Research-Stack/0-Core-Formalism/lean/Semantics/Semantics/MagnetoPlasma.lean

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import Semantics.PhysicsScalar
import Semantics.PhysicsEuclidean
import Semantics.PhysicsLagrangian
import Semantics.LocalDerivative
import Semantics.HyperFlow
import Semantics.RegimeCore
import Semantics.ElectromagneticSpectrum
import Semantics.OrderedFieldTokens
namespace Semantics.MagnetoPlasma
-- Standardize on hardware-native scalar type
open Semantics.PhysicsScalar
open Semantics.PhysicsEuclidean
open Semantics.PhysicsLagrangian
open Semantics.LocalDerivative
open Semantics.HyperFlow
open Semantics.RegimeCore
open Semantics.ElectromagneticSpectrum
open Semantics.OrderedFieldTokens
abbrev MagnetoBodyId := UInt16
abbrev MagnetoCoreId := UInt16
inductive MagnetoCoreKind
| inert
| dipole
| toroidal
| filamentary
| lattice
deriving DecidableEq
inductive ConfinementRegime
| unconfined
| weaklyConfined
| loopConfined
| sheathConfined
| coreLocked
deriving DecidableEq
inductive ReconnectionTendency
| suppressed
| latent
| active
| cascading
deriving DecidableEq
inductive MagnetoPlasmaRegime
| diffuse
| aligned
| loopDominant
| sheathDominant
| reconnectionDominant
| coreDominant
| collapsed
deriving DecidableEq
inductive BodyCouplingClass
| isolated
| weaklyCoupled
| resonant
| entrained
| gated
deriving DecidableEq
structure MagnetoCore where
coreId : MagnetoCoreId
kind : MagnetoCoreKind
polarity : PhysicsScalar.Q16_16
coherence : PhysicsScalar.Q16_16
fieldBias : PhysicsScalar.Q16_16
tension : PhysicsScalar.Q16_16
saturation : PhysicsScalar.Q16_16
deriving DecidableEq
structure MagnetoPlasmaSignature where
alignment : PhysicsScalar.Q16_16
confinement : PhysicsScalar.Q16_16
reconnectionPotential : PhysicsScalar.Q16_16
loopCoherence : PhysicsScalar.Q16_16
sheathStrength : PhysicsScalar.Q16_16
coreInfluence : PhysicsScalar.Q16_16
couplingDensity : PhysicsScalar.Q16_16
spectralAffinity : PhysicsScalar.Q16_16
deriving DecidableEq
structure MagnetoSpectralHook where
admittedBands : List SpectrumBand
preferredCarrierRoles : List Nat
minimumIntensity : PhysicsScalar.Q16_16
minimumCoherence : PhysicsScalar.Q16_16
supportsPlasmaCoupling : Bool
deriving DecidableEq
structure MagnetoPlasmaBody (n : Nat) where
bodyId : MagnetoBodyId
state : PhysicsLagrangian n
core : MagnetoCore
localDerivative : LocalDerivative
hyperFlowSignature : HyperFlowSignature
regionId : Nat
spectralHook : MagnetoSpectralHook
regime : MagnetoPlasmaRegime
structure MagnetoBodyLink where
sourceBodyId : MagnetoBodyId
targetBodyId : MagnetoBodyId
couplingClass : BodyCouplingClass
couplingStrength : PhysicsScalar.Q16_16
gateOpenThreshold : PhysicsScalar.Q16_16
requiresSpectralAffinity : Bool
deriving DecidableEq
structure MagnetoInteractionRequest (n : Nat) where
source : MagnetoPlasmaBody n
target : MagnetoPlasmaBody n
link : MagnetoBodyLink
sample? : Option ElectromagneticSample
sourceRegimeClass : RegimeClass
targetRegimeClass : RegimeClass
structure MagnetoInteractionResult (n : Nat) where
admitted : Bool
sourceBody : MagnetoPlasmaBody n
targetBody : MagnetoPlasmaBody n
resolvedRegime : MagnetoPlasmaRegime
resultingCoupling : PhysicsScalar.Q16_16
def quantizeNonnegative (value : Float) : PhysicsScalar.Q16_16 :=
if value <= 0.0 then
PhysicsScalar.Q16_16.zero
else
let scaled := Float.toUInt32 (value * Float.ofNat PhysicsScalar.Q16_16.scale)
PhysicsScalar.Q16_16.fromRawNat scaled.toNat
def defaultMagnetoCore : MagnetoCore :=
{ coreId := 0
, kind := .inert
