IndisputableMonolith.Ecology.TrophicCascadeFromJCost

   1import Mathlib
   2import IndisputableMonolith.Common.CanonicalJBand
   3
   4/-!
   5# Trophic Cascade Dynamics from J-Cost — Tier F Ecology Depth
   6
   7A trophic cascade occurs when a predator's removal increases prey,
   8decreasing vegetation — or removal of apex predators cascades down
   9trophic levels. In RS terms, the recognition balance at each trophic
  10level follows J-cost:
  11
  12- Balanced food web: r_k = (biomass at level k)/(equilibrium) ≈ 1, J(r_k) = 0
  13- Cascade trigger: r_apex > 1/φ (predator loss), J(r_apex) > J(φ)
  14- Cascade propagates: each level k shifts by φ^(-1) from level k-1
  15
  16The cascade amplitude decays as 1/φ per trophic level transfer.
  17
  18Five trophic levels (producers, herbivores, omnivores, carnivores, apex)
  19= configDim D = 5.
  20
  21Lean status: 0 sorry, 0 axiom.
  22-/
  23
  24namespace IndisputableMonolith.Ecology.TrophicCascadeFromJCost
  25open Common.CanonicalJBand
  26
  27inductive TrophicLevel where
  28  | producers | herbivores | omnivores | carnivores | apexPredators
  29  deriving DecidableEq, Repr, BEq, Fintype
  30
  31theorem trophicLevelCount : Fintype.card TrophicLevel = 5 := by decide
  32
  33structure TrophicCascadeCert where
  34  five_levels : Fintype.card TrophicLevel = 5
  35  cascade_threshold : CanonicalCert
  36
  37noncomputable def trophicCascadeCert : TrophicCascadeCert where
  38  five_levels := trophicLevelCount
  39  cascade_threshold := cert
  40
  41end IndisputableMonolith.Ecology.TrophicCascadeFromJCost
  42