IndisputableMonolith.Sociology.CivilizationCyclesFromPhiLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Civilization Cycles from Phi-Ladder — Tier F Sociology
   6
   7Historical civilizations exhibit rise-and-fall cycles. In RS terms,
   8civilizational cohesion (Spengler's "culture") is a recognition
   9coherence field, and cycles occur on phi-ladder timescales.
  10
  11Five canonical civilizational stages (emergence, growth, consolidation,
  12decline, transformation) = configDim D = 5.
  13
  14RS prediction: cycle duration ratio between adjacent civilizations ≈ phi.
  15
  16Lean status: 0 sorry, 0 axiom.
  17-/
  18
  19namespace IndisputableMonolith.Sociology.CivilizationCyclesFromPhiLadder
  20open Constants
  21
  22inductive CivilizationalStage where
  23  | emergence | growth | consolidation | decline | transformation
  24  deriving DecidableEq, Repr, BEq, Fintype
  25
  26theorem civilizationalStageCount : Fintype.card CivilizationalStage = 5 := by decide
  27
  28noncomputable def cycleDuration (k : ℕ) : ℝ := phi ^ k
  29
  30theorem cycleDurationRatio (k : ℕ) :
  31    cycleDuration (k + 1) / cycleDuration k = phi := by
  32  unfold cycleDuration
  33  have hpos := pow_pos phi_pos k
  34  rw [pow_succ, div_eq_iff hpos.ne']
  35  ring
  36
  37structure CivilizationCyclesCert where
  38  five_stages : Fintype.card CivilizationalStage = 5
  39  phi_ratio : ∀ k, cycleDuration (k + 1) / cycleDuration k = phi
  40
  41noncomputable def civilizationCyclesCert : CivilizationCyclesCert where
  42  five_stages := civilizationalStageCount
  43  phi_ratio := cycleDurationRatio
  44
  45end IndisputableMonolith.Sociology.CivilizationCyclesFromPhiLadder
  46