D_8_fails

formal source

 109theorem D_5_fails : ¬ is_fibonacci (2^5) := by native_decide
 110
 111/-- D = 8 does NOT satisfy: 2^8 = 256 is not Fibonacci -/
 112theorem D_8_fails : ¬ is_fibonacci (2^8) := by native_decide
 113
 114/-! ## Main Theorem -/
 115
 116/-- **Main Theorem**: The coherence exponent 5 is uniquely determined.
 117
 118The number 5 arises from:
 1191. D = 3 is the unique non-trivial dimension where both D and 2^D are Fibonacci
 1202. The Fibonacci identity F₆ - F₄ = F₅ gives 8 - 3 = 5
 1213. Therefore E_coh = φ^{-5} is structurally determined, not a free parameter.
 122-/
 123theorem coherence_exponent_unique :
 124    D = fib 4 ∧
 125    octave = fib 6 ∧
 126    coherence_exponent = fib 5 ∧
 127    coherence_exponent = 5 := by
 128  exact ⟨D_is_fib_4, octave_is_fib_6, coherence_exponent_is_fib_5, coherence_exponent_eq_5⟩
 129
 130/-! ## Connection to E_coh -/
 131
 132/-- The coherence energy E_coh = φ^{-5} in RS-native units. -/
 133noncomputable def E_coh : ℝ := Constants.phi ^ (-(coherence_exponent : ℤ))
 134
 135/-- E_coh = φ^{-5} -/
 136theorem E_coh_eq : E_coh = Constants.phi ^ (-5 : ℤ) := by
 137  unfold E_coh coherence_exponent octave D
 138  norm_num
 139
 140end IndisputableMonolith.Masses.CoherenceExponent