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

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import Semantics.PhysicsScalar
import Semantics.RegimeCore
import Semantics.ManifoldPotential
import Semantics.ManifoldStructures
import Semantics.Errors
namespace Semantics.CausalGeometry
open Semantics.PhysicsScalar
open Semantics.RegimeCore
open Semantics.ManifoldPotential
open Semantics.ManifoldStructures
open Semantics.Errors
abbrev CausalId := UInt16
abbrev NodeId := UInt16
inductive CausalCurvature
| flat
| convergent
| divergent
| singular
| chaotic
deriving DecidableEq
inductive CausalRegime
| linear
| gated
| entrained
| reconnected
| collapsed
deriving DecidableEq
structure CausalCone where
forwardWeight : PhysicsScalar.Q16_16
backwardWeight : PhysicsScalar.Q16_16
lateralWeight : PhysicsScalar.Q16_16
coherence : PhysicsScalar.Q16_16
deriving DecidableEq
structure CausalNode where
nodeId : NodeId
label : String
regionId : RegionId
potential : ManifoldPotential
cone : CausalCone
structure CausalLayer where
layerId : CausalId
nodes : List CausalNode
globalCurvature : PhysicsScalar.Q16_16
structure CausalSignature where
nodeCount : UInt16
avgForwardWeight : PhysicsScalar.Q16_16
avgCoherence : PhysicsScalar.Q16_16
maxCurvature : PhysicsScalar.Q16_16
aliasDetected : Bool
scaffoldingRole : ErrorScaffoldingRole
structure CausalTransitionRequest where
source : CausalLayer
target : CausalLayer
boundary : BoundaryLayer
errorField? : Option ErrorField
structure CausalTransitionResult where
accepted : Bool
mergedLayer : CausalLayer
signature : CausalSignature
stability : PotentialStability
requiresAttention : Bool
def nodeCoherenceOf (node : CausalNode) : PhysicsScalar.Q16_16 :=
let base := node.cone.coherence
let bias := node.potential.gradient.coherence
PhysicsScalar.Q16_16.avg base bias
def classifyCausalCurvature (cone : CausalCone) : CausalCurvature :=
if PhysicsScalar.Q16_16.gt cone.forwardWeight (PhysicsScalar.Q16_16.add PhysicsScalar.Q16_16.one PhysicsScalar.Q16_16.half) then .convergent
else if PhysicsScalar.Q16_16.gt cone.lateralWeight PhysicsScalar.Q16_16.one then .chaotic
else if PhysicsScalar.Q16_16.gt cone.backwardWeight PhysicsScalar.Q16_16.one then .divergent
else .flat
def causalSignatureOf (layer : CausalLayer) : CausalSignature :=
let count := layer.nodes.length
let forwardSum := layer.nodes.foldl (fun acc node => PhysicsScalar.Q16_16.addSaturating acc node.cone.forwardWeight) PhysicsScalar.Q16_16.zero
let coherenceSum := layer.nodes.foldl (fun acc node => PhysicsScalar.Q16_16.addSaturating acc (nodeCoherenceOf node)) PhysicsScalar.Q16_16.zero
let div := if count = 0 then 1 else count
{ nodeCount := UInt16.ofNat count
, avgForwardWeight := PhysicsScalar.Q16_16.divQ16_16 forwardSum (UInt32.ofNat div)
, avgCoherence := PhysicsScalar.Q16_16.divQ16_16 coherenceSum (UInt32.ofNat div)
, maxCurvature := layer.globalCurvature
, aliasDetected := false
, scaffoldingRole := .none }
def mergeLayers (request : CausalTransitionRequest) : CausalLayer :=
let mergedNodes := request.source.nodes ++ request.target.nodes
{ layerId := request.source.layerId
, nodes := mergedNodes
, globalCurvature := PhysicsScalar.Q16_16.avg request.source.globalCurvature request.target.globalCurvature }
def processCausalTransition (request : CausalTransitionRequest) : CausalTransitionResult :=
let merged := mergeLayers request
let signature := causalSignatureOf merged
{ accepted := true
, mergedLayer := merged
, signature := signature
, stability := .pStable
, requiresAttention := false }
end Semantics.CausalGeometry