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283 lines
10 KiB
Text
283 lines
10 KiB
Text
import Semantics.PhysicsScalar
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import Semantics.RegimeCore
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import Semantics.BoundaryDynamics
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import Semantics.CriticalityDynamics
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import Semantics.MultiBodyField
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import Semantics.CosmicStructure
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import Semantics.Errors
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import Semantics.ManifoldStructures
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import Semantics.ExoticSpacetime
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import Semantics.DomainState
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namespace Semantics.ManifoldPotential
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open Semantics.PhysicsScalar
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open Semantics.RegimeCore
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open Semantics.BoundaryDynamics
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open Semantics.CriticalityDynamics
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open Semantics.MultiBodyField
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open Semantics.CosmicStructure
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open Semantics.Errors
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open Semantics.ManifoldStructures
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open Semantics.ExoticSpacetime
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open Semantics.DomainState
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abbrev PotentialId := UInt16
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inductive PotentialMorphology
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| flat
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| basin
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| nestedBasin
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| ridge
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| throat
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| saddle
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| lattice
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| spiral
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| web
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deriving Repr, DecidableEq
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inductive PotentialRegime
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| quiescent
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| guiding
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| trapping
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| critical
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| cascading
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| collapsed
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deriving Repr, DecidableEq
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inductive PotentialBoundaryMode
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| open
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| gated
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| reflective
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| absorptive
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| fluid
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| reconnective
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deriving Repr, DecidableEq
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inductive PotentialStability
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| pStable
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| pMetastable
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| pUnstable
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| pCollapseProne
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deriving Repr, DecidableEq
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structure PotentialCoordinate where
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radial : PhysicsScalar.Q16_16
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angular : PhysicsScalar.Q16_16
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depth : PhysicsScalar.Q16_16
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deriving Repr, DecidableEq
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structure PotentialGradient where
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inward : PhysicsScalar.Q16_16
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tangential : PhysicsScalar.Q16_16
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vertical : PhysicsScalar.Q16_16
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coherence : PhysicsScalar.Q16_16
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deriving Repr, DecidableEq
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structure PotentialBasin where
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centerRegion : RegionId
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radius : PhysicsScalar.Q16_16
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depth : PhysicsScalar.Q16_16
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rimStrength : PhysicsScalar.Q16_16
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nestedDepth : PhysicsScalar.Q16_16
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morphology : PotentialMorphology
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deriving Repr, DecidableEq
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structure PotentialThread where
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sourceRegion : RegionId
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targetRegion : RegionId
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pull : PhysicsScalar.Q16_16
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torsion : PhysicsScalar.Q16_16
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permeability : PhysicsScalar.Q16_16
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deriving Repr, DecidableEq
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structure ManifoldPotential where
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potentialId : PotentialId
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anchorRegion : RegionId
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coordinate : PotentialCoordinate
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gradient : PotentialGradient
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basin : PotentialBasin
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threads : List PotentialThread
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regime : PotentialRegime
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stability : PotentialStability
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boundaryMode : PotentialBoundaryMode
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scaffoldingRole : ErrorScaffoldingRole
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structure PotentialSignature where
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basinDepth : PhysicsScalar.Q16_16
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rimStrength : PhysicsScalar.Q16_16
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threadCount : UInt16
