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theorem proved term proof

complete_ledger_uniqueness

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formal statement (Lean)

 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

proof body

Term-mode proof.

 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-/

depends on (16)

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