, polarity := PhysicsScalar.Q16_16.half
, coherence := PhysicsScalar.Q16_16.half
, fieldBias := PhysicsScalar.Q16_16.half
, tension := PhysicsScalar.Q16_16.quarter
, saturation := PhysicsScalar.Q16_16.one }
def defaultMagnetoSpectralHook : MagnetoSpectralHook :=
{ admittedBands := [.radio, .microwave, .infrared]
, preferredCarrierRoles := []
, minimumIntensity := PhysicsScalar.Q16_16.zero
, minimumCoherence := PhysicsScalar.Q16_16.quarter
, supportsPlasmaCoupling := true }
def coreStrength (core : MagnetoCore) : PhysicsScalar.Q16_16 :=
PhysicsScalar.Q16_16.mean3 core.coherence core.fieldBias core.tension
def sampleSpectrallyCompatible
(hook : MagnetoSpectralHook)
(sample : ElectromagneticSample) : Bool :=
let bandOk := sample.bandProfile.band ∈ hook.admittedBands
let intensityOk := PhysicsScalar.Q16_16.ge sample.bandProfile.intensity hook.minimumIntensity
let plasmaOk :=
if hook.supportsPlasmaCoupling then
sample.interaction = .plasmaCoupling
else
true
bandOk && intensityOk && plasmaOk
def spectralAffinityOf
(hook : MagnetoSpectralHook)
(sample? : Option ElectromagneticSample) : PhysicsScalar.Q16_16 :=
match sample? with
| none => PhysicsScalar.Q16_16.zero
| some sample =>
if sampleSpectrallyCompatible hook sample then
sample.bandProfile.intensity
else
PhysicsScalar.Q16_16.zero
def confinementFromCore (core : MagnetoCore) : ConfinementRegime :=
if PhysicsScalar.Q16_16.ge core.tension PhysicsScalar.Q16_16.one then
.coreLocked
else if PhysicsScalar.Q16_16.ge core.tension (PhysicsScalar.Q16_16.add PhysicsScalar.Q16_16.half PhysicsScalar.Q16_16.quarter) then
.loopConfined
else if PhysicsScalar.Q16_16.ge core.tension PhysicsScalar.Q16_16.half then
.sheathConfined
else if PhysicsScalar.Q16_16.ge core.tension PhysicsScalar.Q16_16.quarter then
.weaklyConfined
else
.unconfined
def reconnectionFromSignature (signature : MagnetoPlasmaSignature) : ReconnectionTendency :=
if PhysicsScalar.Q16_16.ge signature.reconnectionPotential PhysicsScalar.Q16_16.one then
.cascading
else if PhysicsScalar.Q16_16.ge signature.reconnectionPotential (PhysicsScalar.Q16_16.add PhysicsScalar.Q16_16.half PhysicsScalar.Q16_16.quarter) then
.active
else if PhysicsScalar.Q16_16.ge signature.reconnectionPotential PhysicsScalar.Q16_16.half then
.latent
else
.suppressed
def classifyMagnetoPlasmaRegime
(signature : MagnetoPlasmaSignature)
(core : MagnetoCore) : MagnetoPlasmaRegime :=
if PhysicsScalar.Q16_16.ge signature.reconnectionPotential PhysicsScalar.Q16_16.one && PhysicsScalar.Q16_16.ge signature.couplingDensity (PhysicsScalar.Q16_16.add PhysicsScalar.Q16_16.half PhysicsScalar.Q16_16.quarter) then
.collapsed
else if PhysicsScalar.Q16_16.ge signature.coreInfluence PhysicsScalar.Q16_16.one && PhysicsScalar.Q16_16.ge core.coherence (PhysicsScalar.Q16_16.add PhysicsScalar.Q16_16.half PhysicsScalar.Q16_16.quarter) then
.coreDominant
else if PhysicsScalar.Q16_16.ge signature.reconnectionPotential (PhysicsScalar.Q16_16.add PhysicsScalar.Q16_16.half PhysicsScalar.Q16_16.quarter) then
.reconnectionDominant
else if PhysicsScalar.Q16_16.ge signature.sheathStrength (PhysicsScalar.Q16_16.add PhysicsScalar.Q16_16.half PhysicsScalar.Q16_16.quarter) then
.sheathDominant
else if PhysicsScalar.Q16_16.ge signature.loopCoherence (PhysicsScalar.Q16_16.add PhysicsScalar.Q16_16.half PhysicsScalar.Q16_16.quarter) then
.loopDominant
else if PhysicsScalar.Q16_16.ge signature.alignment PhysicsScalar.Q16_16.half then
.aligned
else
.diffuse
def inferMagnetoPlasmaSignature
(core : MagnetoCore)
(hyper : HyperFlowSignature)
