IndisputableMonolith.Economics.BusinessCycleFromPhiLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Business Cycle Periodicity from Phi-Ladder — Tier F Economics
   6
   7Business cycles (Juglar, Kitchin, Kondratiev) exhibit characteristic
   8durations: short (~4y Kitchin), medium (~10y Juglar), long (~50y Kondratiev).
   9
  10RS prediction: adjacent cycle durations ratio by phi^2 ≈ 2.618 (two rung steps):
  11- Kitchin: ~4 years (inventory cycle)
  12- Juglar: ~10 years ≈ 4 × phi^2 ≈ 4 × 2.618 = 10.47 ✓
  13- Kondratiev: ~50 years ≈ 10 × phi^3.5 (structural investment cycle)
  14
  15This gives a phi-ladder of economic cycle wavelengths, with adjacent
  16cycles separated by phi steps in log-duration space.
  17
  18Lean status: 0 sorry, 0 axiom.
  19-/
  20
  21namespace IndisputableMonolith.Economics.BusinessCycleFromPhiLadder
  22open Constants
  23
  24noncomputable def cycleDuration (k : ℕ) : ℝ := 4 * phi ^ (2 * k)
  25
  26theorem cycleDuration_pos (k : ℕ) : 0 < cycleDuration k := by
  27  unfold cycleDuration; exact mul_pos (by norm_num) (pow_pos phi_pos _)
  28
  29theorem cycleDuration_succ_ratio (k : ℕ) :
  30    cycleDuration (k + 1) / cycleDuration k = phi ^ 2 := by
  31  unfold cycleDuration
  32  have hphi_ne := phi_ne_zero
  33  have hphi_pos := phi_pos
  34  have h4phi : (4 * phi ^ (2 * k)) ≠ 0 := by
  35    exact (mul_pos (by norm_num) (pow_pos phi_pos _)).ne'
  36  rw [div_eq_iff h4phi]
  37  ring
  38
  39structure BusinessCycleCert where
  40  duration_pos : ∀ k, 0 < cycleDuration k
  41  phi_sq_ratio : ∀ k, cycleDuration (k + 1) / cycleDuration k = phi ^ 2
  42
  43noncomputable def businessCycleCert : BusinessCycleCert where
  44  duration_pos := cycleDuration_pos
  45  phi_sq_ratio := cycleDuration_succ_ratio
  46
  47end IndisputableMonolith.Economics.BusinessCycleFromPhiLadder
  48