`spectralGap_k2_val`

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module: IndisputableMonolith.NetworkScience.InternetSpectralGapFromPhiLadder
domain: NetworkScience
line: 34 · github
papers citing: none yet

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IndisputableMonolith.NetworkScience.InternetSpectralGapFromPhiLadder on GitHub at line 34.

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depends on

formal source

  31  field_simp [hk, phi_ne_zero]
  32
  33/-- At k=2: spectral gap = 1/φ². -/
  34theorem spectralGap_k2_val : spectralGap 2 = (phi ^ 2)⁻¹ := rfl
  35
  36structure InternetSpectralGapCert where
  37  gap_pos : ∀ k, 0 < spectralGap k
  38  phi_inv_ratio : ∀ k, spectralGap (k + 1) / spectralGap k = phi⁻¹
  39
  40noncomputable def internetSpectralGapCert : InternetSpectralGapCert where
  41  gap_pos := spectralGap_pos
  42  phi_inv_ratio := spectralGapRatio
  43
  44end IndisputableMonolith.NetworkScience.InternetSpectralGapFromPhiLadder

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