IndisputableMonolith.Materials.ThermalConductivityRegimesFromPhiLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Thermal Conductivity Regimes from φ-ladder — B9 Materials Depth
   6
   7Five canonical thermal-conductivity regimes (= configDim D = 5):
   8  ballistic, diffusive, phonon-dominated, electron-dominated,
   9  interface-limited.
  10
  11Adjacent-regime conductivity ratio on the φ-ladder.
  12
  13Lean status: 0 sorry, 0 axiom.
  14-/
  15
  16namespace IndisputableMonolith.Materials.ThermalConductivityRegimesFromPhiLadder
  17open Constants
  18
  19inductive ThermalConductivityRegime where
  20  | ballistic
  21  | diffusive
  22  | phononDominated
  23  | electronDominated
  24  | interfaceLimited
  25  deriving DecidableEq, Repr, BEq, Fintype
  26
  27theorem thermalConductivityRegime_count :
  28    Fintype.card ThermalConductivityRegime = 5 := by decide
  29
  30noncomputable def kappa (k : ℕ) : ℝ := phi ^ k
  31
  32theorem kappa_ratio (k : ℕ) : kappa (k + 1) / kappa k = phi := by
  33  unfold kappa
  34  have hpos : (0 : ℝ) < phi ^ k := pow_pos phi_pos k
  35  rw [div_eq_iff hpos.ne', pow_succ]
  36  ring
  37
  38theorem kappa_pos (k : ℕ) : 0 < kappa k := pow_pos phi_pos k
  39
  40structure ThermalConductivityCert where
  41  five_regimes : Fintype.card ThermalConductivityRegime = 5
  42  phi_ratio : ∀ k, kappa (k + 1) / kappa k = phi
  43  kappa_always_pos : ∀ k, 0 < kappa k
  44
  45noncomputable def thermalConductivityCert : ThermalConductivityCert where
  46  five_regimes := thermalConductivityRegime_count
  47  phi_ratio := kappa_ratio
  48  kappa_always_pos := kappa_pos
  49
  50end IndisputableMonolith.Materials.ThermalConductivityRegimesFromPhiLadder
  51