_3 : correction_D_quad1 3 = 3/2 := by
  96  unfold correction_D_quad1
  97  norm_num
  98
  99theorem D_quad2_at_3 : correction_D_quad2 3 = 3/2 := by
 100  unfold correction_D_quad2
 101  norm_num
 102
 103/-! ## Part 4: F/4 and D/2 are Algebraically Identical -/
 104
 105/-- **Key Identity**: F/4 = D/2 for ALL dimensions.
 106    This is not numerical coincidence—it's algebraic identity. -/
 107theorem F_quarter_eq_D_half : ∀ d : ℕ, correction_F_quarter d = correction_D_half d := by