`InternetSpectralGapCert`

definition

show as: view math explainer →

module: IndisputableMonolith.NetworkScience.InternetSpectralGap
domain: NetworkScience
line: 69 · github
papers citing: none yet

open explainer

Generate a durable explainer page for this declaration.

open lean source

IndisputableMonolith.NetworkScience.InternetSpectralGap on GitHub at line 69.

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

used by

formal source

  66  have hk_pos : 0 < phi ^ (-(k : ℤ)) := zpow_pos Constants.phi_pos _
  67  field_simp [hk_pos.ne']
  68
  69structure InternetSpectralGapCert where
  70  gap_pos : ∀ k, 0 < spectralGap k
  71  strictly_decreasing : ∀ k, spectralGap (k + 1) < spectralGap k
  72  ratio : ∀ k, spectralGap (k + 1) / spectralGap k = phi⁻¹
  73  as_core_pos : 0 < asCoreGap
  74
  75/-- Internet spectral-gap certificate. -/
  76def internetSpectralGapCert : InternetSpectralGapCert where
  77  gap_pos := spectralGap_pos
  78  strictly_decreasing := spectralGap_strictly_decreasing
  79  ratio := spectralGap_ratio
  80  as_core_pos := asCoreGap_pos
  81
  82end
  83end InternetSpectralGap
  84end NetworkScience
  85end IndisputableMonolith

papers checked against this theorem

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