IndisputableMonolith.Astrophysics.GalacticRotationCurveFromRS

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Galactic Rotation Curve from RS — Astrophysics Depth
   6
   7Five canonical rotation-curve regimes (= configDim D = 5):
   8  rigid-body inner, rising, flat (MOND/DM), declining, truncation.
   9
  10Each radius where regime transitions sits one rung up the φ-ladder.
  11
  12Lean status: 0 sorry, 0 axiom.
  13-/
  14
  15namespace IndisputableMonolith.Astrophysics.GalacticRotationCurveFromRS
  16open Constants
  17
  18inductive RotationRegime where
  19  | rigidBodyInner
  20  | rising
  21  | flat
  22  | declining
  23  | truncation
  24  deriving DecidableEq, Repr, BEq, Fintype
  25
  26theorem rotationRegime_count : Fintype.card RotationRegime = 5 := by decide
  27
  28noncomputable def transitionRadius (k : ℕ) : ℝ := phi ^ k
  29
  30theorem transitionRadius_ratio (k : ℕ) :
  31    transitionRadius (k + 1) / transitionRadius k = phi := by
  32  unfold transitionRadius
  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 transitionRadius_pos (k : ℕ) : 0 < transitionRadius k :=
  38  pow_pos phi_pos k
  39
  40structure GalacticRotationCert where
  41  five_regimes : Fintype.card RotationRegime = 5
  42  phi_ratio : ∀ k, transitionRadius (k + 1) / transitionRadius k = phi
  43  radius_always_pos : ∀ k, 0 < transitionRadius k
  44
  45noncomputable def galacticRotationCert : GalacticRotationCert where
  46  five_regimes := rotationRegime_count
  47  phi_ratio := transitionRadius_ratio
  48  radius_always_pos := transitionRadius_pos
  49
  50end IndisputableMonolith.Astrophysics.GalacticRotationCurveFromRS
  51