IndisputableMonolith.Econ.LedgerEconomics

   1import Mathlib
   2import IndisputableMonolith.Constants
   3open IndisputableMonolith.Constants
   4
   5
   6namespace IndisputableMonolith.Econ.LedgerEconomics
   7
   8noncomputable section
   9
  10
  11/-- The 8-tick octave forces exactly 8 economic phases. -/
  12noncomputable def economicPhases : ℝ := octave / tick
  13
  14/-- Phi-scaled business cycle period in ticks: 8 × φ⁵. -/
  15noncomputable def businessCyclePeriod : ℝ := octave * phi ^ 5
  16
  17/-- Double-entry ledger conservation ratio: φ⁻¹ + φ⁻² (forced = 1). -/
  18noncomputable def ledgerConservationRatio : ℝ := 1 / phi + 1 / phi ^ 2
  19
  20/-- Octave growth multiplier: φ⁸ = 21φ + 13. -/
  21noncomputable def octaveGrowthMultiplier : ℝ := phi ^ 8
  22
  23/-- The 8-tick octave forces exactly 8 economic phases. -/
  24theorem eight_economic_phases : economicPhases = 8 := by
  25  unfold economicPhases octave tick; norm_num
  26
  27/-- Business cycle period is positive. -/
  28theorem businessCyclePeriod_pos : 0 < businessCyclePeriod := by
  29  unfold businessCyclePeriod octave tick
  30  have hp := phi_pos; positivity
  31
  32/-- Business cycle period exceeds 85 ticks. -/
  33theorem businessCyclePeriod_lower : (85 : ℝ) < businessCyclePeriod := by
  34  unfold businessCyclePeriod octave tick
  35  rw [phi_fifth_eq]; nlinarith [phi_gt_onePointSixOne]
  36
  37/-- Business cycle period is below 91 ticks. -/
  38theorem businessCyclePeriod_upper : businessCyclePeriod < (91 : ℝ) := by
  39  unfold businessCyclePeriod octave tick
  40  rw [phi_fifth_eq]; nlinarith [phi_lt_onePointSixTwo]
  41
  42/-- Ledger conservation: φ⁻¹ + φ⁻² = 1, forcing double-entry structure. -/
  43theorem ledgerConservation_eq_one : ledgerConservationRatio = 1 := by
  44  unfold ledgerConservationRatio
  45  have hphi : phi ≠ 0 := phi_ne_zero
  46  have hphi2 : phi ^ 2 ≠ 0 := pow_ne_zero _ hphi
  47  have hsq := phi_sq_eq
  48  field_simp
  49  linarith
  50
  51/-- FALSIFIABLE PREDICTION: φ⁸ ∈ (46, 48), bounding an 8-phase economic growth factor.
  52    If empirical compounding per octave (8 years) lies outside this range,
  53    the RS phi-scaling hypothesis for economic cycles is refuted. -/
  54theorem octaveGrowth_bounds :
  55    (46 : ℝ) < octaveGrowthMultiplier ∧ octaveGrowthMultiplier < (48 : ℝ) := by
  56  unfold octaveGrowthMultiplier
  57  rw [phi_eighth_eq]
  58  constructor
  59  · nlinarith [phi_gt_onePointSixOne]
  60  · nlinarith [phi_lt_onePointSixTwo]
  61
  62/-- Business cycle period bounds as a conjunction. -/
  63theorem businessCycle_bounds :
  64    (85 : ℝ) < businessCyclePeriod ∧ businessCyclePeriod < (91 : ℝ) :=
  65  ⟨businessCyclePeriod_lower, businessCyclePeriod_upper⟩
  66
  67end
  68
  69end IndisputableMonolith.Econ.LedgerEconomics