`HTheoremForce`

definition

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module: IndisputableMonolith.Cosmology.PerpetualComplexity
domain: Cosmology
line: 29 · github
papers citing: none yet

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IndisputableMonolith.Cosmology.PerpetualComplexity on GitHub at line 29.

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depends on

formal source

  26/-! ## The Two Forces -/
  27
  28/-- Force 1: H-theorem drives free energy toward zero. -/
  29structure HTheoremForce where
  30  free_energy_decreasing : Prop
  31
  32/-- Force 2: Gap-45 coprimality prevents global phase synchronization. -/
  33structure Gap45Frustration where
  34  recognition_period : ℕ := 8
  35  phase_period : ℕ := 45
  36  coprime : Nat.Coprime recognition_period phase_period
  37  sync_period : ℕ := Nat.lcm recognition_period phase_period
  38
  39/-- The gap-45 frustration is real: gcd(8, 45) = 1. -/
  40def gap45 : Gap45Frustration where
  41  coprime := coprime_3
  42  sync_period := 360
  43
  44/-- The sync period is 360 (proved in SyncMinimization). -/
  45theorem sync_period_eq_360 : gap45.sync_period = 360 := by
  46  simp [gap45, Gap45Frustration.sync_period]
  47  exact syncPeriod_3
  48
  49/-- The sync period is strictly greater than either individual period. -/
  50theorem sync_exceeds_both :
  51    gap45.sync_period > gap45.recognition_period ∧
  52    gap45.sync_period > gap45.phase_period := by
  53  constructor <;> simp [gap45, Gap45Frustration.sync_period,
  54    Gap45Frustration.recognition_period, Gap45Frustration.phase_period,
  55    syncPeriod_3]
  56  all_goals norm_num
  57
  58/-! ## The Perpetual Complexity Theorem -/
  59

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