EruptionRecurrenceCert

formal source

  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
 108  one_step_eq := cumulative_ratio_one_step
 109
 110/-- **ERUPTION RECURRENCE ONE-STATEMENT.** Adjacent-VEI eruption
 111recurrence ratios cluster at `φ² ∈ (2.59, 2.63)`; cumulative
 112recurrence across `k` VEI steps equals `φ^(2k) = (φ²)^k`. -/
 113theorem eruption_recurrence_one_statement :
 114    (2.59 < vei_step_ratio ∧ vei_step_ratio < 2.63) ∧
 115    (∀ k : ℕ, cumulative_ratio k = vei_step_ratio ^ k) ∧
 116    cumulative_ratio 1 = vei_step_ratio :=
 117  ⟨vei_step_ratio_band, cumulative_ratio_factors, cumulative_ratio_one_step⟩
 118
 119end
 120
 121end EruptionRecurrenceLadder
 122end Geology
 123end IndisputableMonolith