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bridge_T5_T6

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formal statement (Lean)

 140theorem bridge_T5_T6
 141    (L : UniformScaleLadder)
 142    (a b : ℕ) (ha : 1 ≤ a) (hb : 1 ≤ b)
 143    (hrec : L.levels 2 = (a : ℝ) * L.levels 1 + (b : ℝ) * L.levels 0)
 144    (hmin : max a b = 1) :
 145    L.ratio = φ := by

proof body

Term-mode proof.

 146  have ⟨ha1, hb1⟩ := zero_param_forces_unit_coefficients a b ha hb hmin
 147  have hfib := unit_coefficients_give_fibonacci L a b ha1 hb1 hrec
 148  exact hierarchy_emergence_forces_phi L hfib
 149
 150/-! ## Structure-Based Interface
 151
 152For downstream code that prefers a bundled representation. -/
 153
 154/-- A uniform scale ladder with local binary recurrence: the level
 155at position k+2 is determined by a linear combination of levels k+1
 156and k with positive integer coefficients.
 157
 158Physical motivation: in a discrete ledger, composing a recognition event
 159at level k+1 with one at level k produces an event at level k+2. The
 160coefficients count how many sub-events of each type participate. Since
 161the ledger is discrete, these counts are positive natural numbers. -/

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