IndisputableMonolith.Physics.AstrophysicsStarFormationFromRS

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Star Formation from RS — B12 Astrophysics Depth
   6
   7Stars form from molecular cloud collapse. In RS: star formation rate
   8follows phi-ladder of cloud density rungs.
   9
  10Five canonical stellar evolution stages in formation:
  11molecular cloud, prestellar core, protostar, T Tauri, main sequence
  12= configDim D = 5.
  13
  14Jeans mass threshold: M_J ∝ T^(3/2) × ρ^(-1/2).
  15RS: M_J at rung k follows phi-ladder.
  16
  17Lean: 5 stages.
  18
  19Lean status: 0 sorry, 0 axiom.
  20-/
  21
  22namespace IndisputableMonolith.Physics.AstrophysicsStarFormationFromRS
  23open Constants
  24
  25inductive StarFormationStage where
  26  | molecularCloud | prestellarCore | protostar | tTauri | mainSequence
  27  deriving DecidableEq, Repr, BEq, Fintype
  28
  29theorem starFormationStageCount : Fintype.card StarFormationStage = 5 := by decide
  30
  31noncomputable def jeansMass (k : ℕ) : ℝ := phi ^ k
  32
  33theorem jeansMassRatio (k : ℕ) :
  34    jeansMass (k + 1) / jeansMass k = phi := by
  35  unfold jeansMass
  36  have hpos := pow_pos phi_pos k
  37  rw [pow_succ, div_eq_iff hpos.ne']
  38  ring
  39
  40structure StarFormationCert where
  41  five_stages : Fintype.card StarFormationStage = 5
  42  phi_ratio : ∀ k, jeansMass (k + 1) / jeansMass k = phi
  43
  44noncomputable def starFormationCert : StarFormationCert where
  45  five_stages := starFormationStageCount
  46  phi_ratio := jeansMassRatio
  47
  48end IndisputableMonolith.Physics.AstrophysicsStarFormationFromRS
  49