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

import Semantics.DynamicCanal
import Semantics.LocalDerivative
import Semantics.MetricCore
import Semantics.RaycastField

namespace Semantics.HyperFlow

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

structure HyperFlowSignature where
  divergence : Fix16
  shearMagnitude : Fix16
  stressMagnitude : Fix16
  transportMagnitude : Fix16
  anisotropy : Fix16
  spectralSpread : Fix16
  couplingDensity : Fix16
  compressibilityIndex : Fix16
  curvatureEnergy : Fix16
  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 := Fix16.mul metric.coupling (matrixFrobeniusNorm ld.jacobian)
  , transportMagnitude := matrixL1Norm ld.jacobian
  , anisotropy := Fix16.zero
  , spectralSpread := matrixL1Norm ld.jacobian
  , couplingDensity := Fix16.zero
  , compressibilityIndex := Fix16.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