cumulative_ratio

formal source

  74
  75/-- The cumulative recurrence ratio across `k` VEI steps:
  76    `φ^(2k)`. -/
  77def cumulative_ratio (k : ℕ) : ℝ := phi ^ (2 * k)
  78
  79theorem cumulative_ratio_pos (k : ℕ) : 0 < cumulative_ratio k := by
  80  unfold cumulative_ratio
  81  exact pow_pos phi_pos _
  82
  83theorem cumulative_ratio_one_step :
  84    cumulative_ratio 1 = vei_step_ratio := by
  85  unfold cumulative_ratio vei_step_ratio
  86  rfl
  87
  88theorem cumulative_ratio_factors (k : ℕ) :
  89    cumulative_ratio k = vei_step_ratio ^ k := by
  90  unfold cumulative_ratio vei_step_ratio
  91  rw [← pow_mul]
  92
  93/-! ## §3. Master certificate -/
  94
  95structure EruptionRecurrenceCert where
  96  step_ratio_pos : 0 < vei_step_ratio
  97  step_ratio_band : 2.59 < vei_step_ratio ∧ vei_step_ratio < 2.63
  98  cumulative_pos : ∀ k : ℕ, 0 < cumulative_ratio k
  99  cumulative_factors : ∀ k : ℕ,
 100    cumulative_ratio k = vei_step_ratio ^ k
 101  one_step_eq : cumulative_ratio 1 = vei_step_ratio
 102
 103def eruptionRecurrenceCert : EruptionRecurrenceCert where
 104  step_ratio_pos := vei_step_ratio_pos
 105  step_ratio_band := vei_step_ratio_band
 106  cumulative_pos := cumulative_ratio_pos
 107  cumulative_factors := cumulative_ratio_factors