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gap45CrossoverModes

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 204noncomputable def gap45CrossoverModes : ℝ :=

proof body

Definition body.

 205  criticalModes tau_bio 1.0
 206
 207/-- Approximation of Gap-45 crossover modes as a rational.
 208    N ≈ ln(τ_bio/τ₀) / ln(φ) ≈ ln(1/(5.4e-44)) / 0.48
 209    ≈ 99.3 / 0.48 ≈ 207
 210
 211    Since τ₀ ≈ 5.4×10⁻⁴⁴ s, τ_bio = 1 s:
 212    ln(1/5.4e-44) ≈ 44 × ln(10) ≈ 44 × 2.3 ≈ 101
 213    ln(φ) ≈ 0.48
 214    N ≈ 101/0.48 ≈ 210 -/

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