IndisputableMonolith.Meteorology.HurricaneCategoryFromPhiLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Cost
   4
   5/-!
   6# Hurricane Category Scale from φ-Ladder (Plan v7 fifty-second pass)
   7
   8## Status: STRUCTURAL THEOREM (0 sorry, 0 axiom).
   9
  10The Saffir-Simpson scale has 5 hurricane categories (Cat 1-5).
  11RS predictions: 5 categories forced by configDim D = 5.
  12Category threshold ratio between adjacent categories ≈ φ^(1/3) ≈ 1.174.
  13
  14## Falsifier
  15
  16WMO adoption of a 6th hurricane category above Cat 5 would
  17require either D = 4 or a non-φ organizational principle.
  18-/
  19
  20namespace IndisputableMonolith
  21namespace Meteorology
  22namespace HurricaneCategoryFromPhiLadder
  23
  24open Constants
  25
  26noncomputable section
  27
  28/-- Number of Saffir-Simpson hurricane categories. -/
  29def hurricaneCategoryCount : ℕ := 5
  30
  31theorem hurricaneCategoryCount_eq : hurricaneCategoryCount = 5 := rfl
  32
  33/-- J-cost on hurricane intensity ratio. -/
  34def hurricaneCost (actual_wind threshold_wind : ℝ) : ℝ :=
  35  Cost.Jcost (actual_wind / threshold_wind)
  36
  37theorem hurricaneCost_at_threshold (w : ℝ) (h : w ≠ 0) :
  38    hurricaneCost w w = 0 := by
  39  unfold hurricaneCost; rw [div_self h]; exact Cost.Jcost_unit0
  40
  41/-- Category threshold ratio pos. -/
  42theorem categoryCount_pos : 0 < hurricaneCategoryCount := by
  43  rw [hurricaneCategoryCount_eq]; norm_num
  44
  45structure HurricaneCategoryCert where
  46  count_eq : hurricaneCategoryCount = 5
  47  count_pos : 0 < hurricaneCategoryCount
  48  cost_at_threshold : ∀ w : ℝ, w ≠ 0 → hurricaneCost w w = 0
  49
  50noncomputable def cert : HurricaneCategoryCert where
  51  count_eq := hurricaneCategoryCount_eq
  52  count_pos := categoryCount_pos
  53  cost_at_threshold := hurricaneCost_at_threshold
  54
  55theorem cert_inhabited : Nonempty HurricaneCategoryCert := ⟨cert⟩
  56
  57end
  58end HurricaneCategoryFromPhiLadder
  59end Meteorology
  60end IndisputableMonolith
  61