IndisputableMonolith.Materials.GlassTransitionFromJCost

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Glass Transition from J-Cost — B15 Depth
   6
   7Five canonical glass-transition regimes (= configDim D = 5):
   8  fragile liquid, strong liquid, supercooled, vitreous, aging.
   9
  10Angell fragility index on φ-ladder; adjacent-regime ratio φ.
  11
  12Lean status: 0 sorry, 0 axiom.
  13-/
  14
  15namespace IndisputableMonolith.Materials.GlassTransitionFromJCost
  16open Constants
  17
  18inductive GlassRegime where
  19  | fragileLiquid
  20  | strongLiquid
  21  | supercooled
  22  | vitreous
  23  | aging
  24  deriving DecidableEq, Repr, BEq, Fintype
  25
  26theorem glassRegime_count : Fintype.card GlassRegime = 5 := by decide
  27
  28noncomputable def fragilityIndex (k : ℕ) : ℝ := phi ^ k
  29
  30theorem fragility_ratio (k : ℕ) :
  31    fragilityIndex (k + 1) / fragilityIndex k = phi := by
  32  unfold fragilityIndex
  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 fragility_pos (k : ℕ) : 0 < fragilityIndex k := pow_pos phi_pos k
  38
  39structure GlassTransitionCert where
  40  five_regimes : Fintype.card GlassRegime = 5
  41  phi_ratio : ∀ k, fragilityIndex (k + 1) / fragilityIndex k = phi
  42  fragility_always_pos : ∀ k, 0 < fragilityIndex k
  43
  44noncomputable def glassTransitionCert : GlassTransitionCert where
  45  five_regimes := glassRegime_count
  46  phi_ratio := fragility_ratio
  47  fragility_always_pos := fragility_pos
  48
  49end IndisputableMonolith.Materials.GlassTransitionFromJCost
  50