`coherence_exponent_unique`

proved

show as: view math explainer →

module: IndisputableMonolith.Masses.CoherenceExponent
domain: Masses
line: 123 · github
papers citing: none yet

open explainer

Generate a durable explainer page for this declaration.

open lean source

IndisputableMonolith.Masses.CoherenceExponent on GitHub at line 123.

browse module

All declarations in this module, on Recognition.

explainer page

Tracked in the explainer inventory; generation is lazy so crawlers do not trigger LLM jobs.

open explainer

depends on

formal source

 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

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.