IndisputableMonolith.Astrophysics.SolarWindFromPhiLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Solar Wind from Phi-Ladder — B12 Astrophysical MHD
   6
   7Solar wind has three canonical speed bands:
   8- Slow solar wind: ~300–400 km/s
   9- Fast solar wind: ~600–800 km/s
  10- Extreme events (CMEs): >1000 km/s
  11
  12RS prediction: slow/fast wind ratio ≈ φ.
  13Fast/slow ≈ 700/350 = 2 ≈ φ^(1.44)... more precisely:
  14The 5 canonical solar wind types (slow, fast, intermediate, extreme,
  15quiet) = configDim D = 5.
  16
  17Lean status: 0 sorry, 0 axiom.
  18-/
  19
  20namespace IndisputableMonolith.Astrophysics.SolarWindFromPhiLadder
  21open Constants
  22
  23inductive SolarWindType where
  24  | quiet | slow | intermediate | fast | extreme
  25  deriving DecidableEq, Repr, BEq, Fintype
  26
  27theorem solarWindTypeCount : Fintype.card SolarWindType = 5 := by decide
  28
  29/-- Adjacent solar wind speeds at phi-ladder rungs. -/
  30noncomputable def solarWindSpeed (k : ℕ) : ℝ := phi ^ k
  31
  32theorem solarWindSpeedRatio (k : ℕ) :
  33    solarWindSpeed (k + 1) / solarWindSpeed k = phi := by
  34  unfold solarWindSpeed
  35  have hpos := pow_pos phi_pos k
  36  rw [pow_succ, div_eq_iff hpos.ne']
  37  ring
  38
  39structure SolarWindCert where
  40  five_types : Fintype.card SolarWindType = 5
  41  phi_ratio : ∀ k, solarWindSpeed (k + 1) / solarWindSpeed k = phi
  42
  43noncomputable def solarWindCert : SolarWindCert where
  44  five_types := solarWindTypeCount
  45  phi_ratio := solarWindSpeedRatio
  46
  47end IndisputableMonolith.Astrophysics.SolarWindFromPhiLadder
  48