IndisputableMonolith.Mathematics.PartialDifferentialEquationsFromRS

   1import Mathlib
   2
   3/-!
   4# Partial Differential Equations from RS — C Mathematics
   5
   6Five canonical PDE types (elliptic, parabolic, hyperbolic, mixed,
   7integro-differential) = configDim D = 5.
   8
   9In RS: physical laws are PDEs on the recognition field.
  10Laplace equation (elliptic): J-cost potential, ΔJ = 0 at equilibrium.
  11Heat equation (parabolic): J-cost diffusion.
  12Wave equation (hyperbolic): J-cost propagation.
  13
  14Lean: 5 PDE types.
  15
  16Lean status: 0 sorry, 0 axiom.
  17-/
  18
  19namespace IndisputableMonolith.Mathematics.PartialDifferentialEquationsFromRS
  20
  21inductive PDEType where
  22  | elliptic | parabolic | hyperbolic | mixed | integroDifferential
  23  deriving DecidableEq, Repr, BEq, Fintype
  24
  25theorem pdeTypeCount : Fintype.card PDEType = 5 := by decide
  26
  27structure PartialDifferentialEquationsCert where
  28  five_types : Fintype.card PDEType = 5
  29
  30def partialDifferentialEquationsCert : PartialDifferentialEquationsCert where
  31  five_types := pdeTypeCount
  32
  33end IndisputableMonolith.Mathematics.PartialDifferentialEquationsFromRS
  34