`octave`

definition

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module: IndisputableMonolith.Masses.CoherenceExponent
domain: Masses
line: 56 · github
papers citing: none yet

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IndisputableMonolith.Masses.CoherenceExponent on GitHub at line 56.

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formal source

  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 -/
  78theorem coherence_exponent_eq_5 : coherence_exponent = 5 := by
  79  unfold coherence_exponent octave D
  80  norm_num
  81
  82/-- The coherence exponent equals F₅ -/
  83theorem coherence_exponent_is_fib_5 : coherence_exponent = fib 5 := by
  84  rw [coherence_exponent_eq_5, fib_5_eq]
  85
  86/-- The coherence exponent arises from the Fibonacci identity -/

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