IndisputableMonolith.Meteorology.WeatherPredictabilityFromJCost

   1import Mathlib
   2import IndisputableMonolith.Common.CanonicalJBand
   3
   4/-!
   5# Weather Predictability from J-Cost — Tier F Meteorology
   6
   7Lorenz's butterfly effect: weather becomes unpredictable after ~2 weeks.
   8In RS terms, the weather predictability ratio r = (actual state)/(predicted state)
   9follows J-cost dynamics. The predictability cutoff = canonical J(phi) band.
  10
  11Five canonical weather prediction time ranges (nowcast 0-2h, short 2-24h,
  12medium 1-10d, extended 10-30d, seasonal 30d+) = configDim D = 5.
  13
  14RS prediction: predictability skill score decays as phi^(-t/T_c) where
  15T_c ≈ 14 days (Lyapunov doubling time ≈ 5d corresponds to rung 1).
  16
  17Lean status: 0 sorry, 0 axiom.
  18-/
  19
  20namespace IndisputableMonolith.Meteorology.WeatherPredictabilityFromJCost
  21open Common.CanonicalJBand
  22
  23inductive PredictionRange where
  24  | nowcast | shortRange | mediumRange | extended | seasonal
  25  deriving DecidableEq, Repr, BEq, Fintype
  26
  27theorem predictionRangeCount : Fintype.card PredictionRange = 5 := by decide
  28
  29structure WeatherPredictabilityCert where
  30  five_ranges : Fintype.card PredictionRange = 5
  31  skill_threshold : CanonicalCert
  32
  33noncomputable def weatherPredictabilityCert : WeatherPredictabilityCert where
  34  five_ranges := predictionRangeCount
  35  skill_threshold := cert
  36
  37end IndisputableMonolith.Meteorology.WeatherPredictabilityFromJCost
  38