k_fib

formal source

  34namespace IndisputableMonolith.Foundation.CoherenceExponentUniqueness
  35
  36/-- Fibonacci deficit: k_fib(D) = 2^D - D. -/
  37def k_fib (D : ℕ) : ℕ := 2^D - D
  38
  39/-- Integration measure: k_int(D) = D + 2. -/
  40def k_int (D : ℕ) : ℕ := D + 2
  41
  42/-- k_fib and k_int agree at D = 3. -/
  43theorem agreement_at_3 : k_fib 3 = k_int 3 := by decide
  44
  45/-- Both equal 5 at D = 3. -/
  46theorem both_equal_5_at_3 : k_fib 3 = 5 ∧ k_int 3 = 5 := by decide
  47
  48/-- Disagreement at D = 1. -/
  49theorem disagreement_at_1 : k_fib 1 ≠ k_int 1 := by decide
  50
  51/-- Disagreement at D = 2. -/
  52theorem disagreement_at_2 : k_fib 2 ≠ k_int 2 := by decide
  53
  54/-- Disagreement at D = 4. -/
  55theorem disagreement_at_4 : k_fib 4 ≠ k_int 4 := by decide
  56
  57/-- D = 3 is the unique dimension in {1,2,3,4} where both routes agree. -/
  58theorem exponent_unique_at_D3 :
  59    ∀ D ∈ ({1, 2, 3, 4} : Finset ℕ), k_fib D = k_int D ↔ D = 3 := by
  60  decide
  61
  62/-- Corollary: k = 5 is uniquely forced at D = 3. -/
  63theorem k5_forced_at_D3 : k_fib 3 = 5 ∧ k_int 3 = 5 ∧ k_fib 3 = k_int 3 := by
  64  decide
  65
  66/-- From k=5: ℏ = φ^(-5) in RS units. -/
  67def coherenceExponent : ℕ := 5