`LSSRegime`

definition

show as: view math explainer →

module: IndisputableMonolith.Cosmology.LargeScaleStructureFromRS
domain: Cosmology
line: 19 · github
papers citing: none yet

open explainer

Generate a durable explainer page for this declaration.

open lean source

IndisputableMonolith.Cosmology.LargeScaleStructureFromRS on GitHub at line 19.

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

used by

formal source

  16namespace IndisputableMonolith.Cosmology.LargeScaleStructureFromRS
  17open Constants
  18
  19inductive LSSRegime where
  20  | cmbAcoustic
  21  | baryonAcousticOscillation
  22  | galaxyCluster
  23  | filament
  24  | cosmicVoid
  25  deriving DecidableEq, Repr, BEq, Fintype
  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

papers checked against this theorem

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