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totalPull : PhysicsScalar.Q16_16
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boundaryFluidity : PhysicsScalar.Q16_16
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criticalScore : PhysicsScalar.Q16_16
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coherence : PhysicsScalar.Q16_16
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aliasDetected : Bool
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scaffoldingRole : ErrorScaffoldingRole
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structure PotentialTransitionRequest where
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source : ManifoldPotential
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target : ManifoldPotential
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boundary : BoundaryLayer
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criticality : CriticalNetwork
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sample? : Option ElectromagneticSample
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sourceTemporalRegime : TemporalRegime
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targetTemporalRegime : TemporalRegime
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errorField? : Option ErrorField
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structure PotentialTransitionResult where
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accepted : Bool
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mergedPotential : ManifoldPotential
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signature : PotentialSignature
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aliasDetected : Bool
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scaffoldingRole : ErrorScaffoldingRole
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requiresAttention : Bool
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def addPulls (threads : List PotentialThread) : PhysicsScalar.Q16_16 :=
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threads.foldl (fun acc thread => PhysicsScalar.Q16_16.addSaturating acc thread.pull) PhysicsScalar.Q16_16.zero
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def explicitAliasDetected (s : ManifoldPotential) (t : ManifoldPotential) (b : BoundaryLayer) : Bool :=
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s.anchorRegion = t.anchorRegion ||
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s.basin.centerRegion = t.basin.centerRegion ||
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b.sourceRegionId = b.targetRegionId
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def threadAliasDetected (threads : List PotentialThread) : Bool :=
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threads.any (fun thread => thread.sourceRegion = thread.targetRegion)
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def scaffoldingRoleOf (errorField? : Option ErrorField) : ErrorScaffoldingRole :=
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match errorField? with
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| none => ErrorScaffoldingRole.none
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| some field => (classifyErrorField field).scaffoldingRole
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def classifyPotentialMorphology (gradient : PotentialGradient) (basin : PotentialBasin) : PotentialMorphology :=
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if PhysicsScalar.Q16_16.gt basin.nestedDepth PhysicsScalar.Q16_16.zero then .nestedBasin
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else if PhysicsScalar.Q16_16.gt basin.rimStrength basin.depth then .ridge
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else if PhysicsScalar.Q16_16.gt gradient.tangential gradient.inward then .spiral
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else if PhysicsScalar.Q16_16.gt gradient.vertical gradient.inward then .throat
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else if PhysicsScalar.Q16_16.gt basin.depth PhysicsScalar.Q16_16.half then .basin
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else .flat
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def boundaryModeOf (boundary : BoundaryLayer) (role : ErrorScaffoldingRole) : PotentialBoundaryMode :=
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let fluidityClass := classifyBoundaryFluidity (boundarySignatureOf {
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boundary := boundary,
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sourceAssignment := { regionId := boundary.sourceRegionId, state := { resolutionStatus := .resolved, stabilityClass := .stable, discreteState := default }, regimeClass := .transitional },
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targetAssignment := { regionId := boundary.targetRegionId, state := { resolutionStatus := .resolved, stabilityClass := .stable, discreteState := default }, regimeClass := .transitional },
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sourceTemporalRegime := .monotonic,
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targetTemporalRegime := .monotonic,
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spikeEvent := none,
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magnetoSignature := none,
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errorField := none })
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match role, fluidityClass with
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| .boundaryScaffold, _ => .fluid
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| .causalScaffold, _ => .gated
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| .criticalScaffold, _ => .reconnective
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| _, .fRigid => .reflective
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| _, .fViscous => .gated
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| _, .fAdaptive => .fluid
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| _, .fDiffuse => .open
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| _, .fTurbulent => .reconnective
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def threadCountOf (threads : List PotentialThread) : UInt16 := UInt16.ofNat threads.length
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def potentialSignatureOf (potential : ManifoldPotential) (boundary : BoundaryLayer) (criticality : CriticalNetwork) : PotentialSignature :=
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{ basinDepth := potential.basin.depth
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, rimStrength := potential.basin.rimStrength
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, threadCount := threadCountOf potential.threads
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, totalPull := addPulls potential.threads
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, boundaryFluidity := boundary.fluidity
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, criticalScore := PhysicsScalar.Q16_16.one
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, coherence := potential.gradient.coherence
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, aliasDetected := threadAliasDetected potential.threads
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, scaffoldingRole := potential.scaffoldingRole }
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def classifyPotentialRegime (signature : PotentialSignature) : PotentialRegime :=
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if signature.aliasDetected then .collapsed
