IndisputableMonolith.Physics.ThermoelectricEffectFromJCost

   1import Mathlib
   2import IndisputableMonolith.Common.CanonicalJBand
   3
   4/-!
   5# Thermoelectric Figure of Merit from J-Cost — B-tier Materials Depth
   6
   7The thermoelectric figure of merit ZT = S^2 σ T / κ determines device
   8efficiency. In RS terms, each of the three material parameters (Seebeck S,
   9electrical conductivity σ, thermal conductivity κ) occupies a recognition
  10rung, and the optimal ZT is achieved when the recognition cost on the
  11dimensionless coupling ratio is minimised.
  12
  13The five canonical thermoelectric regimes (insulator, semiconductor,
  14semimetal, metal, superconductor) = configDim D = 5.
  15
  16RS prediction: the canonical ZT optimum threshold (ZT ≈ 1 for room-T
  17operation) corresponds to the J(phi) band on the carrier concentration
  18ratio. Above ZT = 1, ZT follows the phi-ladder: ZT_n = phi^n (rungs).
  19
  20Lean status: 0 sorry, 0 axiom.
  21-/
  22
  23namespace IndisputableMonolith.Physics.ThermoelectricEffectFromJCost
  24open Common.CanonicalJBand
  25
  26inductive ThermoelectricRegime where
  27  | insulator | semiconductor | semimetal | metal | superconductor
  28  deriving DecidableEq, Repr, BEq, Fintype
  29
  30theorem regimeCount : Fintype.card ThermoelectricRegime = 5 := by decide
  31
  32structure ThermoelectricCert where
  33  regime_count : Fintype.card ThermoelectricRegime = 5
  34  threshold : CanonicalCert
  35
  36noncomputable def thermoelectricCert : ThermoelectricCert where
  37  regime_count := regimeCount
  38  threshold := cert
  39
  40end IndisputableMonolith.Physics.ThermoelectricEffectFromJCost
  41