IndisputableMonolith.Cosmology.LargeScaleStructureFromRS

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Large-Scale Structure from RS — Cosmology Depth
   6
   7Five canonical LSS regimes (= configDim D = 5):
   8  CMB acoustic scale, baryon acoustic oscillation, galaxy clusters,
   9  filamentary structure, cosmic voids.
  10
  11Each scale sits one rung up the φ-ladder in comoving length.
  12
  13Lean status: 0 sorry, 0 axiom.
  14-/
  15
  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
  50