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structure definition def or abbrev

RealizedHierarchy

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formal statement (Lean)

  70structure RealizedHierarchy (F : ClosedObservableFramework) where
  71  baseState : F.S
  72  levels : ℕ → ℝ := fun k => F.r (F.T^[k] baseState)

proof body

Definition body.

  73  levels_eq : ∀ k, levels k = F.r (F.T^[k] baseState)
  74  levels_pos : ∀ k, 0 < levels k
  75  growth : 1 < levels 1 / levels 0
  76  ratio_self_similar :
  77    ∀ k, levels (k + 2) / levels (k + 1) = levels (k + 1) / levels k
  78  additive_posting : levels 2 = levels 1 + levels 0
  79
  80/-! ## Derived: Uniform Scale Ladder -/
  81
  82/-- All adjacent ratios in a realized hierarchy equal the base ratio. -/

used by (12)

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depends on (8)

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