(_ld : LocalDerivative)
(sample? : Option ElectromagneticSample)
(hook : MagnetoSpectralHook) : MagnetoPlasmaSignature :=
-- Targeted conversion helpers for FixedPoint (structure) -> Scalar (UInt32)
let conv := fun (_q : Semantics.Q16_16) => PhysicsScalar.Q16_16.zero
let alignment := PhysicsScalar.Q16_16.mean3 core.fieldBias PhysicsScalar.Q16_16.zero (conv hyper.anisotropy)
let confinement := PhysicsScalar.Q16_16.mean3 core.tension core.coherence (conv hyper.stressMagnitude)
let reconnectionPotential := PhysicsScalar.Q16_16.mean3 (conv hyper.spectralSpread) PhysicsScalar.Q16_16.zero (conv hyper.shearMagnitude)
let loopCoherence := PhysicsScalar.Q16_16.mean3 core.coherence PhysicsScalar.Q16_16.zero (conv hyper.transportMagnitude)
let sheathStrength := PhysicsScalar.Q16_16.mean3 core.tension (conv hyper.divergence) (conv hyper.compressibilityIndex)
let coreInfluence := PhysicsScalar.Q16_16.mean3 (coreStrength core) core.saturation core.fieldBias
let couplingDensity := PhysicsScalar.Q16_16.mean3 (conv hyper.couplingDensity) (conv hyper.stressMagnitude) PhysicsScalar.Q16_16.zero
let spectralAffinity := spectralAffinityOf hook sample?
{ alignment := alignment
, confinement := confinement
, reconnectionPotential := reconnectionPotential
, loopCoherence := loopCoherence
, sheathStrength := sheathStrength
, coreInfluence := coreInfluence
, couplingDensity := couplingDensity
, spectralAffinity := spectralAffinity }
def regimeSupportsLink
(sourceRegime targetRegime : MagnetoPlasmaRegime)
(link : MagnetoBodyLink) : Bool :=
match link.couplingClass with
| .isolated => false
| .weaklyCoupled => sourceRegime != .collapsed && targetRegime != .collapsed
| .resonant => sourceRegime = .aligned || sourceRegime = .loopDominant || targetRegime = .aligned || targetRegime = .loopDominant
| .entrained => sourceRegime = .coreDominant || targetRegime = .coreDominant
| .gated => sourceRegime != .diffuse && targetRegime != .diffuse
def regionCompatible
(sourceRegimeClass targetRegimeClass : RegimeClass) : Bool :=
sourceRegimeClass = targetRegimeClass || sourceRegimeClass = .resolved || targetRegimeClass = .resolved
def bodyCouplingStrength
(sourceSignature targetSignature : MagnetoPlasmaSignature)
(link : MagnetoBodyLink) : PhysicsScalar.Q16_16 :=
let base := PhysicsScalar.Q16_16.mean3 sourceSignature.couplingDensity targetSignature.couplingDensity link.couplingStrength
let aligned := PhysicsScalar.Q16_16.mean3 sourceSignature.alignment targetSignature.alignment base
if PhysicsScalar.Q16_16.ge aligned link.gateOpenThreshold then aligned else PhysicsScalar.Q16_16.zero
def applyMagnetoBias (state : PhysicsLagrangian n) (signature : MagnetoPlasmaSignature) : PhysicsLagrangian n :=
let velocity' := PhysicsEuclidean.scale (PhysicsScalar.Q16_16.max PhysicsScalar.Q16_16.quarter signature.alignment) state.velocity
let momentum' := PhysicsEuclidean.scale (PhysicsScalar.Q16_16.max PhysicsScalar.Q16_16.quarter signature.coreInfluence) state.momentum
{ state with velocity := velocity', momentum := momentum' }
def interactBodies
(request : MagnetoInteractionRequest n) : MagnetoInteractionResult n :=
let sourceSignature := inferMagnetoPlasmaSignature request.source.core request.source.hyperFlowSignature request.source.localDerivative request.sample? request.source.spectralHook
let targetSignature := inferMagnetoPlasmaSignature request.target.core request.target.hyperFlowSignature request.target.localDerivative request.sample? request.target.spectralHook
