`fib_4_eq`

proved

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module: IndisputableMonolith.Masses.CoherenceExponent
domain: Masses
line: 32 · github
papers citing: none yet

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IndisputableMonolith.Masses.CoherenceExponent on GitHub at line 32.

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  29/-! ## Fibonacci Numbers at Key Positions -/
  30
  31/-- F₄ = 3 (the spatial dimension) -/
  32theorem fib_4_eq : fib 4 = 3 := by native_decide
  33
  34/-- F₅ = 5 (the coherence exponent) -/
  35theorem fib_5_eq : fib 5 = 5 := by native_decide
  36
  37/-- F₆ = 8 (the octave = 2^D) -/
  38theorem fib_6_eq : fib 6 = 8 := by native_decide
  39
  40/-! ## The Fibonacci Identity -/
  41
  42/-- The Fibonacci recurrence: F₆ = F₅ + F₄ -/
  43theorem fib_recurrence_at_6 : fib 6 = fib 5 + fib 4 := by
  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

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