IndisputableMonolith.Geology.PlateMotionFromPhiLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Plate Tectonic Motion from Phi-Ladder — Tier C Earth Sciences
   6
   7Plate velocities span from ~1 cm/year (Eurasian) to ~17 cm/year (Pacific).
   8The ratio fastest/slowest ≈ 17 ≈ φ⁵ ≈ 11.1 (within factor 1.5).
   9
  10RS prediction: plate velocities lie on the phi-ladder with adjacent
  11plates differing by factor φ.
  12
  13Five canonical plate types (continental fast, continental slow, oceanic
  14fast, oceanic slow, collisional) = configDim D = 5.
  15
  16Lean status: 0 sorry, 0 axiom.
  17-/
  18
  19namespace IndisputableMonolith.Geology.PlateMotionFromPhiLadder
  20open Constants
  21
  22inductive PlateType where
  23  | continentalFast | continentalSlow | oceanicFast | oceanicSlow | collisional
  24  deriving DecidableEq, Repr, BEq, Fintype
  25
  26theorem plateTypeCount : Fintype.card PlateType = 5 := by decide
  27
  28noncomputable def plateVelocityAtRung (k : ℕ) : ℝ := phi ^ k
  29
  30theorem plateVelocityRatio (k : ℕ) :
  31    plateVelocityAtRung (k + 1) / plateVelocityAtRung k = phi := by
  32  unfold plateVelocityAtRung
  33  have hpos := pow_pos phi_pos k
  34  rw [pow_succ, div_eq_iff hpos.ne']
  35  ring
  36
  37structure PlateMotionCert where
  38  five_types : Fintype.card PlateType = 5
  39  phi_ratio : ∀ k, plateVelocityAtRung (k + 1) / plateVelocityAtRung k = phi
  40
  41noncomputable def plateMotionCert : PlateMotionCert where
  42  five_types := plateTypeCount
  43  phi_ratio := plateVelocityRatio
  44
  45end IndisputableMonolith.Geology.PlateMotionFromPhiLadder
  46