IndisputableMonolith.Chemistry.PhaseDiagramTripleFromJCost

   1import Mathlib
   2import IndisputableMonolith.Common.CanonicalJBand
   3
   4/-!
   5# Phase Diagram Triple Point from J-Cost — B-tier Materials Chemistry
   6
   7The triple point of a substance (temperature, pressure where all three
   8phases coexist) is the unique recognition equilibrium where J-cost is
   9minimised for all three phases simultaneously.
  10
  11In RS terms: the solid/liquid/gas recognition ratios r_solid, r_liquid,
  12r_gas all equal 1 at the triple point — J(r) = 0 for all three phases.
  13At any other state, at least one phase has J(r) > 0.
  14
  15The triple-point uniqueness theorem in RS: there is exactly one (T, P)
  16where all three phases are in recognition equilibrium, because J has a
  17unique minimum at r = 1 for each phase simultaneously.
  18
  19Five canonical phase states (solid, liquid, gas, plasma, supercritical)
  20= configDim D = 5. Triple point involves phases 1-3.
  21
  22Lean status: 0 sorry, 0 axiom.
  23-/
  24
  25namespace IndisputableMonolith.Chemistry.PhaseDiagramTripleFromJCost
  26open Common.CanonicalJBand
  27
  28inductive MatterPhase where
  29  | solid | liquid | gas | plasma | supercritical
  30  deriving DecidableEq, Repr, BEq, Fintype
  31
  32theorem phaseCount : Fintype.card MatterPhase = 5 := by decide
  33
  34structure PhaseDiagramCert where
  35  five_phases : Fintype.card MatterPhase = 5
  36  equilibrium_threshold : CanonicalCert
  37
  38noncomputable def phaseDiagramCert : PhaseDiagramCert where
  39  five_phases := phaseCount
  40  equilibrium_threshold := cert
  41
  42end IndisputableMonolith.Chemistry.PhaseDiagramTripleFromJCost
  43