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

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import Semantics.PhysicsScalar
import Semantics.RegimeCore
import Semantics.BoundaryDynamics
import Semantics.MagnetoPlasma
import Semantics.ExoticSpacetime
import Semantics.SpikingDynamics
import Semantics.ElectromagneticSpectrum
namespace Semantics.MultiBodyField
open Semantics.PhysicsScalar
open Semantics.RegimeCore
open Semantics.BoundaryDynamics
open Semantics.MagnetoPlasma
open Semantics.ExoticSpacetime
open Semantics.SpikingDynamics
open Semantics.ElectromagneticSpectrum
abbrev FieldIntensity := PhysicsScalar.Q16_16
abbrev BodyId := UInt16
inductive FieldInteractionClass
| elastic
| plasma
| spectral
| temporal
| causal
deriving DecidableEq
structure FieldBody where
bodyId : BodyId
label : String
regionId : RegionId
mass : PhysicsScalar.Q16_16
charge : PhysicsScalar.Q16_16
potential : PhysicsScalar.Q16_16
velocity : PhysicsScalar.Q16_16
magnetoSignature? : Option MagnetoPlasmaSignature
spikeEvent? : Option SpikeEvent
inductive FieldSymmetry
| isotropic
| axial
| planar
| chiral
| chaotic
deriving DecidableEq
structure MultiBodyAssembly (n : Nat) where
bodies : Array FieldBody
boundaries : Array BoundaryLayer
interactionClass : FieldInteractionClass
symmetry : FieldSymmetry
globalPotential : PhysicsScalar.Q16_16
structure InteractionResult where
netForce : PhysicsScalar.Q16_16
potentialShift : PhysicsScalar.Q16_16
reconnectionDetected : Bool
aliasingDetected : Bool
deriving Repr, DecidableEq
structure MultiBodySignature where
bodyCount : UInt16
criticalPressure : PhysicsScalar.Q16_16
spectralCoherence : PhysicsScalar.Q16_16
magnetoAlignment : PhysicsScalar.Q16_16
deriving Repr, DecidableEq
def interactionEffectiveMass (body : FieldBody) : PhysicsScalar.Q16_16 :=
match body.magnetoSignature? with
| none => body.mass
| some signature =>
PhysicsScalar.Q16_16.addSaturating body.mass (PhysicsScalar.Q16_16.mulQ16_16 signature.reconnectionPotential signature.loopCoherence)
def interactionEffectiveCharge (body : FieldBody) : PhysicsScalar.Q16_16 :=
match body.spikeEvent? with
| none => body.charge
| some event =>
PhysicsScalar.Q16_16.addSaturating body.charge event.intensity
def bodyDistance (b1 b2 : FieldBody) : PhysicsScalar.Q16_16 :=
PhysicsScalar.Q16_16.absDiff b1.potential b2.potential
def interactionMagnitude (b1 b2 : FieldBody) (interactionClass : FieldInteractionClass) : PhysicsScalar.Q16_16 :=
let m1 := interactionEffectiveMass b1
let m2 := interactionEffectiveMass b2
let q1 := interactionEffectiveCharge b1
let q2 := interactionEffectiveCharge b2
let r := bodyDistance b1 b2
let baseForce :=
match interactionClass with
| FieldInteractionClass.elastic => PhysicsScalar.Q16_16.mulQ16_16 m1 m2
| FieldInteractionClass.plasma => PhysicsScalar.Q16_16.mulQ16_16 q1 q2
| _ => PhysicsScalar.Q16_16.avg (PhysicsScalar.Q16_16.mulQ16_16 m1 m2) (PhysicsScalar.Q16_16.mulQ16_16 q1 q2)
if PhysicsScalar.Q16_16.lt r PhysicsScalar.Q16_16.quarter then
PhysicsScalar.Q16_16.mulQ16_16 baseForce PhysicsScalar.Q16_16.four
else
baseForce
def bodyInteraction (b1 b2 : FieldBody) (interactionClass : FieldInteractionClass) : InteractionResult :=
let force := interactionMagnitude b1 b2 interactionClass
let reconnection :=
match b1.magnetoSignature?, b2.magnetoSignature? with
| some s1, some s2 => PhysicsScalar.Q16_16.ge s1.reconnectionPotential PhysicsScalar.Q16_16.half && PhysicsScalar.Q16_16.ge s2.reconnectionPotential PhysicsScalar.Q16_16.half
| _, _ => false
let aliasing := b1.regionId = b2.regionId && b1.bodyId != b2.bodyId
{ netForce := force
, potentialShift := PhysicsScalar.Q16_16.divQ16_16 force PhysicsScalar.Q16_16.two
, reconnectionDetected := reconnection
, aliasingDetected := aliasing }
def assemblyStability (assembly : MultiBodyAssembly n) : Bool :=
match assembly.interactionClass with
| FieldInteractionClass.causal => PhysicsScalar.Q16_16.le assembly.globalPotential PhysicsScalar.Q16_16.three
| _ => PhysicsScalar.Q16_16.le assembly.globalPotential PhysicsScalar.Q16_16.four
def interactionCoupling (assembly : MultiBodyAssembly n) : PhysicsScalar.Q16_16 :=
match assembly.symmetry with
| FieldSymmetry.chaotic => PhysicsScalar.Q16_16.addSaturating assembly.globalPotential PhysicsScalar.Q16_16.one
| FieldSymmetry.isotropic => PhysicsScalar.Q16_16.divQ16_16 assembly.globalPotential PhysicsScalar.Q16_16.two
| _ => assembly.globalPotential
def multiBodySignatureOf
(assembly : MultiBodyAssembly n)
(sample? : Option ElectromagneticSample) : MultiBodySignature :=
let bodyCount := UInt16.ofNat assembly.bodies.size
let coherence := match sample? with | some s => s.bandProfile.intensity | none => PhysicsScalar.Q16_16.zero
{ bodyCount := bodyCount
, criticalPressure := assembly.globalPotential
, spectralCoherence := coherence
, magnetoAlignment := PhysicsScalar.Q16_16.half }
end Semantics.MultiBodyField