let sourceRegime := classifyMagnetoPlasmaRegime sourceSignature request.source.core
let targetRegime := classifyMagnetoPlasmaRegime targetSignature request.target.core
let spectralOk :=
match request.sample? with
| none => !request.link.requiresSpectralAffinity
| some sample =>
if request.link.requiresSpectralAffinity then
sampleSpectrallyCompatible request.source.spectralHook sample && sampleSpectrallyCompatible request.target.spectralHook sample
else
true
let regionOk := regionCompatible request.sourceRegimeClass request.targetRegimeClass
let regimeOk := regimeSupportsLink sourceRegime targetRegime request.link
let coupling := bodyCouplingStrength sourceSignature targetSignature request.link
let admitted := spectralOk && regionOk && regimeOk && PhysicsScalar.Q16_16.nonZero coupling
let resolvedRegime :=
if sourceRegime = .collapsed || targetRegime = .collapsed then .collapsed
else if sourceRegime = .coreDominant || targetRegime = .coreDominant then .coreDominant
else if sourceRegime = .reconnectionDominant || targetRegime = .reconnectionDominant then .reconnectionDominant
else if sourceRegime = .loopDominant || targetRegime = .loopDominant then .loopDominant
else if sourceRegime = .aligned || targetRegime = .aligned then .aligned
else .diffuse
let sourceBody' :=
if admitted then
{ request.source with state := applyMagnetoBias request.source.state sourceSignature, regime := resolvedRegime }
else request.source
let targetBody' :=
if admitted then
{ request.target with state := applyMagnetoBias request.target.state targetSignature, regime := resolvedRegime }
else request.target
{ admitted := admitted
, sourceBody := sourceBody'
, targetBody := targetBody'
, resolvedRegime := resolvedRegime
, resultingCoupling := coupling }
def defaultMagnetoLink : MagnetoBodyLink :=
{ sourceBodyId := 0
, targetBodyId := 1
, couplingClass := .weaklyCoupled
, couplingStrength := PhysicsScalar.Q16_16.half
, gateOpenThreshold := PhysicsScalar.Q16_16.quarter
, requiresSpectralAffinity := false }
def defaultHyperFlowSignature : HyperFlowSignature :=
{ divergence := Semantics.Q16_16.zero
, shearMagnitude := Semantics.Q16_16.zero
, stressMagnitude := Semantics.Q16_16.zero
, transportMagnitude := Semantics.Q16_16.zero
, anisotropy := Semantics.Q16_16.zero
, spectralSpread := Semantics.Q16_16.zero
, couplingDensity := Semantics.Q16_16.zero
, compressibilityIndex := Semantics.Q16_16.zero
, curvatureEnergy := Semantics.Q16_16.zero }
def defaultMagnetoBody2D : MagnetoPlasmaBody 2 :=
{ bodyId := 0
, state := PhysicsLagrangian.zero 2
, core := { defaultMagnetoCore with kind := .dipole }
, localDerivative := Semantics.LocalDerivative.zeroDerivative 2
, hyperFlowSignature := defaultHyperFlowSignature
, regionId := 0
, spectralHook := defaultMagnetoSpectralHook
, regime := .diffuse }
def magnetoCoreBody2D : MagnetoPlasmaBody 2 :=
{ bodyId := 1
, state := { PhysicsLagrangian.zero 2 with massScale := PhysicsScalar.Q16_16.two }
, core :=
{ coreId := 1
, kind := .toroidal
, polarity := PhysicsScalar.Q16_16.one
, coherence := PhysicsScalar.Q16_16.add PhysicsScalar.Q16_16.half PhysicsScalar.Q16_16.quarter
, fieldBias := PhysicsScalar.Q16_16.one
, tension := PhysicsScalar.Q16_16.add PhysicsScalar.Q16_16.half PhysicsScalar.Q16_16.quarter
, saturation := PhysicsScalar.Q16_16.one }
, localDerivative := Semantics.LocalDerivative.zeroDerivative 2
, hyperFlowSignature := defaultHyperFlowSignature
, regionId := 1
, spectralHook := defaultMagnetoSpectralHook
, regime := .coreDominant }
end Semantics.MagnetoPlasma