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else if PhysicsScalar.Q16_16.gt signature.criticalScore PhysicsScalar.Q16_16.three then .cascading
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else if PhysicsScalar.Q16_16.gt signature.basinDepth PhysicsScalar.Q16_16.two then .trapping
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else if PhysicsScalar.Q16_16.gt signature.totalPull PhysicsScalar.Q16_16.one then .guiding
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else if PhysicsScalar.Q16_16.gt signature.rimStrength PhysicsScalar.Q16_16.two then .critical
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else .quiescent
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def classifyPotentialStability (signature : PotentialSignature) : PotentialStability :=
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if signature.aliasDetected then .pCollapseProne
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else if PhysicsScalar.Q16_16.gt signature.criticalScore PhysicsScalar.Q16_16.three then .pCollapseProne
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else if PhysicsScalar.Q16_16.gt signature.boundaryFluidity PhysicsScalar.Q16_16.two then .pUnstable
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else if PhysicsScalar.Q16_16.gt signature.totalPull PhysicsScalar.Q16_16.two then .pMetastable
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else .pStable
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def potentialCompatibleWithBoundary (potential : ManifoldPotential) (boundary : BoundaryLayer) : Bool :=
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match potential.boundaryMode with
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| .reflective => boundary.targetRegionId != potential.anchorRegion
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| _ => true
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def mergeBasins (left right : PotentialBasin) : PotentialBasin :=
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{ centerRegion := left.centerRegion
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, radius := PhysicsScalar.Q16_16.max left.radius right.radius
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, depth := PhysicsScalar.Q16_16.avg left.depth right.depth
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, rimStrength := PhysicsScalar.Q16_16.avg left.rimStrength right.rimStrength
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, nestedDepth := PhysicsScalar.Q16_16.max left.nestedDepth right.nestedDepth
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, morphology := left.morphology }
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def mergeGradients (left right : PotentialGradient) : PotentialGradient :=
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{ inward := PhysicsScalar.Q16_16.avg left.inward right.inward
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, tangential := PhysicsScalar.Q16_16.avg left.tangential right.tangential
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, vertical := PhysicsScalar.Q16_16.avg left.vertical right.vertical
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, coherence := PhysicsScalar.Q16_16.avg left.coherence right.coherence }
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def mergePotentials (request : PotentialTransitionRequest) : ManifoldPotential :=
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let mergedGradient := mergeGradients request.source.gradient request.target.gradient
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let mergedBasin := mergeBasins request.source.basin request.target.basin
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let mergedThreads := request.source.threads ++ request.target.threads
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let role := scaffoldingRoleOf request.errorField?
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let provisional : ManifoldPotential :=
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{ potentialId := request.source.potentialId
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, anchorRegion := request.source.anchorRegion
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, coordinate := request.source.coordinate
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, gradient := mergedGradient
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, basin := { mergedBasin with morphology := classifyPotentialMorphology mergedGradient mergedBasin }
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, threads := mergedThreads
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, regime := request.source.regime
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, stability := request.source.stability
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, boundaryMode := boundaryModeOf request.boundary role
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, scaffoldingRole := role }
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let signature := potentialSignatureOf provisional request.boundary request.criticality
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{ provisional with
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regime := classifyPotentialRegime signature
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stability := classifyPotentialStability signature }
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def processPotentialTransition (request : PotentialTransitionRequest) : PotentialTransitionResult :=
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let aliasDetected := explicitAliasDetected request.source request.target request.boundary || threadAliasDetected (request.source.threads ++ request.target.threads)
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let allowed :=
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!aliasDetected &&
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potentialCompatibleWithBoundary request.source request.boundary &&
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potentialCompatibleWithBoundary request.target request.boundary
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let merged := if allowed then mergePotentials request else request.source
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let signature := { (potentialSignatureOf merged request.boundary request.criticality) with
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aliasDetected := aliasDetected,
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scaffoldingRole := scaffoldingRoleOf request.errorField? }
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let requiresAttention :=
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match request.errorField? with
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| some field => requiresImmediateAction field || aliasDetected
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| none => aliasDetected
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{ accepted := allowed
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, mergedPotential := merged
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, signature := signature
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, aliasDetected := aliasDetected
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, scaffoldingRole := scaffoldingRoleOf request.errorField?
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, requiresAttention := requiresAttention }
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end Semantics.ManifoldPotential
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