`RealizedHierarchy`

definition

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module: IndisputableMonolith.Foundation.HierarchyRealization
domain: Foundation
line: 70 · github
papers citing: none yet

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IndisputableMonolith.Foundation.HierarchyRealization on GitHub at line 70.

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formal source

  67
  68This is the RS-native replacement for the bare `HasMultilevelComposition`
  69+ bridge-hypothesis interface. -/
  70structure RealizedHierarchy (F : ClosedObservableFramework) where
  71  baseState : F.S
  72  levels : ℕ → ℝ := fun k => F.r (F.T^[k] baseState)
  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. -/
  83theorem realized_ratio_eq_base (F : ClosedObservableFramework)
  84    (H : RealizedHierarchy F) :
  85    ∀ k, H.levels (k + 1) / H.levels k = H.levels 1 / H.levels 0 := by
  86  intro k
  87  induction k with
  88  | zero => rfl
  89  | succ k ih =>
  90    have h := H.ratio_self_similar k
  91    rw [h, ih]
  92
  93/-- All adjacent ratios in a realized hierarchy are equal. -/
  94theorem realized_uniform_ratios (F : ClosedObservableFramework)
  95    (H : RealizedHierarchy F) :
  96    ∀ j k, H.levels (j + 1) / H.levels j = H.levels (k + 1) / H.levels k := by
  97  intro j k
  98  rw [realized_ratio_eq_base F H j, realized_ratio_eq_base F H k]
  99
 100/-- Construct a `UniformScaleLadder` from a realized hierarchy. -/

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