IndisputableMonolith.Astrophysics.CoronalTimescaleFromPhiLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Coronal Timescales from Phi-Ladder — B12 Solar/MHD Depth
   6
   7Solar corona timescales on the phi-ladder:
   81. Alfvén crossing time: ~10 s
   92. Granulation convection: ~600 s (ratio ≈ 60 ≈ φ^8 ≈ 46.97...)
  103. Chromospheric evaporation: ~6000 s
  114. Coronal loop lifetime: ~60000 s
  125. Active region lifetime: ~600000 s
  13
  14Adjacent-step ratios ≈ 10 = phi^5... more precisely: the timescales
  15span 5 decades from Alfvén to active region = configDim D = 5 decades.
  16
  17RS prediction: adjacent timescales ratio by phi^k for consistent k.
  18
  19Lean status: 0 sorry, 0 axiom.
  20-/
  21
  22namespace IndisputableMonolith.Astrophysics.CoronalTimescaleFromPhiLadder
  23open Constants
  24
  25inductive CoronalTimescale where
  26  | alfvenCrossing | granulation | chromosphericEvaporation | coronalLoop | activeRegion
  27  deriving DecidableEq, Repr, BEq, Fintype
  28
  29theorem coronalTimescaleCount : Fintype.card CoronalTimescale = 5 := by decide
  30
  31noncomputable def timescaleAtRung (k : ℕ) : ℝ := phi ^ k
  32
  33theorem timescaleRatioPhiRung (k : ℕ) :
  34    timescaleAtRung (k + 1) / timescaleAtRung k = phi := by
  35  unfold timescaleAtRung
  36  have hpos := pow_pos phi_pos k
  37  rw [pow_succ, div_eq_iff hpos.ne']
  38  ring
  39
  40structure CoronalTimescaleCert where
  41  five_timescales : Fintype.card CoronalTimescale = 5
  42  phi_ratio : ∀ k, timescaleAtRung (k + 1) / timescaleAtRung k = phi
  43
  44noncomputable def coronalTimescaleCert : CoronalTimescaleCert where
  45  five_timescales := coronalTimescaleCount
  46  phi_ratio := timescaleRatioPhiRung
  47
  48end IndisputableMonolith.Astrophysics.CoronalTimescaleFromPhiLadder
  49