fibonacci_deficit

formal source

  44  rw [fib_6_eq, fib_5_eq, fib_4_eq]
  45
  46/-- Key identity: 8 - 3 = 5, or F₆ - F₄ = F₅ -/
  47theorem fibonacci_deficit : fib 6 - fib 4 = fib 5 := by
  48  rw [fib_6_eq, fib_5_eq, fib_4_eq]
  49
  50/-! ## Dimension Constraint -/
  51
  52/-- D = 3 is the spatial dimension (from T8 dimension forcing) -/
  53def D : ℕ := 3
  54
  55/-- The octave period is 2^D -/
  56def octave : ℕ := 2 ^ D
  57
  58/-- Verify: octave = 8 -/
  59theorem octave_eq_8 : octave = 8 := by
  60  unfold octave D
  61  norm_num
  62
  63/-- D equals F₄ -/
  64theorem D_is_fib_4 : D = fib 4 := by
  65  unfold D
  66  rw [fib_4_eq]
  67
  68/-- Octave (2^D) equals F₆ -/
  69theorem octave_is_fib_6 : octave = fib 6 := by
  70  rw [octave_eq_8, fib_6_eq]
  71
  72/-! ## The Coherence Exponent -/
  73
  74/-- The Fibonacci deficit: 2^D - D = 5 -/
  75def coherence_exponent : ℕ := octave - D
  76
  77/-- The coherence exponent equals 5 -/