IndisputableMonolith.Foundation.HierarchyMinimality

   1import Mathlib
   2import IndisputableMonolith.Foundation.PhiForcingDerived
   3import IndisputableMonolith.Foundation.PhiForcing
   4
   5namespace IndisputableMonolith
   6namespace Foundation
   7namespace HierarchyMinimality
   8
   9open PhiForcingDerived
  10open PhiForcing
  11
  12/-!
  13# Hierarchy Minimality
  14
  15This module isolates the minimal algebraic hierarchy data needed for the B1
  16closure step: a discrete geometric ledger together with the smallest closure
  17condition `scale 0 + scale 1 = scale 2`.
  18-/
  19
  20/-- Minimal discrete hierarchy: a geometric scale ladder closed under the first
  21    non-trivial composition step. -/
  22structure MinimalHierarchy where
  23  scales : GeometricScaleSequence
  24  minimalClosure : scales.isClosed
  25
  26/-- The first closure step is exactly the Fibonacci relation. -/
  27theorem hierarchy_forces_golden_equation (H : MinimalHierarchy) :
  28    H.scales.ratio ^ 2 = H.scales.ratio + 1 :=
  29  closure_forces_golden_equation H.scales H.minimalClosure
  30
  31/-- Minimal closure already forces the unique positive self-similar ratio `φ`. -/
  32theorem hierarchy_forces_phi (H : MinimalHierarchy) :
  33    H.scales.ratio = φ :=
  34  closed_ratio_is_phi H.scales H.minimalClosure
  35
  36end HierarchyMinimality
  37end Foundation
  38end IndisputableMonolith
  39