/-
  HyperFlow.lean - Fixed-Point Hyperbolic Flow Dynamics
-/

import Mathlib.Data.Nat.Basic
import Mathlib.Data.Int.Basic
import Semantics.DynamicCanal
import Semantics.LocalDerivative
import Semantics.MetricCore
import Semantics.FixedPoint

namespace Semantics.HyperFlow

open DynamicCanal
open Semantics.LocalDerivative (Scalar StabilityClass LocalDerivative matrixFrobeniusNorm matrixL1Norm divergence antisymmetricPart)
open Semantics.MetricCore (Metric)

structure HyperFlowSignature where
  divergence : Q16_16
  shearMagnitude : Q16_16
  stressMagnitude : Q16_16
  transportMagnitude : Q16_16
  anisotropy : Q16_16
  spectralSpread : Q16_16
  couplingDensity : Q16_16
  compressibilityIndex : Q16_16
  curvatureEnergy : Q16_16
  deriving Repr, DecidableEq, BEq

inductive HyperFlowRegime
| coherent
| shearLayer
| compressive
| dispersive
| turbulentLike
| collapse
  deriving Repr, DecidableEq, BEq

inductive MediumRegime
| incompressibleFluid
| compressibleFluid
| gasLike
| rarefiedGas
| plasmaLike
| magnetizedPlasma
| rarefiedPlasma
| collapse
  deriving Repr, DecidableEq, BEq

inductive PlasmaManifoldRegime
| diffuse
| sheet
| filament
| reconnectionLike
| coherentTorus
| collapsed
  deriving Repr, DecidableEq, BEq

def hyperFlowSignature (ld : LocalDerivative) (metric : Metric) : HyperFlowSignature :=
  { divergence := divergence ld
  , shearMagnitude := matrixFrobeniusNorm (antisymmetricPart ld)
  , stressMagnitude := metric.coupling * (matrixFrobeniusNorm ld.jacobian)
  , transportMagnitude := matrixL1Norm ld.jacobian
  , anisotropy := Q16_16.zero
  , spectralSpread := matrixL1Norm ld.jacobian
  , couplingDensity := Q16_16.zero
  , compressibilityIndex := Q16_16.zero
  , curvatureEnergy := matrixFrobeniusNorm ld.hessian }

def classifyHyperFlow (_signature : HyperFlowSignature) (stability : StabilityClass) : HyperFlowRegime :=
  match stability with
  | .collapsed => .collapse
  | .singular => .compressive
  | .throat => .compressive
  | .unstable => .turbulentLike
  | .stable => .coherent

end Semantics.HyperFlow
