`scale`

definition

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module: IndisputableMonolith.Cosmology.LargeScaleStructureFromRS
domain: Cosmology
line: 29 · github
papers citing: none yet

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IndisputableMonolith.Cosmology.LargeScaleStructureFromRS on GitHub at line 29.

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formal source

  26
  27theorem lssRegime_count : Fintype.card LSSRegime = 5 := by decide
  28
  29noncomputable def scale (k : ℕ) : ℝ := phi ^ k
  30
  31theorem scale_ratio (k : ℕ) : scale (k + 1) / scale k = phi := by
  32  unfold scale
  33  have hpos : (0 : ℝ) < phi ^ k := pow_pos phi_pos k
  34  rw [div_eq_iff hpos.ne', pow_succ]
  35  ring
  36
  37theorem scale_pos (k : ℕ) : 0 < scale k := pow_pos phi_pos k
  38
  39structure LargeScaleStructureCert where
  40  five_regimes : Fintype.card LSSRegime = 5
  41  phi_ratio : ∀ k, scale (k + 1) / scale k = phi
  42  scale_always_pos : ∀ k, 0 < scale k
  43
  44noncomputable def largeScaleStructureCert : LargeScaleStructureCert where
  45  five_regimes := lssRegime_count
  46  phi_ratio := scale_ratio
  47  scale_always_pos := scale_pos
  48
  49end IndisputableMonolith.Cosmology.LargeScaleStructureFromRS

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