complete_ledger_uniqueness

formal source

 201  exact ⟨{ dimension := 3, ratio := phi, cycleLength := 8 }, rfl, rfl, rfl⟩
 202
 203/-- Combined uniqueness: φ, Q₃, 8-tick are all forced. -/
 204theorem complete_ledger_uniqueness :
 205    -- φ is forced by cost fixed point
 206    (∀ x : ℝ, x > 0 → x^2 = x + 1 → x = phi) ∧
 207    -- Q₃ is forced by linking
 208    (∀ D : ℕ, D ≥ 2 → (linkingNumber D ≠ 0 ↔ D = 3)) ∧
 209    -- 8-tick is forced by Gray code
 210    (grayCodeCycleLength 3 = 8) := by
 211  constructor
 212  · exact phi_unique_fixed_point
 213  constructor
 214  · exact Q3_unique_linking_dimension
 215  · exact eight_tick_minimal
 216
 217/-! ## Summary -/
 218
 219/-- The RS Ledger is the unique discrete conservative structure.
 220
 221    This closes Gap 9: There are no alternative ledgers because:
 222    - φ is the only cost fixed point
 223    - D=3 is the only linking dimension
 224    - 8 is the only complete cycle length
 225
 226    The objection "there could be other discrete ledgers" fails because
 227    each component is uniquely determined by its constraint.
 228-/
 229theorem rs_ledger_is_unique :
 230    ∀ (altPhi : ℝ) (altD : ℕ) (altT : ℕ),
 231      -- If an alternative satisfies the same constraints...
 232      (altPhi > 0 ∧ altPhi^2 = altPhi + 1) →
 233      (altD ≥ 2 ∧ linkingNumber altD ≠ 0) →
 234      (altT = grayCodeCycleLength altD) →